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Versions: (draft-selander-ace-cose-ecdhe) 00

Network Working Group                                        G. Selander
Internet-Draft                                               J. Mattsson
Intended status: Standards Track                            F. Palombini
Expires: May 7, 2020                                         Ericsson AB
                                                       November 04, 2019


               Ephemeral Diffie-Hellman Over COSE (EDHOC)
                      draft-selander-lake-edhoc-00

Abstract

   This document specifies Ephemeral Diffie-Hellman Over COSE (EDHOC), a
   very compact, and lightweight authenticated Diffie-Hellman key
   exchange with ephemeral keys.  EDHOC provides mutual authentication,
   perfect forward secrecy, and identity protection.  EDHOC is intended
   for usage in constrained scenarios and a main use case is to
   establish an OSCORE security context.  By reusing COSE for
   cryptography, CBOR for encoding, and CoAP for transport, the
   additional code footprint can be kept very low.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on May 7, 2020.

Copyright Notice

   Copyright (c) 2019 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (https://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect



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   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Rationale for EDHOC . . . . . . . . . . . . . . . . . . .   5
     1.2.  Terminology and Requirements Language . . . . . . . . . .   6
   2.  Background  . . . . . . . . . . . . . . . . . . . . . . . . .   6
   3.  EDHOC Overview  . . . . . . . . . . . . . . . . . . . . . . .   8
     3.1.  Cipher Suites . . . . . . . . . . . . . . . . . . . . . .   9
     3.2.  Ephemeral Public Keys . . . . . . . . . . . . . . . . . .   9
     3.3.  Key Derivation  . . . . . . . . . . . . . . . . . . . . .  10
   4.  EDHOC Authenticated with Signature Keys . . . . . . . . . . .  12
     4.1.  Overview  . . . . . . . . . . . . . . . . . . . . . . . .  12
     4.2.  EDHOC Message 1 . . . . . . . . . . . . . . . . . . . . .  14
     4.3.  EDHOC Message 2 . . . . . . . . . . . . . . . . . . . . .  16
     4.4.  EDHOC Message 3 . . . . . . . . . . . . . . . . . . . . .  19
   5.  EDHOC Authenticated with Symmetric Keys . . . . . . . . . . .  22
     5.1.  Overview  . . . . . . . . . . . . . . . . . . . . . . . .  22
     5.2.  EDHOC Message 1 . . . . . . . . . . . . . . . . . . . . .  23
     5.3.  EDHOC Message 2 . . . . . . . . . . . . . . . . . . . . .  23
     5.4.  EDHOC Message 3 . . . . . . . . . . . . . . . . . . . . .  24
   6.  EDHOC Authenticated with Static Diffie-Hellman Keys . . . . .  24
     6.1.  Overview  . . . . . . . . . . . . . . . . . . . . . . . .  24
     6.2.  EDHOC Message 1 . . . . . . . . . . . . . . . . . . . . .  25
     6.3.  EDHOC Message 2 . . . . . . . . . . . . . . . . . . . . .  25
     6.4.  EDHOC Message 3 . . . . . . . . . . . . . . . . . . . . .  26
     6.5.  EDHOC-Exporter Interface  . . . . . . . . . . . . . . . .  26
     6.6.  Security Considerations . . . . . . . . . . . . . . . . .  26
     6.7.  Message Sizes . . . . . . . . . . . . . . . . . . . . . .  27
   7.  Error Handling  . . . . . . . . . . . . . . . . . . . . . . .  27
     7.1.  EDHOC Error Message . . . . . . . . . . . . . . . . . . .  27
   8.  Transferring EDHOC and Deriving Application Keys  . . . . . .  29
     8.1.  Transferring EDHOC in CoAP  . . . . . . . . . . . . . . .  29
     8.2.  Transferring EDHOC over Other Protocols . . . . . . . . .  32
   9.  Security Considerations . . . . . . . . . . . . . . . . . . .  32
     9.1.  Security Properties . . . . . . . . . . . . . . . . . . .  32
     9.2.  Cryptographic Considerations  . . . . . . . . . . . . . .  33
     9.3.  Cipher Suites . . . . . . . . . . . . . . . . . . . . . .  34
     9.4.  Unprotected Data  . . . . . . . . . . . . . . . . . . . .  34
     9.5.  Denial-of-Service . . . . . . . . . . . . . . . . . . . .  34
     9.6.  Implementation Considerations . . . . . . . . . . . . . .  35
     9.7.  Other Documents Referencing EDHOC . . . . . . . . . . . .  36
   10. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  36
     10.1.  EDHOC Cipher Suites Registry . . . . . . . . . . . . . .  36



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     10.2.  EDHOC Method Type Registry . . . . . . . . . . . . . . .  36
     10.3.  The Well-Known URI Registry  . . . . . . . . . . . . . .  37
     10.4.  Media Types Registry . . . . . . . . . . . . . . . . . .  37
     10.5.  CoAP Content-Formats Registry  . . . . . . . . . . . . .  38
     10.6.  Expert Review Instructions . . . . . . . . . . . . . . .  38
   11. References  . . . . . . . . . . . . . . . . . . . . . . . . .  39
     11.1.  Normative References . . . . . . . . . . . . . . . . . .  39
     11.2.  Informative References . . . . . . . . . . . . . . . . .  41
   Appendix A.  Use of CBOR, CDDL and COSE in EDHOC  . . . . . . . .  43
     A.1.  CBOR and CDDL . . . . . . . . . . . . . . . . . . . . . .  43
     A.2.  COSE  . . . . . . . . . . . . . . . . . . . . . . . . . .  44
   Appendix B.  Test Vectors . . . . . . . . . . . . . . . . . . . .  44
     B.1.  Test Vectors for EDHOC Authenticated with Signature Keys
           (RPK) . . . . . . . . . . . . . . . . . . . . . . . . . .  45
     B.2.  Test Vectors for EDHOC Authenticated with Symmetric Keys
           (PSK) . . . . . . . . . . . . . . . . . . . . . . . . . .  60
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  73
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  74

1.  Introduction

   Security at the application layer provides an attractive option for
   protecting Internet of Things (IoT) deployments, for example where
   transport layer security is not sufficient
   [I-D.hartke-core-e2e-security-reqs] or where the protection needs to
   work over a variety of underlying protocols.  IoT devices may be
   constrained in various ways, including memory, storage, processing
   capacity, and energy [RFC7228].  A method for protecting individual
   messages at the application layer suitable for constrained devices,
   is provided by CBOR Object Signing and Encryption (COSE) [RFC8152]),
   which builds on the Concise Binary Object Representation (CBOR)
   [I-D.ietf-cbor-7049bis].  Object Security for Constrained RESTful
   Environments (OSCORE) [RFC8613] is a method for application-layer
   protection of the Constrained Application Protocol (CoAP), using
   COSE.

   In order for a communication session to provide forward secrecy, the
   communicating parties can run an Elliptic Curve Diffie-Hellman (ECDH)
   key exchange protocol with ephemeral keys, from which shared key
   material can be derived.  This document specifies Ephemeral Diffie-
   Hellman Over COSE (EDHOC), a lightweight key exchange protocol
   providing perfect forward secrecy and identity protection.
   Authentication is based on credentials established out of band, e.g.
   from a trusted third party, such as an Authorization Server as
   specified by [I-D.ietf-ace-oauth-authz].  EDHOC supports
   authentication using pre-shared keys (PSK), raw public keys (RPK),
   and public key certificates.  After successful completion of the
   EDHOC protocol, application keys and other application specific data



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   can be derived using the EDHOC-Exporter interface.  A main use case
   for EDHOC is to establish an OSCORE security context.  EDHOC uses
   COSE for cryptography, CBOR for encoding, and CoAP for transport.  By
   reusing existing libraries, the additional code footprint can be kept
   very low.  Note that this document focuses on authentication and key
   establishment: for integration with authorization of resource access,
   refer to [I-D.ietf-ace-oscore-profile].

   EDHOC is designed to work in highly constrained scenarios making it
   especially suitable for network technologies such as Cellular IoT,
   6TiSCH [I-D.ietf-6tisch-dtsecurity-zerotouch-join], and LoRaWAN
   [LoRa1][LoRa2].  These network technologies are characterized by
   their low throughput, low power consumption, and small frame sizes.
   Compared to the DTLS 1.3 handshake [I-D.ietf-tls-dtls13] with ECDH
   and connection ID, the number of bytes in EDHOC is less than 1/4 when
   PSK authentication is used and less than 1/3 when RPK authentication
   is used, see [I-D.ietf-lwig-security-protocol-comparison].  Typical
   message sizes for EDHOC with pre-shared keys, raw public keys, and
   X.509 certificates are shown in Figure 1.

   =====================================================================
                  PSK       RPK       x5t     x5chain
   ---------------------------------------------------------------------
   message_1       40        38        38        38
   message_2       45       114       126       116 + Certificate chain
   message_3       11        80        91        81 + Certificate chain
   ---------------------------------------------------------------------
   Total           96       232       255       235 + Certificate chains
   =====================================================================

                 Figure 1: Typical message sizes in bytes

   The ECDH exchange and the key derivation follow [SIGMA], NIST SP-
   800-56A [SP-800-56A], and HKDF [RFC5869].  CBOR
   [I-D.ietf-cbor-7049bis] and COSE [RFC8152] are used to implement
   these standards.  The use of COSE provides crypto agility and enables
   use of future algorithms and headers designed for constrained IoT.

   This document is organized as follows: Section 2 describes how EDHOC
   builds on SIGMA-I, Section 3 specifies general properties of EDHOC,
   including message flow, formatting of the ephemeral public keys, and
   key derivation, Section 4 specifies EDHOC with signature key
   authentication, Section 5 specifies EDHOC with symmetric key
   authentication, Section 6 specifies EDHOC with static Diffie-Hellman
   key authentication, Section 7 specifies the EDHOC error message, and
   Section 8 describes how EDHOC can be transferred in CoAP and used to
   establish an OSCORE security context.




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1.1.  Rationale for EDHOC

   Many constrained IoT systems today do not use any security at all,
   and when they do, they often do not follow best practices.  One
   reason is that many current security protocols are not designed with
   constrained IoT in mind.  Constrained IoT systems often deal with
   personal information, valuable business data, and actuators
   interacting with the physical world.  Not only do such systems need
   security and privacy, they often need end-to-end protection with
   source authentication and perfect forward secrecy.  EDHOC and OSCORE
   [RFC8613] enables security following current best practices to
   devices and systems where current security protocols are impractical.

   EDHOC is optimized for small message sizes and can therefore be sent
   over a small number of radio frames.  The message size of a key
   exchange protocol may have a large impact on the performance of an
   IoT deployment, especially in noisy environments.  For example, in a
   network bootstrapping setting a large number of devices turned on in
   a short period of time may result in large latencies caused by
   parallel key exchanges.  Requirements on network formation time in
   constrained environments can be translated into key exchange
   overhead.  In networks technologies with transmission back-off time,
   each additional frame significantly increases the latency even if no
   other devices are transmitting.

   Power consumption for wireless devices is highly dependent on message
   transmission, listening, and reception.  For devices that only send a
   few bytes occasionally, the battery lifetime may be significantly
   reduced by a heavy key exchange protocol.  Moreover, a key exchange
   may need to be executed more than once, e.g. due to a device losing
   power or rebooting for other reasons.

   EDHOC is adapted to primitives and protocols designed for the
   Internet of Things: EDHOC is built on CBOR and COSE which enables
   small message overhead and efficient parsing in constrained devices.
   EDHOC is not bound to a particular transport layer, but it is
   recommended to transport the EDHOC message in CoAP payloads.  EDHOC
   is not bound to a particular communication security protocol but
   works off-the-shelf with OSCORE [RFC8613] providing the necessary
   input parameters with required properties.  Maximum code complexity
   (ROM/Flash) is often a constraint in many devices and by reusing
   already existing libraries, the additional code footprint for EDHOC +
   OSCORE can be kept very low.








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1.2.  Terminology and Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

   The word "encryption" without qualification always refers to
   authenticated encryption, in practice implemented with an
   Authenticated Encryption with Additional Data (AEAD) algorithm, see
   [RFC5116].

   Readers are expected to be familiar with the terms and concepts
   described in CBOR [I-D.ietf-cbor-7049bis], COSE [RFC8152], and CDDL
   [RFC8610].  The Concise Data Definition Language (CDDL) is used to
   express CBOR data structures [I-D.ietf-cbor-7049bis].  Examples of
   CBOR and CDDL are provided in Appendix A.1.

2.  Background

   SIGMA (SIGn-and-MAc) is a family of theoretical protocols with a
   large number of variants [SIGMA].  Like IKEv2 and (D)TLS 1.3
   [RFC8446], EDHOC is built on a variant of the SIGMA protocol which
   provide identity protection of the initiator (SIGMA-I), and like
   (D)TLS 1.3, EDHOC implements the SIGMA-I variant as Sign-then-MAC.
   The SIGMA-I protocol using an authenticated encryption algorithm is
   shown in Figure 2.

     Party U                                                   Party V
        |                          G_X                            |
        +-------------------------------------------------------->|
        |                                                         |
        |  G_Y, AEAD( K_2; ID_CRED_V, Sig(V; CRED_V, G_X, G_Y) )  |
        |<--------------------------------------------------------+
        |                                                         |
        |     AEAD( K_3; ID_CRED_U, Sig(U; CRED_U, G_Y, G_X) )    |
        +-------------------------------------------------------->|
        |                                                         |

    Figure 2: Authenticated encryption variant of the SIGMA-I protocol.

   The parties exchanging messages are called "U" and "V".  They
   exchange identities and ephemeral public keys, compute the shared
   secret, and derive symmetric application keys.

   o  G_X and G_Y are the ECDH ephemeral public keys of U and V,
      respectively.



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   o  CRED_U and CRED_V are the credentials containing the public
      authentication keys of U and V, respectively.

   o  ID_CRED_U and ID_CRED_V are data enabling the recipient party to
      retrieve the credential of U and V, respectively.

   o  Sig(U; . ) and S(V; . ) denote signatures made with the private
      authentication key of U and V, respectively.

   o  AEAD(K; . ) denotes authenticated encryption with additional data
      using the key K derived from the shared secret.  The authenticated
      encryption MUST NOT be replaced by plain encryption, see
      Section 9.

   In order to create a "full-fledged" protocol some additional protocol
   elements are needed.  EDHOC adds:

   o  Explicit connection identifiers C_U, C_V chosen by U and V,
      respectively, enabling the recipient to find the protocol state.

   o  Transcript hashes TH_2, TH_3, TH_4 used for key derivation and as
      additional authenticated data.

   o  Computationally independent keys derived from the ECDH shared
      secret and used for encryption of different messages.

   o  Verification of a common preferred cipher suite (AEAD algorithm,
      ECDH algorithm, ECDH curve, signature algorithm):

      *  U lists supported cipher suites in order of preference

      *  V verifies that the selected cipher suite is the first
         supported cipher suite

   o  Method types and error handling.

   o  Transport of opaque application defined data.

   EDHOC is designed to encrypt and integrity protect as much
   information as possible, and all symmetric keys are derived using as
   much previous information as possible.  EDHOC is furthermore designed
   to be as compact and lightweight as possible, in terms of message
   sizes, processing, and the ability to reuse already existing CBOR,
   COSE, and CoAP libraries.

   To simplify for implementors, the use of CBOR in EDHOC is summarized
   in Appendix A and test vectors including CBOR diagnostic notation are
   given in Appendix B.



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3.  EDHOC Overview

   EDHOC consists of three flights (message_1, message_2, message_3)
   that maps directly to the three messages in SIGMA-I, plus an EDHOC
   error message.  EDHOC messages are CBOR Sequences
   [I-D.ietf-cbor-sequence], where the first data item of message_1 is
   an int (TYPE) specifying the method (singature, static DH, symmetric)
   and the correlation properties of the transport used.

   While EDHOC uses the COSE_Key, COSE_Sign1, and COSE_Encrypt0
   structures, only a subset of the parameters is included in the EDHOC
   messages.  After creating EDHOC message_3, Party U can derive
   symmetric application keys, and application protected data can
   therefore be sent in parallel with EDHOC message_3.  The application
   may protect data using the algorithms (AEAD, HMAC, etc.) in the
   selected cipher suite and the connection identifiers (C_U, C_V).
   EDHOC may be used with the media type application/edhoc defined in
   Section 10.

      Party U                                                 Party V
         |                                                       |
         | ------------------ EDHOC message_1 -----------------> |
         |                                                       |
         | <----------------- EDHOC message_2 ------------------ |
         |                                                       |
         | ------------------ EDHOC message_3 -----------------> |
         |                                                       |
         | <----------- Application Protected Data ------------> |
         |                                                       |

                       Figure 3: EDHOC message flow

   The EDHOC message exchange may be authenticated using pre-shared keys
   (PSK), raw public keys (RPK), or public key certificates.  The
   certificates and RPKs can contain signature keys are static Diffie-
   Hellman keys.  EDHOC assumes the existence of mechanisms
   (certification authority, manual distribution, etc.) for binding
   identities with authentication keys (public or pre-shared).  When a
   public key infrastructure is used, the identity is included in the
   certificate and bound to the authentication key by trust in the
   certification authority.  When the credential is manually distributed
   (PSK, RPK, self-signed certificate), the identity and authentication
   key is distributed out-of-band and bound together by trust in the
   distribution method.  EDHOC with symmetric key authentication is very
   similar to EDHOC with signature key authentication, the difference
   being that information is only MACed, not signed, and that session
   keys are derived from the ECDH shared secret and the PSK.




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   EDHOC allows opaque application data (UAD and PAD) to be sent in the
   EDHOC messages.  Unprotected Application Data (UAD_1, UAD_2) may be
   sent in message_1 and message_2 and can be e.g. be used to transfer
   access tokens that are protected outside of EDHOC.  Protected
   application data (PAD_3) may be used to transfer any application data
   in message_3.

   Cryptographically, EDHOC does not put requirements on the lower
   layers.  EDHOC is not bound to a particular transport layer, and can
   be used in environments without IP.  It is recommended to transport
   the EDHOC message in CoAP payloads, see Section 8.  An implementation
   may support only Party U or only Party V.

3.1.  Cipher Suites

   EDHOC cipher suites consist of an ordered set of COSE algorithms: an
   AEAD algorithm, an HMAC algorithm, an ECDH curve, a signature
   algorithm, and signature algorithm parameters.  The signature
   algorithm is not used when EDHOC is authenticated with symmetric
   keys.  Each cipher suite is either identified with a pre-defined int
   label or with an array of labels and values from the COSE Algorithms
   and Elliptic Curves registries.

      suite = int / [ 4*4 algs: int / tstr, ? para: any ]

   This document specifies two pre-defined cipher suites.

      0. [ 10, 5, 4, -8, 6 ]
         (AES-CCM-16-64-128, HMAC 256/256, X25519, EdDSA, Ed25519)

      1. [ 10, 5, 1, -7, 1 ]
         (AES-CCM-16-64-128, HMAC 256/256, P-256, ES256, P-256)

3.2.  Ephemeral Public Keys

   The ECDH ephemeral public keys are formatted as a COSE_Key of type
   EC2 or OKP according to Sections 13.1 and 13.2 of [RFC8152], but only
   the x-coordinate is included in the EDHOC messages.  For Elliptic
   Curve Keys of type EC2, compact representation as per [RFC6090] MAY
   be used also in the COSE_Key.  If the COSE implementation requires an
   y-coordinate, any of the possible values of the y-coordinate can be
   used, see Appendix C of [RFC6090].  COSE [RFC8152] always use compact
   output for Elliptic Curve Keys of type EC2.








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3.3.  Key Derivation

   Key and IV derivation SHALL be performed with HKDF [RFC5869]
   following the specification in Section 11 of [RFC8152] using the HMAC
   algorithm in the selected cipher suite.  The pseudorandom key (PRK)
   is derived using HKDF-Extract [RFC5869]

      PRK = HKDF-Extract( salt, IKM )

   with the following input:

   o  The salt SHALL be the PSK when EDHOC is authenticated with
      symmetric keys, and the empty byte string when EDHOC is
      authenticated with asymmetric keys (signature or static DH).  The
      PSK is used as 'salt' to simplify implementation.  Note that
      [RFC5869] specifies that if the salt is not provided, it is set to
      a string of zeros (see Section 2.2 of [RFC5869]).  For
      implementation purposes, not providing the salt is the same as
      setting the salt to the empty byte string.

   o  The input keying material (IKM) SHALL be the ECDH shared secret
      G_XY (calculated from G_X and Y or G_Y and X) as defined in
      Section 12.4.1 of [RFC8152].  When using the curve25519, the ECDH
      shared secret is the output of the X25519 function [RFC7748].

   Example: Assuming use of HMAC 256/256 the extract phase of HKDF
   produces a PRK as follows:

      PRK = HMAC-SHA-256( salt, G_XY )

   where salt = 0x (the empty byte string) in the asymmetric case and
   salt = PSK in the symmetric case.

   The keys and IVs used in EDHOC are derived from PRK using HKDF-Expand
   [RFC5869]

      OKM = HKDF-Expand( PRK, info, L )

   where L is the length of output keying material (OKM) in bytes and
   info is the CBOR encoding of a COSE_KDF_Context

   info = [
     AlgorithmID,
     [ null, null, null ],
     [ null, null, null ],
     [ keyDataLength, h'', other ]
   ]




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   where

   o  AlgorithmID is an int or tstr, see below

   o  keyDataLength is a uint set to the length of output keying
      material in bits, see below

   o  other is a bstr set to one of the transcript hashes TH_2, TH_3, or
      TH_4 as defined in Sections 4.3.1, 4.4.1, and 3.3.1.

   For message_2 and message_3, the keys K_2 and K_3 SHALL be derived
   using transcript hashes TH_2 and TH_3 respectively.  The key SHALL be
   derived using AlgorithmID set to the integer value of the AEAD in the
   selected cipher suite, and keyDataLength equal to the key length of
   the AEAD.

   If the AEAD algorithm uses an IV, then IV_2 and IV_3 for message_2
   and message_3 SHALL be derived using the transcript hashes TH_2 and
   TH_3 respectively.  The IV SHALL be derived using AlgorithmID = "IV-
   GENERATION" as specified in Section 12.1.2. of [RFC8152], and
   keyDataLength equal to the IV length of the AEAD.

   Assuming the output OKM length L is smaller than the hash function
   output size, the expand phase of HKDF consists of a single HMAC
   invocation

      OKM = first L bytes of HMAC( PRK, info || 0x01 )

   where || means byte string concatenation.

   Example: Assuming use of the algorithm AES-CCM-16-64-128 and HMAC
   256/256, K_i and IV_i are therefore the first 16 and 13 bytes,
   respectively, of

      HMAC-SHA-256( PRK, info || 0x01 )

   calculated with (AlgorithmID, keyDataLength) = (10, 128) and
   (AlgorithmID, keyDataLength) = ("IV-GENERATION", 104), respectively.

3.3.1.  EDHOC-Exporter Interface

   Application keys and other application specific data can be derived
   using the EDHOC-Exporter interface defined as:

      EDHOC-Exporter( label, length ) = HKDF-Expand( PRK, info, length )

   The output of the EDHOC-Exporter function SHALL be derived using
   AlgorithmID = label, keyDataLength = 8 * length, and other = TH_4



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   where label is a tstr defined by the application and length is a uint
   defined by the application.  The label SHALL be different for each
   different exporter value.  The transcript hash TH_4 is a CBOR encoded
   bstr and the input to the hash function is a CBOR Sequence.

      TH_4 = H( TH_3, CIPHERTEXT_3 )

   where H() is the hash function in the HMAC algorithm.  Example use of
   the EDHOC-Exporter is given in Sections 3.3.2 and 8.1.1.

3.3.2.  EDHOC PSK Chaining

   An application using EDHOC may want to derive new PSKs to use for
   authentication in future EDHOC exchanges.  In this case, the new PSK
   and the ID_PSK 'kid_value' parameter SHOULD be derived as follows
   where length is the key length (in bytes) of the AEAD Algorithm.

      PSK    = EDHOC-Exporter( "EDHOC Chaining PSK", length )
      ID_PSK = EDHOC-Exporter( "EDHOC Chaining ID_PSK", 4 )

4.  EDHOC Authenticated with Signature Keys

4.1.  Overview

   EDHOC supports authentication with raw public keys (RPK) and public
   key certificates with static Diffe-Hellman keys with the requirements
   that:

   o  Only Party V SHALL have access to the private authentication key
      of Party V,

   o  Only Party U SHALL have access to the private authentication key
      of Party U,

   o  Party U is able to retrieve Party V's public authentication key
      using ID_CRED_V,

   o  Party V is able to retrieve Party U's public authentication key
      using ID_CRED_U,

   where the identifiers ID_CRED_U and ID_CRED_V are COSE header_maps,
   i.e. a CBOR map containing COSE Common Header Parameters, see
   [RFC8152]).  ID_CRED_U and ID_CRED_V need to contain parameters that
   can identify a public authentication key, see Appendix A.2.  In the
   following we give some examples of possible COSE header parameters.

   Raw public keys are most optimally stored as COSE_Key objects and
   identified with a 'kid' parameter (see [RFC8152]):



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   o  ID_CRED_x = { 4 : kid_value }, where kid_value : bstr, for x = U
      or V.

   Public key certificates can be identified in different ways.  Several
   header parameters for identifying X.509 certificates are defined in
   [I-D.ietf-cose-x509] (the exact labels are TBD):

   o  by a hash value with the 'x5t' parameter;

      *  ID_CRED_x = { TBD1 : COSE_CertHash }, for x = U or V,

   o  by a URL with the 'x5u' parameter;

      *  ID_CRED_x = { TBD2 : uri }, for x = U or V,

   o  or by a bag of certificates with the 'x5bag' parameter;

      *  ID_CRED_x = { TBD3 : COSE_X509 }, for x = U or V.

   o  by a certificate chain with the 'x5chain' parameter;

      *  ID_CRED_x = { TBD4 : COSE_X509 }, for x = U or V,

   In the latter two examples, ID_CRED_U and ID_CRED_V contain the
   actual credential used for authentication.  The purpose of ID_CRED_U
   and ID_CRED_V is to facilitate retrieval of a public authentication
   key and when they do not contain the actual credential, they may be
   very short.  It is RECOMMENDED that they uniquely identify the public
   authentication key as the recipient may otherwise have to try several
   keys.  ID_CRED_U and ID_CRED_V are transported in the ciphertext, see
   Section 4.3.2 and Section 4.4.2.

   The actual credentials CRED_U and CRED_V (e.g. a COSE_Key or a single
   X.509 certificate) are signed by party U and V, respectively to
   prevent duplicate-signature key selection (DSKS) attacks, see
   Section 4.4.1 and Section 4.3.1.  Party U and Party V MAY use
   different types of credentials, e.g. one uses RPK and the other uses
   certificate.  When included in the signature payload, COSE_Keys of
   type OKP SHALL only include the parameters 1 (kty), -1 (crv), and -2
   (x-coordinate).  COSE_Keys of type EC2 SHALL only include the
   parameters 1 (kty), -1 (crv), -2 (x-coordinate), and -3
   (y-coordinate).  The parameters SHALL be encoded in decreasing order.

   The connection identifiers C_U and C_V do not have any cryptographic
   purpose in EDHOC.  They contain information facilitating retrieval of
   the protocol state and may therefore be very short.  The connection
   identifier MAY be used with an application protocol (e.g.  OSCORE)
   for which EDHOC establishes keys, in which case the connection



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   identifiers SHALL adhere to the requirements for that protocol.  Each
   party choses a connection identifier it desires the other party to
   use in outgoing messages.

   The first data item of message_1 is an int TYPE = 4 * method + corr
   specifying the method and the correlation properties of the transport
   used. corr = 0 is used when there is no external correlation
   mechanism. corr = 1 is used when there is an external correlation
   mechanism (e.g. the Token in CoAP) that enables Party U to correlate
   message_1 and message_2. corr = 2 is used when there is an external
   correlation mechanism that enables Party V to correlate message_2 and
   message_3. corr = 3 is used when there is an external correlation
   mechanism that enables the parties to correlate all the messages.
   The use of the correlation parameter is exemplified in Section 8.1.

   1 byte connection and credential identifiers are realistic in many
   scenarios as most constrained devices only have a few keys and
   connections.  In cases where a node only has one connection or key,
   the identifiers may even be the empty byte string.

   Party U                                                       Party V
   |                  TYPE, SUITES_U, G_X, C_U, UAD_1                  |
   +------------------------------------------------------------------>|
   |                             message_1                             |
   |                                                                   |
   |  C_U, G_Y, C_V, AEAD(K_2; ID_CRED_V, Sig(V; CRED_V, TH_2), UAD_2) |
   |<------------------------------------------------------------------+
   |                             message_2                             |
   |                                                                   |
   |       C_V, AEAD(K_3; ID_CRED_U, Sig(U; CRED_U, TH_3), PAD_3)      |
   +------------------------------------------------------------------>|
   |                             message_3                             |

      Figure 4: Overview of EDHOC with signature key authentication.

4.2.  EDHOC Message 1

4.2.1.  Formatting of Message 1

   message_1 SHALL be a CBOR Sequence (see Appendix A.1) as defined
   below










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   message_1 = (
     TYPE : int,
     SUITES_U : suite / [ index : uint, 2* suite ],
     G_X : bstr,
     C_U : bstr,
     ? UAD_1 : bstr,
   )

   where:

   o  TYPE = 4 * method + corr, where the method = 0 and the correlation
      parameter corr is chosen based on the transport and determines
      which connection identifiers that are omitted (see Section 4.1).

   o  SUITES_U - cipher suites which Party U supports in order of
      decreasing preference.  One cipher suite is selected.  If a single
      cipher suite is conveyed then that cipher suite is selected.  If
      multiple cipher suites are conveyed then zero-based index (i.e. 0
      for the first suite, 1 for the second suite, etc.) identifies the
      selected cipher suite out of the array elements listing the cipher
      suites (see Section 7).

   o  G_X - the x-coordinate of the ephemeral public key of Party U

   o  C_U - variable length connection identifier

   o  UAD_1 - bstr containing unprotected opaque application data

4.2.2.  Party U Processing of Message 1

   Party U SHALL compose message_1 as follows:

   o  The supported cipher suites and the order of preference MUST NOT
      be changed based on previous error messages.  However, the list
      SUITES_U sent to Party V MAY be truncated such that cipher suites
      which are the least preferred are omitted.  The amount of
      truncation MAY be changed between sessions, e.g. based on previous
      error messages (see next bullet), but all cipher suites which are
      more preferred than the least preferred cipher suite in the list
      MUST be included in the list.

   o  Determine the cipher suite to use with Party V in message_1.  If
      Party U previously received from Party V an error message to
      message_1 with diagnostic payload identifying a cipher suite that
      U supports, then U SHALL use that cipher suite.  Otherwise the
      first cipher suite in SUITES_U MUST be used.





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   o  Generate an ephemeral ECDH key pair as specified in Section 5 of
      [SP-800-56A] using the curve in the selected cipher suite.  Let
      G_X be the x-coordinate of the ephemeral public key.

   o  Choose a connection identifier C_U and store it for the length of
      the protocol.

   o  Encode message_1 as a sequence of CBOR encoded data items as
      specified in Section 4.2.1

4.2.3.  Party V Processing of Message 1

   Party V SHALL process message_1 as follows:

   o  Decode message_1 (see Appendix A.1).

   o  Verify that the selected cipher suite is supported and that no
      prior cipher suites in SUITES_U are supported.

   o  Validate that there is a solution to the curve definition for the
      given x-coordinate G_X.

   o  Pass UAD_1 to the application.

   If any verification step fails, Party V MUST send an EDHOC error
   message back, formatted as defined in Section 7, and the protocol
   MUST be discontinued.  If V does not support the selected cipher
   suite, then SUITES_V MUST include one or more supported cipher
   suites.  If V does not support the selected cipher suite, but
   supports another cipher suite in SUITES_U, then SUITES_V MUST include
   the first supported cipher suite in SUITES_U.

4.3.  EDHOC Message 2

4.3.1.  Formatting of Message 2

   message_2 and data_2 SHALL be CBOR Sequences (see Appendix A.1) as
   defined below

   message_2 = (
     data_2,
     CIPHERTEXT_2 : bstr,
   )








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   data_2 = (
     ? C_U : bstr,
     G_Y : bstr,
     C_V : bstr,
   )

   where:

   o  G_Y - the x-coordinate of the ephemeral public key of Party V

   o  C_V - variable length connection identifier

4.3.2.  Party V Processing of Message 2

   Party V SHALL compose message_2 as follows:

   o  If TYPE mod 4 equals 1 or 3, C_U is omitted, otherwise C_U is not
      omitted.

   o  Generate an ephemeral ECDH key pair as specified in Section 5 of
      [SP-800-56A] using the curve in the selected cipher suite.  Let
      G_Y be the x-coordinate of the ephemeral public key.

   o  Choose a connection identifier C_V and store it for the length of
      the protocol.

   o  Compute the transcript hash TH_2 = H( message_1, data_2 ) where
      H() is the hash function in the HMAC algorithm.  The transcript
      hash TH_2 is a CBOR encoded bstr and the input to the hash
      function is a CBOR Sequence.

   o  Compute COSE_Sign1 as defined in Section 4.4 of [RFC8152], using
      the signature algorithm in the selected cipher suite, the private
      authentication key of Party V, and the parameters below.  Note
      that only 'signature' of the COSE_Sign1 object is used to create
      message_2, see next bullet.  The unprotected header (not included
      in the EDHOC message) MAY contain parameters (e.g. 'alg').

      *  protected = bstr .cbor ID_CRED_V

      *  payload = CRED_V

      *  external_aad = TH_2

      *  ID_CRED_V - identifier to facilitate retrieval of CRED_V, see
         Section 4.1





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      *  CRED_V - bstr credential containing the credential of Party V,
         e.g. its public authentication key or X.509 certificate see
         Section 4.1.  The public key must be a signature key.  Note
         that if objects that are not bstr are used, such as COSE_Key
         for public authentication keys, these objects must be wrapped
         in a CBOR bstr.

      COSE constructs the input to the Signature Algorithm as follows:

      *  The key is the private authentication key of V.

      *  The message M to be signed is the CBOR encoding of:

         [ "Signature1", << ID_CRED_V >>, TH_2, CRED_V ]

   o  Compute COSE_Encrypt0 as defined in Section 5.3 of [RFC8152], with
      the AEAD algorithm in the selected cipher suite, K_2, IV_2, and
      the parameters below.  Note that only 'ciphertext' of the
      COSE_Encrypt0 object is used to create message_2, see next bullet.
      The protected header SHALL be empty.  The unprotected header (not
      included in the EDHOC message) MAY contain parameters (e.g.
      'alg').

      *  plaintext = ( ID_CRED_V / kid_value, signature, ? UAD_2 )

      *  external_aad = TH_2

      *  UAD_2 = bstr containing opaque unprotected application data

      where signature is taken from the COSE_Sign1 object, ID_CRED_V is
      a COSE header_map (i.e. a CBOR map containing COSE Common Header
      Parameters, see [RFC8152]), and kid_value is a bstr.  If ID_CRED_V
      contains a single 'kid' parameter, i.e., ID_CRED_V = { 4 :
      kid_value }, only kid_value is conveyed in the plaintext.

      COSE constructs the input to the AEAD [RFC5116] as follows:

      *  Key K = K_2

      *  Nonce N = IV_2

      *  Plaintext P = ( ID_CRED_V / kid_value, signature, ? UAD_2 )

      *  Associated data A = [ "Encrypt0", h'', TH_2 ]

   o  Encode message_2 as a sequence of CBOR encoded data items as
      specified in Section 4.3.1.  CIPHERTEXT_2 is the COSE_Encrypt0
      ciphertext.



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4.3.3.  Party U Processing of Message 2

   Party U SHALL process message_2 as follows:

   o  Decode message_2 (see Appendix A.1).

   o  Retrieve the protocol state using the connection identifier C_U
      and/or other external information such as the CoAP Token and the
      5-tuple.

   o  Validate that there is a solution to the curve definition for the
      given x-coordinate G_Y.

   o  Decrypt and verify COSE_Encrypt0 as defined in Section 5.3 of
      [RFC8152], with the AEAD algorithm in the selected cipher suite,
      K_2, and IV_2.

   o  Verify COSE_Sign1 as defined in Section 4.4 of [RFC8152], using
      the signature algorithm in the selected cipher suite and the
      public authentication key of Party V.

   If any verification step fails, Party U MUST send an EDHOC error
   message back, formatted as defined in Section 7, and the protocol
   MUST be discontinued.

4.4.  EDHOC Message 3

4.4.1.  Formatting of Message 3

   message_3 and data_3 SHALL be CBOR Sequences (see Appendix A.1) as
   defined below

   message_3 = (
     data_3,
     CIPHERTEXT_3 : bstr,
   )

   data_3 = (
     ? C_V : bstr,
   )

4.4.2.  Party U Processing of Message 3

   Party U SHALL compose message_3 as follows:

   o  If TYPE mod 4 equals 2 or 3, C_V is omitted, otherwise C_V is not
      omitted.




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   o  Compute the transcript hash TH_3 = H( TH_2 , CIPHERTEXT_2, data_3
      ) where H() is the hash function in the HMAC algorithm.  The
      transcript hash TH_3 is a CBOR encoded bstr and the input to the
      hash function is a CBOR Sequence.

   o  Compute COSE_Sign1 as defined in Section 4.4 of [RFC8152], using
      the signature algorithm in the selected cipher suite, the private
      authentication key of Party U, and the parameters below.  Note
      that only 'signature' of the COSE_Sign1 object is used to create
      message_3, see next bullet.  The unprotected header (not included
      in the EDHOC message) MAY contain parameters (e.g. 'alg').

      *  protected = bstr .cbor ID_CRED_U

      *  payload = CRED_U

      *  external_aad = TH_3

      *  ID_CRED_U - identifier to facilitate retrieval of CRED_U, see
         Section 4.1

      *  CRED_U - bstr credential containing the credential of Party U,
         e.g. its public authentication key or X.509 certificate see
         Section 4.1.  The public key must be a signature key.  Note
         that if objects that are not bstr are used, such as COSE_Key
         for public authentication keys, these objects must be wrapped
         in a CBOR bstr.

      COSE constructs the input to the Signature Algorithm as follows:

      *  The key is the private authentication key of U.

      *  The message M to be signed is the CBOR encoding of:

         [ "Signature1", << ID_CRED_U >>, TH_3, CRED_U ]

   o  Compute COSE_Encrypt0 as defined in Section 5.3 of [RFC8152], with
      the AEAD algorithm in the selected cipher suite, K_3, and IV_3 and
      the parameters below.  Note that only 'ciphertext' of the
      COSE_Encrypt0 object is used to create message_3, see next bullet.
      The protected header SHALL be empty.  The unprotected header (not
      included in the EDHOC message) MAY contain parameters (e.g.
      'alg').

      *  plaintext = ( ID_CRED_U / kid_value, signature, ? PAD_3 )

      *  external_aad = TH_3




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      *  PAD_3 = bstr containing opaque protected application data

      where signature is taken from the COSE_Sign1 object, ID_CRED_U is
      a COSE header_map (i.e. a CBOR map containing COSE Common Header
      Parameters, see [RFC8152]), and kid_value is a bstr.  If ID_CRED_U
      contains a single 'kid' parameter, i.e., ID_CRED_U = { 4 :
      kid_value }, only kid_value is conveyed in the plaintext.

      COSE constructs the input to the AEAD [RFC5116] as follows:

      *  Key K = K_3

      *  Nonce N = IV_2

      *  Plaintext P = ( ID_CRED_U / kid_value, signature, ? PAD_3 )

      *  Associated data A = [ "Encrypt0", h'', TH_3 ]

   o  Encode message_3 as a sequence of CBOR encoded data items as
      specified in Section 4.4.1.  CIPHERTEXT_3 is the COSE_Encrypt0
      ciphertext.

   o  Pass the connection identifiers (C_U, C_V) and the selected cipher
      suite to the application.  The application can now derive
      application keys using the EDHOC-Exporter interface.

4.4.3.  Party V Processing of Message 3

   Party V SHALL process message_3 as follows:

   o  Decode message_3 (see Appendix A.1).

   o  Retrieve the protocol state using the connection identifier C_V
      and/or other external information such as the CoAP Token and the
      5-tuple.

   o  Decrypt and verify COSE_Encrypt0 as defined in Section 5.3 of
      [RFC8152], with the AEAD algorithm in the selected cipher suite,
      K_3, and IV_3.

   o  Verify COSE_Sign1 as defined in Section 4.4 of [RFC8152], using
      the signature algorithm in the selected cipher suite and the
      public authentication key of Party U.

   If any verification step fails, Party V MUST send an EDHOC error
   message back, formatted as defined in Section 7, and the protocol
   MUST be discontinued.




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   o  Pass PAD_3, the connection identifiers (C_U, C_V), and the
      selected cipher suite to the application.  The application can now
      derive application keys using the EDHOC-Exporter interface.

5.  EDHOC Authenticated with Symmetric Keys

5.1.  Overview

   EDHOC supports authentication with pre-shared keys.  Party U and V
   are assumed to have a pre-shared key (PSK) with a good amount of
   randomness and the requirement that:

   o  Only Party U and Party V SHALL have access to the PSK,

   o  Party V is able to retrieve the PSK using ID_PSK.

   where the identifier ID_PSK is a COSE header_map (i.e. a CBOR map
   containing COSE Common Header Parameters, see [RFC8152]) containing
   COSE header parameter that can identify a pre-shared key.  Pre-shared
   keys are typically stored as COSE_Key objects and identified with a
   'kid' parameter (see [RFC8152]):

   o  ID_PSK = { 4 : kid_value } , where kid_value : bstr

   The purpose of ID_PSK is to facilitate retrieval of the PSK and in
   the case a 'kid' parameter is used it may be very short.  It is
   RECOMMENDED that it uniquely identify the PSK as the recipient may
   otherwise have to try several keys.

   EDHOC with symmetric key authentication is illustrated in Figure 5.

   Party U                                                       Party V
   |              TYPE, SUITES_U, G_X, C_U, ID_PSK, UAD_1              |
   +------------------------------------------------------------------>|
   |                             message_1                             |
   |                                                                   |
   |               C_U, G_Y, C_V, AEAD(K_2; TH_2, UAD_2)               |
   |<------------------------------------------------------------------+
   |                             message_2                             |
   |                                                                   |
   |                    C_V, AEAD(K_3; TH_3, PAD_3)                    |
   +------------------------------------------------------------------>|
   |                             message_3                             |

      Figure 5: Overview of EDHOC with symmetric key authentication.

   EDHOC with symmetric key authentication is very similar to EDHOC with
   signature key authentication.  In the following subsections the



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   differences compared to EDHOC with signature key authentication are
   described.

5.2.  EDHOC Message 1

5.2.1.  Formatting of Message 1

   message_1 SHALL be a CBOR Sequence (see Appendix A.1) as defined
   below

   message_1 = (
     TYPE : int,
     SUITES_U : suite / [ index : uint, 2* suite ],
     G_X : bstr,
     C_U : bstr,
     ID_PSK : header_map // kid_value : bstr,
     ? UAD_1 : bstr,
   )

   where:

   o  TYPE = 4 * method + corr, where the method = 1 and the connection
      parameter corr is chosen based on the transport and determines
      which connection identifiers that are omitted (see Section 4.1).

   o  ID_PSK - identifier to facilitate retrieval of the pre-shared key.
      If ID_PSK contains a single 'kid' parameter, i.e., ID_PSK = { 4 :
      kid_value }, with kid_value: bstr, only kid_value is conveyed.

5.3.  EDHOC Message 2

5.3.1.  Processing of Message 2

   o  COSE_Sign1 is not used.

   o  COSE_Encrypt0 is computed as defined in Section 5.3 of [RFC8152],
      with the AEAD algorithm in the selected cipher suite, K_2, IV_2,
      and the following parameters.  The protected header SHALL be
      empty.  The unprotected header MAY contain parameters (e.g.
      'alg').

      *  external_aad = TH_2

      *  plaintext = ? UAD_2

      *  UAD_2 = bstr containing opaque unprotected application data





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5.4.  EDHOC Message 3

5.4.1.  Processing of Message 3

   o  COSE_Sign1 is not used.

   o  COSE_Encrypt0 is computed as defined in Section 5.3 of [RFC8152],
      with the AEAD algorithm in the selected cipher suite, K_3, IV_3,
      and the following parameters.  The protected header SHALL be
      empty.  The unprotected header MAY contain parameters (e.g.
      'alg').

      *  external_aad = TH_3

      *  plaintext = ? PAD_3

      *  PAD_3 = bstr containing opaque protected application data

6.  EDHOC Authenticated with Static Diffie-Hellman Keys

   NOTE: This section is more work-in-progress that the other parts.
   The current format and processing is a conservative design with
   format and processing as close to the signature key authentication as
   possible.  Many different choices can be made for the message format
   and what to include in the key derivations.  In a future version the
   key derivation, security considerations, and message sizes should be
   integrated with the rest of the document.

6.1.  Overview

   EDHOC authenticated with static Diffie-Hellman keys is very similar
   to EDHOC authenticated with signature keys.  Instead of signature
   authentication keys, U and V have static Diffie-Hellman
   authentication keys called G_U and G_V, respectively.  This means
   that the credentials (certificates, RPK) must include a public key
   that can be used for Diffie-Hellman key exchange.  The authentication
   is provided by a MAC computed from an ephemeral-static ECDH shared
   secret which enables significant reductions in message sizes.

   In the following subsections only the differences compared to EDHOC
   authenticated with signature keys are described.  EDHOC authenticated
   with static Diffie-Hellman keys is illustrated in Figure 6.









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   Party U                                                       Party V
   |                     TYPE, SUITES_U, G_X, C_U                      |
   +------------------------------------------------------------------>|
   |                             message_1                             |
   |                                                                   |
   |  C_U, G_Y, C_V, AEAD( K_2; ID_CRED_V, AEAD(G_VX; CRED_V, TH_2) )  |
   |<------------------------------------------------------------------+
   |                             message_2                             |
   |                                                                   |
   |        C_V, AEAD(K_3; ID_CRED_U, AEAD(G_UY; CRED_V, TH_2) )       |
   +------------------------------------------------------------------>|
   |                             message_3                             |

   Figure 6: Overview of EDHOC authenticated with static Diffie-Hellman
                                   keys.

6.2.  EDHOC Message 1

6.2.1.  Formatting of Message 1

   o  TYPE = 4 * method + corr, where the method = 2 and the correlation
      parameter corr is chosen based on the transport and determines
      which connection identifiers that are omitted (see Section 4.1).

6.3.  EDHOC Message 2

6.3.1.  Processing of Message 2

   o  COSE_Sign1 is not used and 'signature' is replaced with the
      'ciphertext' from an inner COSE_Encrypt0.  The inner COSE_Encrypt0
      in computed with the AEAD algorithm in the selected cipher suite,
      K_V, IV_V, and the parameters below.

      *  PRK_V = HKDF-Extract( "", G_VX ), where G_VX is the ECDH shared
         secret calculated from G_V and X, or G_X and V)

      *  K_V = HKDF-Expand( PRK_V, info, L ), where other = TH_2

      *  IV_V = HKDF-Expand( PRK_V, info, L ), where other = TH_2

      *  plaintext = 0x (the empty string)

      *  external_aad = [ "Signature1", << ID_CRED_V >>, TH_2,
         << CRED_V >> ]

      *  CRED_V - bstr credential containing the public authentication
         key of Party V, see Section 4.1.  The public key must be a
         Diffie-Hellman key.



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6.4.  EDHOC Message 3

6.4.1.  Processing of Message 3

   o  COSE_Sign1 is not used and 'signature' is replaced with the
      'ciphertext' from an inner COSE_Encrypt0.  The inner COSE_Encrypt0
      in computed with the AEAD algorithm in the selected cipher suite,
      K_U, IV_U, and the parameters below.

      *  PRK_U = HKDF-Extract( "", G_UY ), where G_UY is the ECDH shared
         secret calculated from G_U and Y, or G_Y and U)

      *  K_U = HKDF-Expand( PRK_U, info, L ), where other = TH_3

      *  IV_U = HKDF-Expand( PRK_U, info, L ), where other = TH_3

      *  plaintext = 0x (the empty string)

      *  external_aad = [ "Signature1", << ID_CRED_U >>, TH_3,
         << CRED_U >> ]

      *  CRED_U - bstr credential containing the public authentication
         key of Party U, see Section 4.1.  The public key must be a
         Diffie-Hellman key.

6.5.  EDHOC-Exporter Interface

   The EDHOC-Exporter interface uses the key PRK_Export instead of PRK

      PRK_Export = HKDF-Extract( "", PRK || PRK_V || PRK_U )

   EDHOC-Exporter( label, length ) = HKDF-Expand( PRK_Export, info, length )

6.6.  Security Considerations

   EDHOC authenticated with static Diffie-Hellman keys have similar
   security properties as EDHOC authenticated with signature keys with a
   few small differences:

   o  Repudiation: In EDHOC authenticated with signature keys, Party U
      could theoretically prove that Party V performed a run of the
      protocol by presenting the private ephemeral key, and vice versa.
      Note that storing the private ephemeral keys violates the protocol
      requirements.  With static Diffie-Hellman key authentication, both
      parties can always deny having participated in the protocol, this
      is similar to EDHOC with symmetric key authentication.





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   o  Key compromise impersonation (KCI): In EDHOC authenticated with
      signature keys, EDHOC provides KCI protection against an attacker
      having access to the long term key or the ephemeral secret key.
      In EDHOC authenticated with symmetric keys, EDHOC provides KCI
      protection against an attacker having access to the ephemeral
      secret key, but not against an attacker having access to the long-
      term PSK.  With static Diffie-Hellman key authentication, KCI
      protection would be provided against an attacker having access to
      the long-term Diffie-Hellman key, but not to an attacker having
      access to the ephemeral secret key.  Note that the term KCI has
      typically been used for compromise of long-term keys, and that an
      attacker with access to the ephemeral secret key can only attack
      that specific protocol run.

6.7.  Message Sizes

   Authentication with static Diffie-Hellman keys provide significant
   reductions in message sizes compared to signature keys.  The relative
   differences are particulare large for PRKs where the signatures make
   up a large part of the total number of bytes.

   =====================================================================
                  PSK     RPK (Signature key)     RPK (ECDH key)
   ---------------------------------------------------------------------
   message_1       40              38                   38
   message_2       45             114                   56
   message_3       11              80                   22
   ---------------------------------------------------------------------
   Total           96             232                  116
   =====================================================================

                 Figure 7: Typical message sizes in bytes

7.  Error Handling

7.1.  EDHOC Error Message

   This section defines a message format for the EDHOC error message,
   used during the protocol.  An EDHOC error message can be sent by both
   parties as a reply to any non-error EDHOC message.  After sending an
   error message, the protocol MUST be discontinued.  Errors at the
   EDHOC layer are sent as normal successful messages in the lower
   layers (e.g.  CoAP POST and 2.04 Changed).  An advantage of using
   such a construction is to avoid issues created by usage of cross
   protocol proxies (e.g.  UDP to TCP).

   error SHALL be a CBOR Sequence (see Appendix A.1) as defined below




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   error = (
     ? C_x : bstr,
     ERR_MSG : tstr,
     ? SUITES_V : suite / [ 2* suite ],
   )

   where:

   o  C_x - if error is sent by Party V and TYPE mod 4 equals 0 or 2
      then C_x is set to C_U, else if error is sent by Party U and TYPE
      mod 4 equals 0 or 1 then C_x is set to C_V, else C_x is omitted.

   o  ERR_MSG - text string containing the diagnostic payload, defined
      in the same way as in Section 5.5.2 of [RFC7252].  ERR_MSG MAY be
      a 0-length text string.

   o  SUITES_V - cipher suites from SUITES_U or the EDHOC cipher suites
      registry that V supports.  Note that SUITES_V only contains the
      values from the EDHOC cipher suites registry and no index.
      SUITES_V MUST only be included in replies to message_1.

7.1.1.  Example Use of EDHOC Error Message with SUITES_V

   Assuming that Party U supports the five cipher suites {5, 6, 7, 8, 9}
   in decreasing order of preference, Figures 8 and 9 show examples of
   how Party U can truncate SUITES_U and how SUITES_V is used by Party V
   to give Party U information about the cipher suites that Party V
   supports.  In Figure 8, Party V supports cipher suite 6 but not the
   selected cipher suite 5.

   Party U                                                       Party V
   |            TYPE, SUITES_U {0, 5, 6, 7}, G_X, C_U, UAD_1           |
   +------------------------------------------------------------------>|
   |                             message_1                             |
   |                                                                   |
   |                     C_U, ERR_MSG, SUITES_V {6}                    |
   |<------------------------------------------------------------------+
   |                               error                               |
   |                                                                   |
   |             TYPE, SUITES_U {1, 5, 6}, G_X, C_U, UAD_1             |
   +------------------------------------------------------------------>|
   |                             message_1                             |

           Figure 8: Example use of error message with SUITES_V.

   In Figure 9, Party V supports cipher suite 7 but not cipher suites 5
   and 6.




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   Party U                                                       Party V
   |             TYPE, SUITES_U {0, 5, 6}, G_X, C_U, UAD_1             |
   +------------------------------------------------------------------>|
   |                             message_1                             |
   |                                                                   |
   |                    C_U, ERR_MSG, SUITES_V {7, 9}                  |
   |<------------------------------------------------------------------+
   |                               error                               |
   |                                                                   |
   |            TYPE, SUITES_U {2, 5, 6, 7}, G_X, C_U, UAD_1           |
   +------------------------------------------------------------------>|
   |                             message_1                             |

           Figure 9: Example use of error message with SUITES_V.

   As Party U's list of supported cipher suites and order of preference
   is fixed, and Party V only accepts message_1 if the selected cipher
   suite is the first cipher suite in SUITES_U that Party V supports,
   the parties can verify that the selected cipher suite is the most
   preferred (by Party U) cipher suite supported by both parties.  If
   the selected cipher suite is not the first cipher suite in SUITES_U
   that Party V supports, Party V will discontinue the protocol.

8.  Transferring EDHOC and Deriving Application Keys

8.1.  Transferring EDHOC in CoAP

   It is recommended to transport EDHOC as an exchange of CoAP [RFC7252]
   messages.  CoAP is a reliable transport that can preserve packet
   ordering and handle message duplication.  CoAP can also perform
   fragmentation and protect against denial of service attacks.  It is
   recommended to carry the EDHOC flights in Confirmable messages,
   especially if fragmentation is used.

   By default, the CoAP client is Party U and the CoAP server is Party
   V, but the roles SHOULD be chosen to protect the most sensitive
   identity, see Section 9.  By default, EDHOC is transferred in POST
   requests and 2.04 (Changed) responses to the Uri-Path: "/.well-known/
   edhoc", but an application may define its own path that can be
   discovered e.g. using resource directory
   [I-D.ietf-core-resource-directory].

   By default, the message flow is as follows: EDHOC message_1 is sent
   in the payload of a POST request from the client to the server's
   resource for EDHOC.  EDHOC message_2 or the EDHOC error message is
   sent from the server to the client in the payload of a 2.04 (Changed)
   response.  EDHOC message_3 or the EDHOC error message is sent from
   the client to the server's resource in the payload of a POST request.



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   If needed, an EDHOC error message is sent from the server to the
   client in the payload of a 2.04 (Changed) response.

   An example of a successful EDHOC exchange using CoAP is shown in
   Figure 10.  In this case the CoAP Token enables Party U to correlate
   message_1 and message_2 so the correlation parameter corr = 1.

             Client    Server
               |          |
               +--------->| Header: POST (Code=0.02)
               |   POST   | Uri-Path: "/.well-known/edhoc"
               |          | Content-Format: application/edhoc
               |          | Payload: EDHOC message_1
               |          |
               |<---------+ Header: 2.04 Changed
               |   2.04   | Content-Format: application/edhoc
               |          | Payload: EDHOC message_2
               |          |
               +--------->| Header: POST (Code=0.02)
               |   POST   | Uri-Path: "/.well-known/edhoc"
               |          | Content-Format: application/edhoc
               |          | Payload: EDHOC message_3
               |          |
               |<---------+ Header: 2.04 Changed
               |   2.04   |
               |          |

                   Figure 10: Transferring EDHOC in CoAP

   The exchange in Figure 10 protects the client identity against active
   attackers and the server identity against passive attackers.  An
   alternative exchange that protects the server identity against active
   attackers and the client identity against passive attackers is shown
   in Figure 11.  In this case the CoAP Token enables Party V to
   correlate message_2 and message_3 so the correlation parameter corr =
   2.















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             Client    Server
               |          |
               +--------->| Header: POST (Code=0.02)
               |   POST   | Uri-Path: "/.well-known/edhoc"
               |          |
               |<---------+ Header: 2.04 Changed
               |   2.04   | Content-Format: application/edhoc
               |          | Payload: EDHOC message_1
               |          |
               +--------->| Header: POST (Code=0.02)
               |   POST   | Uri-Path: "/.well-known/edhoc"
               |          | Content-Format: application/edhoc
               |          | Payload: EDHOC message_2
               |          |
               |<---------+ Header: 2.04 Changed
               |   2.04   | Content-Format: application/edhoc
               |          | Payload: EDHOC message_3
               |          |

                   Figure 11: Transferring EDHOC in CoAP

   To protect against denial-of-service attacks, the CoAP server MAY
   respond to the first POST request with a 4.01 (Unauthorized)
   containing an Echo option [I-D.ietf-core-echo-request-tag].  This
   forces the initiator to demonstrate its reachability at its apparent
   network address.  If message fragmentation is needed, the EDHOC
   messages may be fragmented using the CoAP Block-Wise Transfer
   mechanism [RFC7959].

8.1.1.  Deriving an OSCORE Context from EDHOC

   When EDHOC is used to derive parameters for OSCORE [RFC8613], the
   parties must make sure that the EDHOC connection identifiers are
   unique, i.e. C_V MUST NOT be equal to C_U.  The CoAP client and
   server MUST be able to retrieve the OSCORE protocol state using its
   chosen connection identifier and optionally other information such as
   the 5-tuple.  In case that the CoAP client is party U and the CoAP
   server is party V:

   o  The client's OSCORE Sender ID is C_V and the server's OSCORE
      Sender ID is C_U, as defined in this document

   o  The AEAD Algorithm and the HMAC algorithms are the AEAD and HMAC
      algorithms in the selected cipher suite.

   o  The Master Secret and Master Salt are derived as follows where
      length is the key length (in bytes) of the AEAD Algorithm.




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      Master Secret = EDHOC-Exporter( "OSCORE Master Secret", length )
      Master Salt   = EDHOC-Exporter( "OSCORE Master Salt", 8 )

8.2.  Transferring EDHOC over Other Protocols

   EDHOC may be transported over a different transport than CoAP.  In
   this case the lower layers need to handle message loss, reordering,
   message duplication, fragmentation, and denial of service protection.

9.  Security Considerations

9.1.  Security Properties

   EDHOC inherits its security properties from the theoretical SIGMA-I
   protocol [SIGMA].  Using the terminology from [SIGMA], EDHOC provides
   perfect forward secrecy, mutual authentication with aliveness,
   consistency, peer awareness, and identity protection.  As described
   in [SIGMA], peer awareness is provided to Party V, but not to Party
   U.  EDHOC also inherits Key Compromise Impersonation (KCI) resistance
   from SIGMA-I.

   EDHOC with asymmetric authentication (signature, static DH) offers
   identity protection of Party U against active attacks and identity
   protection of Party V against passive attacks.  The roles should be
   assigned to protect the most sensitive identity, typically that which
   is not possible to infer from routing information in the lower
   layers.  EDHOC with symmetric authentication does not offer
   protection of the PSK identifier ID_PSK.  Protection of PSK
   identifiers are posible but requires a four message protocol to
   achieve mutual authentication.

   Compared to [SIGMA], EDHOC adds an explicit method type and expands
   the message authentication coverage to additional elements such as
   algorithms, application data, and previous messages.  This protects
   against an attacker replaying messages or injecting messages from
   another session.

   EDHOC also adds negotiation of connection identifiers and downgrade
   protected negotiation of cryptographic parameters, i.e. an attacker
   cannot affect the negotiated parameters.  A single session of EDHOC
   does not include negotiation of cipher suites, but it enables Party V
   to verify that the selected cipher suite is the most preferred cipher
   suite by U which is supported by both U and V.

   As required by [RFC7258], IETF protocols need to mitigate pervasive
   monitoring when possible.  One way to mitigate pervasive monitoring
   is to use a key exchange that provides perfect forward secrecy.
   EDHOC therefore only supports methods with perfect forward secrecy.



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   To limit the effect of breaches, it is important to limit the use of
   symmetrical group keys for bootstrapping.  EDHOC therefore strives to
   make the additional cost of using raw public keys and self-signed
   certificates as small as possible.  Raw public keys and self-signed
   certificates are not a replacement for a public key infrastructure,
   but SHOULD be used instead of symmetrical group keys for
   bootstrapping.

   Compromise of the long-term keys (PSK or private authentication keys)
   does not compromise the security of completed EDHOC exchanges.
   Compromising the private authentication keys of one party lets an
   active attacker impersonate that compromised party in EDHOC exchanges
   with other parties, but does not let the attacker impersonate other
   parties in EDHOC exchanges with the compromised party.  Compromising
   the PSK lets an active attacker impersonate Party U in EDHOC
   exchanges with Party V and impersonate Party V in EDHOC exchanges
   with Party U.  Compromise of the long-term keys does not enable a
   passive attacker to compromise future session keys.  Compromise of
   the HDKF input parameters (ECDH shared secret and/or PSK) leads to
   compromise of all session keys derived from that compromised shared
   secret.  Compromise of one session key does not compromise other
   session keys.

9.2.  Cryptographic Considerations

   The security of the SIGMA protocol requires the MAC to be bound to
   the identity of the signer.  Hence the message authenticating
   functionality of the authenticated encryption in EDHOC is critical:
   authenticated encryption MUST NOT be replaced by plain encryption
   only, even if authentication is provided at another level or through
   a different mechanism.  EDHOC implements SIGMA-I using the same Sign-
   then-MAC approach as TLS 1.3.

   To reduce message overhead EDHOC does not use explicit nonces and
   instead rely on the ephemeral public keys to provide randomness to
   each session.  A good amount of randomness is important for the key
   generation, to provide liveness, and to protect against interleaving
   attacks.  For this reason, the ephemeral keys MUST NOT be reused, and
   both parties SHALL generate fresh random ephemeral key pairs.

   The choice of key length used in the different algorithms needs to be
   harmonized, so that a sufficient security level is maintained for
   certificates, EDHOC, and the protection of application data.  Party U
   and V should enforce a minimum security level.

   The data rates in many IoT deployments are very limited.  Given that
   the application keys are protected as well as the long-term
   authentication keys they can often be used for years or even decades



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   before the cryptographic limits are reached.  If the application keys
   established through EDHOC need to be renewed, the communicating
   parties can derive application keys with other labels or run EDHOC
   again.

9.3.  Cipher Suites

   Cipher suite number 0 (AES-CCM-64-64-128, ECDH-SS + HKDF-256, X25519,
   Ed25519) is mandatory to implement.  For many constrained IoT devices
   it is problematic to support more than one cipher suites, so some
   deployments with P-256 may not support the mandatory cipher suite.
   This is not a problem for local deployments.

   The HMAC algorithm HMAC 256/64 (HMAC w/ SHA-256 truncated to 64 bits)
   SHALL NOT be supported for use in EDHOC.

9.4.  Unprotected Data

   Party U and V must make sure that unprotected data and metadata do
   not reveal any sensitive information.  This also applies for
   encrypted data sent to an unauthenticated party.  In particular, it
   applies to UAD_1, ID_CRED_V, UAD_2, and ERR_MSG in the asymmetric
   case, and ID_PSK, UAD_1, and ERR_MSG in the symmetric case.  Using
   the same ID_PSK or UAD_1 in several EDHOC sessions allows passive
   eavesdroppers to correlate the different sessions.  The communicating
   parties may therefore anonymize ID_PSK.  Another consideration is
   that the list of supported cipher suites may be used to identify the
   application.

   Party U and V must also make sure that unauthenticated data does not
   trigger any harmful actions.  In particular, this applies to UAD_1
   and ERR_MSG in the asymmetric case, and ID_PSK, UAD_1, and ERR_MSG in
   the symmetric case.

9.5.  Denial-of-Service

   EDHOC itself does not provide countermeasures against Denial-of-
   Service attacks.  By sending a number of new or replayed message_1 an
   attacker may cause Party V to allocate state, perform cryptographic
   operations, and amplify messages.  To mitigate such attacks, an
   implementation SHOULD rely on lower layer mechanisms such as the Echo
   option in CoAP [I-D.ietf-core-echo-request-tag] that forces the
   initiator to demonstrate reachability at its apparent network
   address.







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9.6.  Implementation Considerations

   The availability of a secure pseudorandom number generator and truly
   random seeds are essential for the security of EDHOC.  If no true
   random number generator is available, a truly random seed must be
   provided from an external source.  As each pseudoranom number must
   only be used once, an implementation need to get a new truly random
   seed after reboot, or continously store state in nonvolatile memory,
   see ([RFC8613], Appendix B.1.1) for issues and solution approaches
   for writing to nonvolatile memory.  If ECDSA is supported,
   "deterministic ECDSA" as specified in [RFC6979] is RECOMMENDED.

   The referenced processing instructions in [SP-800-56A] must be
   complied with, including deleting the intermediate computed values
   along with any ephemeral ECDH secrets after the key derivation is
   completed.  The ECDH shared secret, keys (K_2, K_3), and IVs (IV_2,
   IV_3) MUST be secret.  Implementations should provide countermeasures
   to side-channel attacks such as timing attacks.

   Party U and V are responsible for verifying the integrity of
   certificates.  The selection of trusted CAs should be done very
   carefully and certificate revocation should be supported.  The
   private authentication keys and the PSK (even though it is used as
   salt) MUST be kept secret.

   Party U and V are allowed to select the connection identifiers C_U
   and C_V, respectively, for the other party to use in the ongoing
   EDHOC protocol as well as in a subsequent application protocol (e.g.
   OSCORE [RFC8613]).  The choice of connection identifier is not
   security critical in EDHOC but intended to simplify the retrieval of
   the right security context in combination with using short
   identifiers.  If the wrong connection identifier of the other party
   is used in a protocol message it will result in the receiving party
   not being able to retrieve a security context (which will terminate
   the protocol) or retrieve the wrong security context (which also
   terminates the protocol as the message cannot be verified).

   Party V MUST finish the verification step of message_3 before passing
   PAD_3 to the application.

   If two nodes unintentionally initiate two simultaneous EDHOC message
   exchanges with each other even if they only want to complete a single
   EDHOC message exchange, they MAY terminate the exchange with the
   lexicographically smallest G_X.  If the two G_X values are equal, the
   received message_1 MUST be discarded to mitigate reflection attacks.
   Note that in the case of two simultaneous EDHOC exchanges where the
   nodes only complete one and where the nodes have different preferred




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   cipher suites, an attacker can affect which of the two nodes'
   preferred cipher suites will be used by blocking the other exchange.

9.7.  Other Documents Referencing EDHOC

   EDHOC has been analyzed in several other documents.  A formal
   verification of EDHOC was done in [SSR18], an analysis of EDHOC for
   certificate enrollment was done in [Kron18], the use of EDHOC in
   LoRaWAN is analyzed in [LoRa1] and [LoRa2], the use of EDHOC in IoT
   bootstrapping is analyzed in [Perez18], and the use of EDHOC in
   6TiSCH is described in [I-D.ietf-6tisch-dtsecurity-zerotouch-join].

10.  IANA Considerations

10.1.  EDHOC Cipher Suites Registry

   IANA has created a new registry titled "EDHOC Cipher Suites" under
   the new heading "EDHOC".  The registration procedure is "Expert
   Review".  The columns of the registry are Value, Array, Description,
   and Reference, where Value is an integer and the other columns are
   text strings.  The initial contents of the registry are:

   Value: 1
   Array: [ 10, 5, 1, -7, 1 ]
   Desc: AES-CCM-16-64-128, HMAC 256/256, P-256, ES256, P-256
   Reference: [[this document]]

   Value: 0
   Array: [ 10, 5, 4, -8, 6 ]
   Desc: AES-CCM-16-64-128, HMAC 256/256, X25519, EdDSA, Ed25519
   Reference: [[this document]]

   Value: -5
   Array:
   Desc: Reserved for Private Use
   Reference: [[this document]]

   Value: -6
   Array:
   Desc: Reserved for Private Use
   Reference: [[this document]]

10.2.  EDHOC Method Type Registry

   IANA has created a new registry titled "EDHOC Method Type" under the
   new heading "EDHOC".  The registration procedure is "Expert Review".
   The columns of the registry are Value, Description, and Reference,




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   where Value is an integer and the other columns are text strings.
   The initial contents of the registry are:

+-------+------------------------------------------+-------------------+
| Value | Specification                            | Reference         |
+-------+------------------------------------------+-------------------+
|     0 | EDHOC Authenticated with Signature Keys  | [[this document]] |
|     1 | EDHOC Authenticated with Symmetric Keys  | [[this document]] |
|     2 | EDHOC Authenticated with Static DH Keys  | [[this document]] |
+-------+------------------------------------------+-------------------+

10.3.  The Well-Known URI Registry

   IANA has added the well-known URI 'edhoc' to the Well-Known URIs
   registry.

   o  URI suffix: edhoc

   o  Change controller: IETF

   o  Specification document(s): [[this document]]

   o  Related information: None

10.4.  Media Types Registry

   IANA has added the media type 'application/edhoc' to the Media Types
   registry.

   o  Type name: application

   o  Subtype name: edhoc

   o  Required parameters: N/A

   o  Optional parameters: N/A

   o  Encoding considerations: binary

   o  Security considerations: See Section 7 of this document.

   o  Interoperability considerations: N/A

   o  Published specification: [[this document]] (this document)

   o  Applications that use this media type: To be identified

   o  Fragment identifier considerations: N/A



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   o  Additional information:

      *  Magic number(s): N/A

      *  File extension(s): N/A

      *  Macintosh file type code(s): N/A

   o  Person & email address to contact for further information: See
      "Authors' Addresses" section.

   o  Intended usage: COMMON

   o  Restrictions on usage: N/A

   o  Author: See "Authors' Addresses" section.

   o  Change Controller: IESG

10.5.  CoAP Content-Formats Registry

   IANA has added the media type 'application/edhoc' to the CoAP
   Content-Formats registry.

   o  Media Type: application/edhoc

   o  Encoding:

   o  ID: TBD42

   o  Reference: [[this document]]

10.6.  Expert Review Instructions

   The IANA Registries established in this document is defined as
   "Expert Review".  This section gives some general guidelines for what
   the experts should be looking for, but they are being designated as
   experts for a reason so they should be given substantial latitude.

   Expert reviewers should take into consideration the following points:

   o  Clarity and correctness of registrations.  Experts are expected to
      check the clarity of purpose and use of the requested entries.
      Expert needs to make sure the values of algorithms are taken from
      the right registry, when that's required.  Expert should consider
      requesting an opinion on the correctness of registered parameters
      from relevant IETF working groups.  Encodings that do not meet




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      these objective of clarity and completeness should not be
      registered.

   o  Experts should take into account the expected usage of fields when
      approving point assignment.  The length of the encoded value
      should be weighed against how many code points of that length are
      left, the size of device it will be used on, and the number of
      code points left that encode to that size.

   o  Specifications are recommended.  When specifications are not
      provided, the description provided needs to have sufficient
      information to verify the points above.

11.  References

11.1.  Normative References

   [I-D.ietf-cbor-7049bis]
              Bormann, C. and P. Hoffman, "Concise Binary Object
              Representation (CBOR)", draft-ietf-cbor-7049bis-07 (work
              in progress), August 2019.

   [I-D.ietf-cbor-sequence]
              Bormann, C., "Concise Binary Object Representation (CBOR)
              Sequences", draft-ietf-cbor-sequence-02 (work in
              progress), September 2019.

   [I-D.ietf-core-echo-request-tag]
              Amsuess, C., Mattsson, J., and G. Selander, "CoAP: Echo,
              Request-Tag, and Token Processing", draft-ietf-core-echo-
              request-tag-07 (work in progress), September 2019.

   [I-D.ietf-cose-x509]
              Schaad, J., "CBOR Object Signing and Encryption (COSE):
              Headers for carrying and referencing X.509 certificates",
              draft-ietf-cose-x509-04 (work in progress), September
              2019.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC5116]  McGrew, D., "An Interface and Algorithms for Authenticated
              Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
              <https://www.rfc-editor.org/info/rfc5116>.





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   [RFC5869]  Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869,
              DOI 10.17487/RFC5869, May 2010,
              <https://www.rfc-editor.org/info/rfc5869>.

   [RFC6090]  McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic
              Curve Cryptography Algorithms", RFC 6090,
              DOI 10.17487/RFC6090, February 2011,
              <https://www.rfc-editor.org/info/rfc6090>.

   [RFC6979]  Pornin, T., "Deterministic Usage of the Digital Signature
              Algorithm (DSA) and Elliptic Curve Digital Signature
              Algorithm (ECDSA)", RFC 6979, DOI 10.17487/RFC6979, August
              2013, <https://www.rfc-editor.org/info/rfc6979>.

   [RFC7252]  Shelby, Z., Hartke, K., and C. Bormann, "The Constrained
              Application Protocol (CoAP)", RFC 7252,
              DOI 10.17487/RFC7252, June 2014,
              <https://www.rfc-editor.org/info/rfc7252>.

   [RFC7748]  Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
              for Security", RFC 7748, DOI 10.17487/RFC7748, January
              2016, <https://www.rfc-editor.org/info/rfc7748>.

   [RFC7959]  Bormann, C. and Z. Shelby, Ed., "Block-Wise Transfers in
              the Constrained Application Protocol (CoAP)", RFC 7959,
              DOI 10.17487/RFC7959, August 2016,
              <https://www.rfc-editor.org/info/rfc7959>.

   [RFC8152]  Schaad, J., "CBOR Object Signing and Encryption (COSE)",
              RFC 8152, DOI 10.17487/RFC8152, July 2017,
              <https://www.rfc-editor.org/info/rfc8152>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [RFC8610]  Birkholz, H., Vigano, C., and C. Bormann, "Concise Data
              Definition Language (CDDL): A Notational Convention to
              Express Concise Binary Object Representation (CBOR) and
              JSON Data Structures", RFC 8610, DOI 10.17487/RFC8610,
              June 2019, <https://www.rfc-editor.org/info/rfc8610>.

   [RFC8613]  Selander, G., Mattsson, J., Palombini, F., and L. Seitz,
              "Object Security for Constrained RESTful Environments
              (OSCORE)", RFC 8613, DOI 10.17487/RFC8613, July 2019,
              <https://www.rfc-editor.org/info/rfc8613>.




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   [SIGMA]    Krawczyk, H., "SIGMA - The 'SIGn-and-MAc' Approach to
              Authenticated Diffie-Hellman and Its Use in the IKE-
              Protocols (Long version)", June 2003,
              <http://webee.technion.ac.il/~hugo/sigma-pdf.pdf>.

   [SP-800-56A]
              Barker, E., Chen, L., Roginsky, A., Vassilev, A., and R.
              Davis, "Recommendation for Pair-Wise Key-Establishment
              Schemes Using Discrete Logarithm Cryptography",
              NIST Special Publication 800-56A Revision 3, April 2018,
              <https://doi.org/10.6028/NIST.SP.800-56Ar3>.

11.2.  Informative References

   [CborMe]   Bormann, C., "CBOR Playground", May 2018,
              <http://cbor.me/>.

   [I-D.hartke-core-e2e-security-reqs]
              Selander, G., Palombini, F., and K. Hartke, "Requirements
              for CoAP End-To-End Security", draft-hartke-core-e2e-
              security-reqs-03 (work in progress), July 2017.

   [I-D.ietf-6tisch-dtsecurity-zerotouch-join]
              Richardson, M., "6tisch Zero-Touch Secure Join protocol",
              draft-ietf-6tisch-dtsecurity-zerotouch-join-04 (work in
              progress), July 2019.

   [I-D.ietf-ace-oauth-authz]
              Seitz, L., Selander, G., Wahlstroem, E., Erdtman, S., and
              H. Tschofenig, "Authentication and Authorization for
              Constrained Environments (ACE) using the OAuth 2.0
              Framework (ACE-OAuth)", draft-ietf-ace-oauth-authz-25
              (work in progress), October 2019.

   [I-D.ietf-ace-oscore-profile]
              Palombini, F., Seitz, L., Selander, G., and M. Gunnarsson,
              "OSCORE profile of the Authentication and Authorization
              for Constrained Environments Framework", draft-ietf-ace-
              oscore-profile-08 (work in progress), July 2019.

   [I-D.ietf-core-resource-directory]
              Shelby, Z., Koster, M., Bormann, C., Stok, P., and C.
              Amsuess, "CoRE Resource Directory", draft-ietf-core-
              resource-directory-23 (work in progress), July 2019.







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   [I-D.ietf-lwig-security-protocol-comparison]
              Mattsson, J. and F. Palombini, "Comparison of CoAP
              Security Protocols", draft-ietf-lwig-security-protocol-
              comparison-03 (work in progress), March 2019.

   [I-D.ietf-tls-dtls13]
              Rescorla, E., Tschofenig, H., and N. Modadugu, "The
              Datagram Transport Layer Security (DTLS) Protocol Version
              1.3", draft-ietf-tls-dtls13-33 (work in progress), October
              2019.

   [Kron18]   Krontiris, A., "Evaluation of Certificate Enrollment over
              Application Layer Security", May 2018,
              <https://www.nada.kth.se/~ann/exjobb/
              alexandros_krontiris.pdf>.

   [LoRa1]    Sanchez-Iborra, R., Sanchez-Gomez, J., Perez, S.,
              Fernandez, P., Santa, J., Hernandez-Ramos, J., and A.
              Skarmeta, "Enhancing LoRaWAN Security through a
              Lightweight and Authenticated Key Management Approach",
              June 2018,
              <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6021899/pdf/
              sensors-18-01833.pdf>.

   [LoRa2]    Sanchez-Iborra, R., Sanchez-Gomez, J., Perez, S.,
              Fernandez, P., Santa, J., Hernandez-Ramos, J., and A.
              Skarmeta, "Internet Access for LoRaWAN Devices Considering
              Security Issues", June 2018,
              <https://ants.inf.um.es/~josesanta/doc/GIoTS1.pdf>.

   [OPTLS]    Krawczyk, H. and H. Wee, "The OPTLS Protocol and TLS 1.3",
              October 2015, <https://eprint.iacr.org/2015/978.pdf>.

   [Perez18]  Perez, S., Garcia-Carrillo, D., Marin-Lopez, R.,
              Hernandez-Ramos, J., Marin-Perez, R., and A. Skarmeta,
              "Architecture of security association establishment based
              on bootstrapping technologies for enabling critical IoT
              infrastructures", October 2018, <http://www.anastacia-
              h2020.eu/publications/Architecture_of_security_association
              _establishment_based_on_bootstrapping_technologies_for_ena
              bling_critical_IoT_infrastructures.pdf>.

   [RFC7228]  Bormann, C., Ersue, M., and A. Keranen, "Terminology for
              Constrained-Node Networks", RFC 7228,
              DOI 10.17487/RFC7228, May 2014,
              <https://www.rfc-editor.org/info/rfc7228>.





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   [RFC7258]  Farrell, S. and H. Tschofenig, "Pervasive Monitoring Is an
              Attack", BCP 188, RFC 7258, DOI 10.17487/RFC7258, May
              2014, <https://www.rfc-editor.org/info/rfc7258>.

   [RFC8446]  Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
              <https://www.rfc-editor.org/info/rfc8446>.

   [SSR18]    Bruni, A., Sahl Joergensen, T., Groenbech Petersen, T.,
              and C. Schuermann, "Formal Verification of Ephemeral
              Diffie-Hellman Over COSE (EDHOC)", November 2018,
              <https://www.springerprofessional.de/en/formal-
              verification-of-ephemeral-diffie-hellman-over-cose-
              edhoc/16284348>.

Appendix A.  Use of CBOR, CDDL and COSE in EDHOC

   This Appendix is intended to simplify for implementors not familiar
   with CBOR [I-D.ietf-cbor-7049bis], CDDL [RFC8610], COSE [RFC8152],
   and HKDF [RFC5869].

A.1.  CBOR and CDDL

   The Concise Binary Object Representation (CBOR)
   [I-D.ietf-cbor-7049bis] is a data format designed for small code size
   and small message size.  CBOR builds on the JSON data model but
   extends it by e.g. encoding binary data directly without base64
   conversion.  In addition to the binary CBOR encoding, CBOR also has a
   diagnostic notation that is readable and editable by humans.  The
   Concise Data Definition Language (CDDL) [RFC8610] provides a way to
   express structures for protocol messages and APIs that use CBOR.
   [RFC8610] also extends the diagnostic notation.

   CBOR data items are encoded to or decoded from byte strings using a
   type-length-value encoding scheme, where the three highest order bits
   of the initial byte contain information about the major type.  CBOR
   supports several different types of data items, in addition to
   integers (int, uint), simple values (e.g. null), byte strings (bstr),
   and text strings (tstr), CBOR also supports arrays [] of data items,
   maps {} of pairs of data items, and sequences
   [I-D.ietf-cbor-sequence] of data items.  Some examples are given
   below.  For a complete specification and more examples, see
   [I-D.ietf-cbor-7049bis] and [RFC8610].  We recommend implementors to
   get used to CBOR by using the CBOR playground [CborMe].







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    Diagnostic          Encoded              Type
    ------------------------------------------------------------------
    1                   0x01                 unsigned integer
    24                  0x1818               unsigned integer
    -24                 0x37                 negative integer
    -25                 0x3818               negative integer
    null                0xf6                 simple value
    h'12cd'             0x4212cd             byte string
    '12cd'              0x4431326364         byte string
    "12cd"              0x6431326364         text string
    { 4 : h'cd' }       0xa10441cd           map
    << 1, 2, null >>    0x430102f6           byte string
    [ 1, 2, null ]      0x830102f6           array
    ( 1, 2, null )      0x0102f6             sequence
    1, 2, null          0x0102f6             sequence
    ------------------------------------------------------------------

   EDHOC messages are CBOR Sequences [I-D.ietf-cbor-sequence].  The
   message format specification uses the construct '.cbor' enabling
   conversion between different CDDL types matching different CBOR items
   with different encodings.  Some examples are given below.

   A type (e.g. an uint) may be wrapped in a byte string (bstr):

    CDDL Type                       Diagnostic                Encoded
    ------------------------------------------------------------------
    uint                            24                        0x1818
    bstr .cbor uint                 << 24 >>                  0x421818
    ------------------------------------------------------------------

A.2.  COSE

   CBOR Object Signing and Encryption (COSE) [RFC8152] describes how to
   create and process signatures, message authentication codes, and
   encryption using CBOR.  COSE builds on JOSE, but is adapted to allow
   more efficient processing in constrained devices.  EDHOC makes use of
   COSE_Key, COSE_Encrypt0, COSE_Sign1, and COSE_KDF_Context objects.

Appendix B.  Test Vectors

   This appendix provides detailed test vectors to ease implementation
   and ensure interoperability.  In addition to hexadecimal, all CBOR
   data items and sequences are given in CBOR diagnostic notation.  The
   test vectors use 1 byte key identifiers, 1 byte connection IDs, and
   the default mapping to CoAP where Party U is CoAP client (this means
   that corr = 1).





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B.1.  Test Vectors for EDHOC Authenticated with Signature Keys (RPK)

   EDHOC with signature authentication is used:

   method (Signature Authentication)
   0

   CoaP is used as trandsport and Party U is CoAP client:

   corr (Party U can correlate message_1 and message_2)
   1

   No unprotected opaque application data is sent in the message
   exchanges.

   The pre-defined Cipher Suite 0 is in place both on Party U and Party
   V, see Section 3.1.

B.1.1.  Input for Party U

   The following are the parameters that are set in Party U before the
   first message exchange.

Party U's private authentication key (32 bytes)
53 21 fc 01 c2 98 20 06 3a 72 50 8f c6 39 25 1d c8 30 e2 f7 68 3e b8 e3 8a
f1 64 a5 b9 af 9b e3

Party U's public authentication key (32 bytes)
42 4c 75 6a b7 7c c6 fd ec f0 b3 ec fc ff b7 53 10 c0 15 bf 5c ba 2e c0 a2
36 e6 65 0c 8a b9 c7

   kid value to identify U's public authentication key (1 bytes)
   a2

   This test vector uses COSE_Key objects to store the raw public keys.
   Moreover, EC2 keys with curve Ed25519 are used.  That is in agreement
   with the Cipher Suite 0.

CRED_U =
<< {
  1:  1,
 -1:  6,
 -2:  h'424c756ab77cc6fdecf0b3ecfcffb75310c015bf5cba2ec0a236e6650c8ab9c7'
} >>

CRED_U (COSE_Key) (CBOR-encoded) (42 bytes)
58 28 a3 01 01 20 06 21 58 20 42 4c 75 6a b7 7c c6 fd ec f0 b3 ec fc ff b7
53 10 c0 15 bf 5c ba 2e c0 a2 36 e6 65 0c 8a b9 c7



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   Because COSE_Keys are used, and because kid = h'a2':

   ID_CRED_U =
   {
     4:  h'a2'
   }

   Note that since the map for ID_CRED_U contains a single 'kid'
   parameter, ID_CRED_U is used when transported in the protected header
   of the COSE Object, but only the kid_value is used when added to the
   plaintext (see Section 4.4.2):

   ID_CRED_U (in protected header) (CBOR-encoded) (4 bytes)
   a1 04 41 a2

   kid_value (in plaintext) (CBOR-encoded) (2 bytes)
   41 a2

B.1.2.  Input for Party V

   The following are the parameters that are set in Party V before the
   first message exchange.

Party V's private authentication key (32 bytes)
74 56 b3 a3 e5 8d 8d 26 dd 36 bc 75 d5 5b 88 63 a8 5d 34 72 f4 a0 1f 02 24
62 1b 1c b8 16 6d a9

Party V's public authentication key (32 bytes)
1b 66 1e e5 d5 ef 16 72 a2 d8 77 cd 5b c2 0f 46 30 dc 78 a1 14 de 65 9c 7e
50 4d 0f 52 9a 6b d3

   kid value to identify U's public authentication key (1 bytes)
   a3

   This test vector uses COSE_Key objects to store the raw public keys.
   Moreover, EC2 keys with curve Ed25519 are used.  That is in agreement
   with the Cipher Suite 0.

CRED_V =
<< {
  1:  1,
 -1:  6,
 -2:  h'1b661ee5d5ef1672a2d877cd5bc20f4630dc78a114de659c7e504d0f529a6bd3'
} >>

CRED_V (COSE_Key) (CBOR-encoded) (42 bytes)
58 28 a3 01 01 20 06 21 58 20 1b 66 1e e5 d5 ef 16 72 a2 d8 77 cd 5b c2 0f
46 30 dc 78 a1 14 de 65 9c 7e 50 4d 0f 52 9a 6b d3



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   Because COSE_Keys are used, and because kid = h'a3':

   ID_CRED_V =
   {
     4:  h'a3'
   }

   Note that since the map for ID_CRED_U contains a single 'kid'
   parameter, ID_CRED_U is used when transported in the protected header
   of the COSE Object, but only the kid_value is used when added to the
   plaintext (see Section 4.4.2):

   ID_CRED_V (in protected header) (CBOR-encoded) (4 bytes)
   a1 04 41 a3

   kid_value (in plaintext) (CBOR-encoded) (2 bytes)
   41 a3

B.1.3.  Message 1

   From the input parameters (in Appendix B.1.1):

   TYPE (4 * method + corr)
   1

   suite
   0

   SUITES_U : suite
   0

G_X (X-coordinate of the ephemeral public key of Party U) (32 bytes)
b1 a3 e8 94 60 e8 8d 3a 8d 54 21 1d c9 5f 0b 90 3f f2 05 eb 71 91 2d 6d b8
f4 af 98 0d 2d b8 3a

   C_U (Connection identifier chosen by U) (1 bytes)
   c3

   No UAD_1 is provided, so UAD_1 is absent from message_1.

   Message_1 is constructed, as the CBOR Sequence of the CBOR data items
   above.









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  message_1 =
  (
    1,
    0,
    h'b1a3e89460e88d3a8d54211dc95f0b903ff205eb71912d6db8f4af980d2db83a',
    h'c3'
  )

message_1 (CBOR Sequence) (38 bytes)
01 00 58 20 b1 a3 e8 94 60 e8 8d 3a 8d 54 21 1d c9 5f 0b 90 3f f2 05 eb 71
91 2d 6d b8 f4 af 98 0d 2d b8 3a 41 c3

B.1.4.  Message 2

   Since TYPE mod 4 equals 1, C_U is omitted from data_2.

G_Y (X-coordinate of the ephemeral public key of Party V) (32 bytes)
8d b5 77 f9 b9 c2 74 47 98 98 7d b5 57 bf 31 ca 48 ac d2 05 a9 db 8c 32 0e
5d 49 f3 02 a9 64 74

   C_V (Connection identifier chosen by V) (1 bytes)
   c4

   Data_2 is constructed, as the CBOR Sequence of the CBOR data items
   above.

  data_2 =
  (
    h'8db577f9b9c2744798987db557bf31ca48acd205a9db8c320e5d49f302a96474',
    h'c4'
  )

data_2 (CBOR Sequence) (36 bytes)
58 20 8d b5 77 f9 b9 c2 74 47 98 98 7d b5 57 bf 31 ca 48 ac d2 05 a9 db 8c
32 0e 5d 49 f3 02 a9 64 74 41 c4

   From data_2 and message_1 (from Appendix B.1.3), compute the input to
   the transcript hash TH_2 = H( message_1, data_2 ), as a CBOR Sequence
   of these 2 data items.

( message_1, data_2 ) (CBOR Sequence)
(74 bytes)
01 00 58 20 b1 a3 e8 94 60 e8 8d 3a 8d 54 21 1d c9 5f 0b 90 3f f2 05 eb 71
91 2d 6d b8 f4 af 98 0d 2d b8 3a 41 c3 58 20 8d b5 77 f9 b9 c2 74 47 98 98
7d b5 57 bf 31 ca 48 ac d2 05 a9 db 8c 32 0e 5d 49 f3 02 a9 64 74 41 c4

   And from there, compute the transcript hash TH_2 = SHA-256(
   message_1, data_2 )



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TH_2 value (32 bytes)
55 50 b3 dc 59 84 b0 20 9a e7 4e a2 6a 18 91 89 57 50 8e 30 33 2b 11 da 68
1d c2 af dd 87 03 55

   When encoded as a CBOR bstr, that gives:

TH_2 (CBOR-encoded) (34 bytes)
58 20 55 50 b3 dc 59 84 b0 20 9a e7 4e a2 6a 18 91 89 57 50 8e 30 33 2b 11
da 68 1d c2 af dd 87 03 55

B.1.4.1.  Signature Computation

   COSE_Sign1 is computed with the following parameters.  From
   Appendix B.1.2:

   o  protected = bstr .cbor ID_CRED_V

   o  payload = CRED_V

   And from Appendix B.1.4:

   o  external_aad = TH_2

   The Sig_structure M_V to be signed is: [ "Signature1",
   << ID_CRED_V >>, TH_2, CRED_V ] , as defined in Section 4.3.2:

M_V =
[
  "Signature1",
  << { 4: h'a3' } >>,
  h'5550b3dc5984b0209ae74ea26a18918957508e30332b11da681dc2afdd870355',
  << {
    1:  1,
   -1:  6,
   -2:  h'1b661ee5d5ef1672a2d877cd5bc20f4630dc78a114de659c7e504d0f529a6b
          d3'
  } >>
]

   Which encodes to the following byte string ToBeSigned:

M_V (message to be signed with Ed25519) (CBOR-encoded) (93 bytes)
84 6a 53 69 67 6e 61 74 75 72 65 31 44 a1 04 41 a3 58 20 55 50 b3 dc 59 84
b0 20 9a e7 4e a2 6a 18 91 89 57 50 8e 30 33 2b 11 da 68 1d c2 af dd 87 03
55 58 28 a3 01 01 20 06 21 58 20 1b 66 1e e5 d5 ef 16 72 a2 d8 77 cd 5b c2
0f 46 30 dc 78 a1 14 de 65 9c 7e 50 4d 0f 52 9a 6b d3





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   The message is signed using the private authentication key of V, and
   produces the following signature:

V's signature (64 bytes)
52 3d 99 6d fd 9e 2f 77 c7 68 71 8a 30 c3 48 77 8c 5e b8 64 dd 53 7e 55 5e
4a 00 05 e2 09 53 07 13 ca 14 62 0d e8 18 7e 81 99 6e e8 04 d1 53 b8 a1 f6
08 49 6f dc d9 3d 30 fc 1c 8b 45 be cc 06

B.1.4.2.  Key and Nonce Computation

   The key and nonce for calculating the ciphertext are calculated as
   follows, as specified in Section 3.3.

   HKDF SHA-256 is the HKDF used (as defined by cipher suite 0).

   PRK = HMAC-SHA-256(salt, G_XY)

   Since this is the asymmetric case, salt is the empty byte string.

   G_XY is the shared secret, and since the curve25519 is used, the ECDH
   shared secret is the output of the X25519 function.

G_XY (32 bytes)
c6 1e 09 09 a1 9d 64 24 01 63 ec 26 2e 9c c4 f8 8c e7 7b e1 23 c5 ab 53 8d
26 b0 69 22 a5 20 67

   From there, PRK is computed:

PRK (32 bytes)
ba 9c 2c a1 c5 62 14 a6 e0 f6 13 ed a8 91 86 8a 4c a3 e3 fa bc c7 79 8f dc
01 60 80 07 59 16 71

   Key K_2 is the output of HKDF-Expand(PRK, info, L).

   info is defined as follows:

info for K_2
[
  10,
  [ null, null, null ],
  [ null, null, null ],
  [ 128, h'', h'5550b3dc5984b0209ae74ea26a18918957508e30332b11da681dc2afdd
                870355' ]
]

   Which as a CBOR encoded data item is:





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info (K_2) (CBOR-encoded) (48 bytes)
84 0a 83 f6 f6 f6 83 f6 f6 f6 83 18 80 40 58 20 55 50 b3 dc 59 84 b0 20 9a
e7 4e a2 6a 18 91 89 57 50 8e 30 33 2b 11 da 68 1d c2 af dd 87 03 55

   L is the length of K_2, so 16 bytes.

   From these parameters, K_2 is computed:

   K_2 (16 bytes)
   da d7 44 af 07 c4 da 27 d1 f0 a3 8a 0c 4b 87 38

   Nonce IV_2 is the output of HKDF-Expand(PRK, info, L).

   info is defined as follows:

info for IV_2
[
  "IV-GENERATION",
  [ null, null, null ],
  [ null, null, null ],
  [ 104, h'', h'5550b3dc5984b0209ae74ea26a18918957508e30332b11da681dc2afdd
                870355' ]
]

   Which as a CBOR encoded data item is:

info (IV_2) (CBOR-encoded) (61 bytes)
84 6d 49 56 2d 47 45 4e 45 52 41 54 49 4f 4e 83 f6 f6 f6 83 f6 f6 f6 83 18
68 40 58 20 55 50 b3 dc 59 84 b0 20 9a e7 4e a2 6a 18 91 89 57 50 8e 30 33
2b 11 da 68 1d c2 af dd 87 03 55

   L is the length of IV_2, so 13 bytes.

   From these parameters, IV_2 is computed:

   IV_2 (13 bytes)
   fb a1 65 d9 08 da a7 8e 4f 84 41 42 d0

B.1.4.3.  Ciphertext Computation

   COSE_Encrypt0 is computed with the following parameters.  Note that
   UAD_2 is omitted.

   o  empty protected header

   o  external_aad = TH_2





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   o  plaintext = CBOR Sequence of the items kid_value, signature, in
      this order.

   with kid_value taken from Appendix B.1.2, and signature as calculated
   in Appendix B.1.4.1.

   The plaintext is the following:

P_2 (68 bytes)
41 a3 58 40 52 3d 99 6d fd 9e 2f 77 c7 68 71 8a 30 c3 48 77 8c 5e b8 64 dd
53 7e 55 5e 4a 00 05 e2 09 53 07 13 ca 14 62 0d e8 18 7e 81 99 6e e8 04 d1
53 b8 a1 f6 08 49 6f dc d9 3d 30 fc 1c 8b 45 be cc 06

   From the parameters above, the Enc_structure A_2 is computed.

   A_2 =
   [
     "Encrypt0",
     h'',
     h'5550b3dc5984b0209ae74ea26a18918957508e30332b11da681dc2afdd870355'
   ]

   Which encodes to the following byte string to be used as Additional
   Authenticated Data:

A_2 (CBOR-encoded) (45 bytes)
83 68 45 6e 63 72 79 70 74 30 40 58 20 55 50 b3 dc 59 84 b0 20 9a e7 4e a2
6a 18 91 89 57 50 8e 30 33 2b 11 da 68 1d c2 af dd 87 03 55

   The key and nonce used are defined in Appendix B.1.4.2:

   o  key = K_2

   o  nonce = IV_2

   Using the parameters above, the ciphertext CIPHERTEXT_2 can be
   computed:

CIPHERTEXT_2 (76 bytes)
1e 6b fe 0e 77 99 ce f0 66 a3 4f 08 ef aa 90 00 6d b4 4c 90 1c f7 9b 23 85
3a b9 7f d8 db c8 53 39 d5 ed 80 87 78 3c f7 a4 a7 e0 ea 38 c2 21 78 9f a3
71 be 64 e9 3c 43 a7 db 47 d1 e3 fb 14 78 8e 96 7f dd 78 d8 80 78 e4 9b 78
bf








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B.1.4.4.  message_2

   From the parameter computed in Appendix B.1.4 and Appendix B.1.4.3,
   message_2 is computed, as the CBOR Sequence of the following items:
   (G_Y, C_V, CIPHERTEXT_2).

message_2 =
(
  h'8db577f9b9c2744798987db557bf31ca48acd205a9db8c320e5d49f302a96474',
  h'c4',
  h'1e6bfe0e7799cef066a34f08efaa90006db44c901cf79b23853ab97fd8dbc85339d5ed
  8087783cf7a4a7e0ea38c221789fa371be64e93c43a7db47d1e3fb14788e967fdd78d880
  78e49b78bf'
)

   Which encodes to the following byte string:

message_2 (CBOR Sequence) (114 bytes)
58 20 8d b5 77 f9 b9 c2 74 47 98 98 7d b5 57 bf 31 ca 48 ac d2 05 a9 db 8c
32 0e 5d 49 f3 02 a9 64 74 41 c4 58 4c 1e 6b fe 0e 77 99 ce f0 66 a3 4f 08
ef aa 90 00 6d b4 4c 90 1c f7 9b 23 85 3a b9 7f d8 db c8 53 39 d5 ed 80 87
78 3c f7 a4 a7 e0 ea 38 c2 21 78 9f a3 71 be 64 e9 3c 43 a7 db 47 d1 e3 fb
14 78 8e 96 7f dd 78 d8 80 78 e4 9b 78 bf

B.1.5.  Message 3

   Since TYPE mod 4 equals 1, C_V is not omitted from data_3.

   C_V (1 bytes)
   c4

   Data_3 is constructed, as the CBOR Sequence of the CBOR data item
   above.

   data_3 =
   (
     h'c4'
   )

   data_3 (CBOR Sequence) (2 bytes)
   41 c4

   From data_3, CIPHERTEXT_2 (Appendix B.1.4.3), and TH_2
   (Appendix B.1.4), compute the input to the transcript hash TH_2 =
   H(TH_2 , CIPHERTEXT_2, data_3), as a CBOR Sequence of these 3 data
   items.





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( TH_2, CIPHERTEXT_2, data_3 )
(CBOR Sequence) (114 bytes)
58 20 55 50 b3 dc 59 84 b0 20 9a e7 4e a2 6a 18 91 89 57 50 8e 30 33 2b 11
da 68 1d c2 af dd 87 03 55 58 4c 1e 6b fe 0e 77 99 ce f0 66 a3 4f 08 ef aa
90 00 6d b4 4c 90 1c f7 9b 23 85 3a b9 7f d8 db c8 53 39 d5 ed 80 87 78 3c
f7 a4 a7 e0 ea 38 c2 21 78 9f a3 71 be 64 e9 3c 43 a7 db 47 d1 e3 fb 14 78
8e 96 7f dd 78 d8 80 78 e4 9b 78 bf 41 c4

   And from there, compute the transcript hash TH_3 = SHA-256(TH_2 ,
   CIPHERTEXT_2, data_3)

TH_3 value (32 bytes)
21 cc b6 78 b7 91 14 96 09 55 88 5b 90 a2 b8 2e 3b 2c a2 7e 8e 37 4a 79 07
f3 e7 85 43 67 fc 22

   When encoded as a CBOR bstr, that gives:

TH_3 (CBOR-encoded) (34 bytes)
58 20 21 cc b6 78 b7 91 14 96 09 55 88 5b 90 a2 b8 2e 3b 2c a2 7e 8e 37 4a
79 07 f3 e7 85 43 67 fc 22

B.1.5.1.  Signature Computation

   COSE_Sign1 is computed with the following parameters.  From
   Appendix B.1.2:

   o  protected = bstr .cbor ID_CRED_U

   o  payload = CRED_U

   And from Appendix B.1.4:

   o  external_aad = TH_3

   The Sig_structure M_V to be signed is: [ "Signature1",
   << ID_CRED_U >>, TH_3, CRED_U ] , as defined in Section 4.4.2:















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M_U =
[
  "Signature1",
  << { 4: h'a2' } >>,
  h'734bef323d867a12956127c2e62ade42c0f119e5487750c0c31fd093376dceed',
  << {
    1:  1,
   -1:  6,
   -2:  h'424c756ab77cc6fdecf0b3ecfcffb75310c015bf5cba2ec0a236e6650c8ab9
   c7'
  } >>
]

   Which encodes to the following byte string ToBeSigned:

M_U (message to be signed with Ed25519) (CBOR-encoded) (93 bytes)
84 6a 53 69 67 6e 61 74 75 72 65 31 44 a1 04 41 a2 58 20 73 4b ef 32 3d 86
7a 12 95 61 27 c2 e6 2a de 42 c0 f1 19 e5 48 77 50 c0 c3 1f d0 93 37 6d ce
ed 58 28 a3 01 01 20 06 21 58 20 42 4c 75 6a b7 7c c6 fd ec f0 b3 ec fc ff
b7 53 10 c0 15 bf 5c ba 2e c0 a2 36 e6 65 0c 8a b9 c7

   The message is signed using the private authentication key of U, and
   produces the following signature:

U's signature (64 bytes)
5c 7d 7d 64 c9 61 c5 f5 2d cf 33 91 25 92 a1 af f0 2c 33 62 b0 e7 55 0e 4b
c5 66 b7 0c 20 61 f3 c5 f6 49 e5 ed 32 3d 30 a2 6c 61 2f bb 5c bd 25 f3 1c
27 22 8c ea ec 64 29 31 95 41 fe 07 8e 0e

B.1.5.2.  Key and Nonce Computation

   The key and nonce for calculating the ciphertext are calculated as
   follows, as specified in Section 3.3.

   HKDF SHA-256 is the HKDF used (as defined by cipher suite 0).

   PRK = HMAC-SHA-256(salt, G_XY)

   Since this is the asymmetric case, salt is the empty byte string.

   G_XY is the shared secret, and since the curve25519 is used, the ECDH
   shared secret is the output of the X25519 function.

G_XY (32 bytes)
c6 1e 09 09 a1 9d 64 24 01 63 ec 26 2e 9c c4 f8 8c e7 7b e1 23 c5 ab 53 8d
26 b0 69 22 a5 20 67

   From there, PRK is computed:



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PRK (32 bytes)
ba 9c 2c a1 c5 62 14 a6 e0 f6 13 ed a8 91 86 8a 4c a3 e3 fa bc c7 79 8f dc
01 60 80 07 59 16 71

   Key K_3 is the output of HKDF-Expand(PRK, info, L).

   info is defined as follows:

info for K_3
[
  10,
  [ null, null, null ],
  [ null, null, null ],
  [ 128, h'', h'21ccb678b79114960955885b90a2b82e3b2ca27e8e374a7907f3e78543
  67fc22' ]
]

   Which as a CBOR encoded data item is:

info (K_3) (CBOR-encoded) (48 bytes)
84 0a 83 f6 f6 f6 83 f6 f6 f6 83 18 80 40 58 20 21 cc b6 78 b7 91 14 96 09
55 88 5b 90 a2 b8 2e 3b 2c a2 7e 8e 37 4a 79 07 f3 e7 85 43 67 fc 22

   L is the length of K_3, so 16 bytes.

   From these parameters, K_3 is computed:

   K_3 (16 bytes)
   e1 ac d4 76 f5 96 a4 60 72 44 a8 da 8c ff 49 df

   Nonce IV_3 is the output of HKDF-Expand(PRK, info, L).

   info is defined as follows:

info for IV_3
[
  "IV-GENERATION",
  [ null, null, null ],
  [ null, null, null ],
  [ 104, h'', h'21ccb678b79114960955885b90a2b82e3b2ca27e8e374a7907f3e78543
  67fc22' ]
]

   Which as a CBOR encoded data item is:







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info (IV_3) (CBOR-encoded) (61 bytes)
84 6d 49 56 2d 47 45 4e 45 52 41 54 49 4f 4e 83 f6 f6 f6 83 f6 f6 f6 83 18
68 40 58 20 21 cc b6 78 b7 91 14 96 09 55 88 5b 90 a2 b8 2e 3b 2c a2 7e 8e
37 4a 79 07 f3 e7 85 43 67 fc 22

   L is the length of IV_3, so 13 bytes.

   From these parameters, IV_3 is computed:

   IV_3 (13 bytes)
   de 53 02 13 ab a2 6a 47 1a 51 f3 d6 fb

B.1.5.3.  Ciphertext Computation

   COSE_Encrypt0 is computed with the following parameters.  Note that
   PAD_3 is omitted.

   o  empty protected header

   o  external_aad = TH_3

   o  plaintext = CBOR Sequence of the items kid_value, signature, in
      this order.

   with kid_value taken from Appendix B.1.1, and signature as calculated
   in Appendix B.1.5.1.

   The plaintext is the following:

P_3 (68 bytes)
41 a2 58 40 5c 7d 7d 64 c9 61 c5 f5 2d cf 33 91 25 92 a1 af f0 2c 33 62 b0
e7 55 0e 4b c5 66 b7 0c 20 61 f3 c5 f6 49 e5 ed 32 3d 30 a2 6c 61 2f bb 5c
bd 25 f3 1c 27 22 8c ea ec 64 29 31 95 41 fe 07 8e 0e

   From the parameters above, the Enc_structure A_3 is computed.

   A_3 =
   [
     "Encrypt0",
     h'',
     h'21ccb678b79114960955885b90a2b82e3b2ca27e8e374a7907f3e7854367fc22'
   ]

   Which encodes to the following byte string to be used as Additional
   Authenticated Data:






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A_2 (CBOR-encoded) (45 bytes)
83 68 45 6e 63 72 79 70 74 30 40 58 20 21 cc b6 78 b7 91 14 96 09 55 88 5b
90 a2 b8 2e 3b 2c a2 7e 8e 37 4a 79 07 f3 e7 85 43 67 fc 22

   The key and nonce used are defined in Appendix B.1.4.2:

   o  key = K_3

   o  nonce = IV_3

   Using the parameters above, the ciphertext CIPHERTEXT_3 can be
   computed:

CIPHERTEXT_3 (76 bytes)
de 4a 83 3d 48 b6 64 74 14 2c c9 bd ce 87 d9 3a f8 35 57 9c 2d bf 1b 9e 2f
b4 dc 66 60 0d ba c6 bb 3c c0 5c 29 0e f3 5d 51 5b 4d 7d 64 83 f5 09 61 43
b5 56 44 cf af d1 ff aa 7f 2b a3 86 36 57 83 1d d2 e5 bd 04 04 38 60 14 0d
c8

B.1.5.4.  message_3

   From the parameter computed in Appendix B.1.5 and Appendix B.1.5.3,
   message_3 is computed, as the CBOR Sequence of the following items:
   (C_V, CIPHERTEXT_3).

message_3 =
(
  h'c4',
  h'de4a833d48b66474142cc9bdce87d93af835579c2dbf1b9e2fb4dc66600dbac6bb3cc0
  5c290ef35d515b4d7d6483f5096143b55644cfafd1ffaa7f2ba3863657831dd2e5bd0404
  3860140dc8'
)

   Which encodes to the following byte string:

message_3 (CBOR Sequence) (80 bytes)
41 c4 58 4c de 4a 83 3d 48 b6 64 74 14 2c c9 bd ce 87 d9 3a f8 35 57 9c 2d bf 1b 9e 2f b4 dc 66 60 0d ba c6 bb 3c c0 5c 29 0e f3 5d 51 5b 4d 7d 64 83 f5 09 61 43 b5 56 44 cf af d1 ff aa 7f 2b a3 86 36 57 83 1d d2 e5 bd 04 04 38 60 14 0d c8

B.1.5.5.  OSCORE Security Context Derivation

   From the previous message exchange, the Common Security Context for
   OSCORE [RFC8613] can be derived, as specified in Section 3.3.1.

   First af all, TH_4 is computed: TH_4 = H( TH_3, CIPHERTEXT_3 ), where
   the input to the hash function is the CBOR Sequence of TH_3 and
   CIPHERTEXT_3





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( TH_3, CIPHERTEXT_3 )
(CBOR Sequence) (112 bytes)
58 20 21 cc b6 78 b7 91 14 96 09 55 88 5b 90 a2 b8 2e 3b 2c a2 7e 8e 37 4a
79 07 f3 e7 85 43 67 fc 22 58 4c de 4a 83 3d 48 b6 64 74 14 2c c9 bd ce 87
d9 3a f8 35 57 9c 2d bf 1b 9e 2f b4 dc 66 60 0d ba c6 bb 3c c0 5c 29 0e f3
5d 51 5b 4d 7d 64 83 f5 09 61 43 b5 56 44 cf af d1 ff aa 7f 2b a3 86 36 57
83 1d d2 e5 bd 04 04 38 60 14 0d c8

   And from there, compute the transcript hash TH_4 = SHA-256( TH_3,
   CIPHERTEXT_3 )

TH_4 value (32 bytes)
51 ed 39 32 bc ba e8 90 1c 1d 4d eb 94 bd 67 3a b4 d3 8c 34 81 96 09 ee 0d
5c 9d a6 e9 80 7f e5

   When encoded as a CBOR bstr, that gives:

TH_4 (CBOR-encoded) (34 bytes)
58 20 51 ed 39 32 bc ba e8 90 1c 1d 4d eb 94 bd 67 3a b4 d3 8c 34 81 96 09
ee 0d 5c 9d a6 e9 80 7f e5

   To derive the Master Secret and Master Salt the same HKDF-Expand
   (PRK, info, L) is used, with different info and L.

   For Master Secret:

   L for Master Secret = 16

Info for Master Secret =
[
  "OSCORE Master Secret",
  [ null, null, null ],
  [ null, null, null ],
  [ 128, h'', h'51ed3932bcbae8901c1d4deb94bd673ab4d38c34819609ee0d5c9da6e9
  807fe5' ]
]

   When encoded as a CBOR bstr, that gives:

info (OSCORE Master Secret) (CBOR-encoded) (68 bytes)
84 74 4f 53 43 4f 52 45 20 4d 61 73 74 65 72 20 53 65 63 72 65 74 83 f6 f6
f6 83 f6 f6 f6 83 18 80 40 58 20 51 ed 39 32 bc ba e8 90 1c 1d 4d eb 94 bd
67 3a b4 d3 8c 34 81 96 09 ee 0d 5c 9d a6 e9 80 7f e5

   Finally, the Master Secret value computed is:

   OSCORE Master Secret (16 bytes)
   09 02 9d b0 0c 3e 01 27 42 c3 a8 69 04 07 4c 0e



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   For Master Salt:

   L for Master Secret = 8

Info for Master Salt =
[
  "OSCORE Master Salt",
  [ null, null, null ],
  [ null, null, null ],
  [ 64, h'', h'51ed3932bcbae8901c1d4deb94bd673ab4d38c34819609ee0d5c9da6e98
  07fe5' ]
]

   When encoded as a CBOR bstr, that gives:

info (OSCORE Master Salt) (CBOR-encoded) (66 bytes)
84 72 4f 53 43 4f 52 45 20 4d 61 73 74 65 72 20 53 61 6c 74 83 f6 f6 f6 83
f6 f6 f6 83 18 40 40 58 20 51 ed 39 32 bc ba e8 90 1c 1d 4d eb 94 bd 67 3a
b4 d3 8c 34 81 96 09 ee 0d 5c 9d a6 e9 80 7f e5

   Finally, the Master Secret value computed is:

   OSCORE Master Salt (8 bytes)
   81 02 97 22 a2 30 4a 06

   The Client's Sender ID takes the value of C_V:

   Client's OSCORE Sender ID (1 bytes)
   c4

   The Server's Sender ID takes the value of C_U:

   Server's OSCORE Sender ID (1 bytes)
   c3

   The algorithms are those negociated in the cipher suite:

   AEAD Algorithm
   10

   HMAC Algorithm
   5

B.2.  Test Vectors for EDHOC Authenticated with Symmetric Keys (PSK)

   Symmetric EDHOC is used:





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   method (Symmetric Authentication)
   1

   CoaP is used as trandsport and Party U is CoAP client:

   corr (Party U can correlate message_1 and message_2)
   1

   No unprotected opaque application data is sent in the message
   exchanges.

   The pre-defined Cipher Suite 0 is in place both on Party U and Party
   V, see Section 3.1.

B.2.1.  Input for Party U

   The following are the parameters that are set in Party U before the
   first message exchange.

Party U's ephemeral private key (32 bytes)
f4 0c ea f8 6e 57 76 92 33 32 b8 d8 fd 3b ef 84 9c ad b1 9c 69 96 bc 27 2a
f1 f6 48 d9 56 6a 4c

Party U's ephemeral public key (value of X_U) (32 bytes)
ab 2f ca 32 89 83 22 c2 08 fb 2d ab 50 48 bd 43 c3 55 c6 43 0f 58 88 97 cb
57 49 61 cf a9 80 6f

   Connection identifier chosen by U (value of C_U) (1 bytes)
   c1

   Pre-shared Key (PSK) (16 bytes)
   a1 1f 8f 12 d0 87 6f 73 6d 2d 8f d2 6e 14 c2 de

   kid value to identify PSK (1 bytes)
   a1

   So ID_PSK is defined as the following:

   ID_PSK =
   {
     4:  h'a1'
   }

   This test vector uses COSE_Key objects to store the pre-shared key.

   Note that since the map for ID_PSK contains a single 'kid' parameter,
   ID_PSK is used when transported in the protected header of the COSE




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   Object, but only the kid_value is used when added to the plaintext
   (see Section 5.1):

   ID_PSK (in protected header) (CBOR-encoded) (4 bytes)
   a1 04 41 a1

   kid_value (in plaintext) (CBOR-encoded) (2 bytes)
   41 a1

B.2.2.  Input for Party V

   The following are the parameters that are set in Party U before the
   first message exchange.

Party V's ephemeral private key (32 bytes)
d9 81 80 87 de 72 44 ab c1 b5 fc f2 8e 55 e4 2c 7f f9 c6 78 c0 60 51 81 f3
7a c5 d7 41 4a 7b 95

Party V's ephemeral public key (value of X_V) (32 bytes)
fc 3b 33 93 67 a5 22 5d 53 a9 2d 38 03 23 af d0 35 d7 81 7b 6d 1b e4 7d 94
6f 6b 09 a9 cb dc 06

   Connection identifier chosen by V (value of C_V) (1 bytes)
   c2

   Pre-shared Key (PSK) (16 bytes)
   a1 1f 8f 12 d0 87 6f 73 6d 2d 8f d2 6e 14 c2 de

   kid value to identify PSK (1 bytes)
   a1

   So ID_PSK is defined as the following:

   ID_PSK =
   {
     4:  h'a1'
   }

   This test vector uses COSE_Key objects to store the pre-shared key.

   Note that since the map for ID_PSK contains a single 'kid' parameter,
   ID_PSK is used when transported in the protected header of the COSE
   Object, but only the kid_value is used when added to the plaintext
   (see Section 5.1):

   ID_PSK (in protected header) (CBOR-encoded) (4 bytes)
   a1 04 41 a1




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   kid_value (in plaintext) (CBOR-encoded) (2 bytes)
   41 a1

B.2.3.  Message 1

   From the input parameters (in Appendix B.2.1):

   TYPE (4 * method + corr)
   5

   suite
   0

   SUITES_U : suite
   0

G_X (X-coordinate of the ephemeral public key of Party U) (32 bytes)
ab 2f ca 32 89 83 22 c2 08 fb 2d ab 50 48 bd 43 c3 55 c6 43 0f 58 88 97 cb
57 49 61 cf a9 80 6f

   C_U (Connection identifier chosen by U) (CBOR encoded) (2 bytes)
   41 c1

   kid_value of ID_PSK (CBOR encoded) (2 bytes)
   41 a1

   No UAD_1 is provided, so UAD_1 is absent from message_1.

   Message_1 is constructed, as the CBOR Sequence of the CBOR data items
   above.

  message_1 =
  (
    5,
    0,
    h'ab2fca32898322c208fb2dab5048bd43c355c6430f588897cb574961cfa9806f',
    h'c1',
    h'a1'
  )

message_1 (CBOR Sequence) (40 bytes)
05 00 58 20 ab 2f ca 32 89 83 22 c2 08 fb 2d ab 50 48 bd 43 c3 55 c6 43 0f
58 88 97 cb 57 49 61 cf a9 80 6f 41 c1 41 a1








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B.2.4.  Message 2

   Since TYPE mod 4 equals 1, C_U is omitted from data_2.

G_Y (X-coordinate of the ephemeral public key of Party V) (32 bytes)
fc 3b 33 93 67 a5 22 5d 53 a9 2d 38 03 23 af d0 35 d7 81 7b 6d 1b e4 7d 94
6f 6b 09 a9 cb dc 06

   C_V (Connection identifier chosen by V) (1 bytes)
   c2

   Data_2 is constructed, as the CBOR Sequence of the CBOR data items
   above.

  data_2 =
  (
    h'fc3b339367a5225d53a92d380323afd035d7817b6d1be47d946f6b09a9cbdc06',
    h'c2'
  )

data_2 (CBOR Sequence) (36 bytes)
58 20 fc 3b 33 93 67 a5 22 5d 53 a9 2d 38 03 23 af d0 35 d7 81 7b 6d 1b e4
7d 94 6f 6b 09 a9 cb dc 06 41 c2

   From data_2 and message_1 (from Appendix B.2.3), compute the input to
   the transcript hash TH_2 = H( message_1, data_2 ), as a CBOR Sequence
   of these 2 data items.

( message_1, data_2 ) (CBOR Sequence)
(76 bytes)
05 00 58 20 ab 2f ca 32 89 83 22 c2 08 fb 2d ab 50 48 bd 43 c3 55 c6 43 0f
58 88 97 cb 57 49 61 cf a9 80 6f 41 c1 41 a1 58 20 fc 3b 33 93 67 a5 22 5d
53 a9 2d 38 03 23 af d0 35 d7 81 7b 6d 1b e4 7d 94 6f 6b 09 a9 cb dc 06 41
c2

   And from there, compute the transcript hash TH_2 = SHA-256(
   message_1, data_2 )

TH_2 value (32 bytes)
16 4f 44 d8 56 dd 15 22 2f a4 63 f2 02 d9 c6 0b e3 c6 9b 40 f7 35 8d 34 1c
db 7b 07 de e1 70 ca

   When encoded as a CBOR bstr, that gives:

TH_2 (CBOR-encoded) (34 bytes)
58 20 16 4f 44 d8 56 dd 15 22 2f a4 63 f2 02 d9 c6 0b e3 c6 9b 40 f7 35 8d
34 1c db 7b 07 de e1 70 ca




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B.2.4.1.  Key and Nonce Computation

   The key and nonce for calculating the ciphertext are calculated as
   follows, as specified in Section 3.3.

   HKDF SHA-256 is the HKDF used (as defined by cipher suite 0).

   PRK = HMAC-SHA-256(salt, G_XY)

   Since this is the symmetric case, salt is the PSK:

   salt (16 bytes)
   a1 1f 8f 12 d0 87 6f 73 6d 2d 8f d2 6e 14 c2 de

   G_XY is the shared secret, and since the curve25519 is used, the ECDH
   shared secret is the output of the X25519 function.

G_XY (32 bytes)
d5 75 05 50 6d 8f 30 a8 60 a0 63 d0 1b 5b 7a d7 6a 09 4f 70 61 3b 4a e6 6c
5a 90 e5 c2 1f 23 11

   From there, PRK is computed:

PRK (32 bytes)
aa b2 f1 3c cb 1a 4f f7 96 a9 7a 32 a4 d2 fb 62 47 ef 0b 6b 06 da 04 d3 d1
06 39 4b 28 76 e2 8c

   Key K_2 is the output of HKDF-Expand(PRK, info, L).

   info is defined as follows:

info for K_2
[
  10,
  [ null, null, null ],
  [ null, null, null ],
  [ 128, h'', h'164f44d856dd15222fa463f202d9c60be3c69b40f7358d341cdb7b07de
  e170ca' ]
]

   Which as a CBOR encoded data item is:

info (K_2) (CBOR-encoded) (48 bytes)
84 0a 83 f6 f6 f6 83 f6 f6 f6 83 18 80 40 58 20 16 4f 44 d8 56 dd 15 22 2f
a4 63 f2 02 d9 c6 0b e3 c6 9b 40 f7 35 8d 34 1c db 7b 07 de e1 70 ca

   L is the length of K_2, so 16 bytes.




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   From these parameters, K_2 is computed:

   K_2 (16 bytes)
   ac 42 6e 5e 7d 7a d6 ae 3b 19 aa bd e0 f6 25 57

   Nonce IV_2 is the output of HKDF-Expand(PRK, info, L).

   info is defined as follows:

info for IV_2
[
  "IV-GENERATION",
  [ null, null, null ],
  [ null, null, null ],
  [ 104, h'', h'164f44d856dd15222fa463f202d9c60be3c69b40f7358d341cdb7b07de
  e170ca' ]
]

   Which as a CBOR encoded data item is:

info (IV_2) (CBOR-encoded) (61 bytes)
84 6d 49 56 2d 47 45 4e 45 52 41 54 49 4f 4e 83 f6 f6 f6 83 f6 f6 f6 83 18
68 40 58 20 16 4f 44 d8 56 dd 15 22 2f a4 63 f2 02 d9 c6 0b e3 c6 9b 40 f7
35 8d 34 1c db 7b 07 de e1 70 ca

   L is the length of IV_2, so 13 bytes.

   From these parameters, IV_2 is computed:

   IV_2 (13 bytes)
   ff 11 2e 1c 26 8a a2 a7 7c c3 ee 6c 4d

B.2.4.2.  Ciphertext Computation

   COSE_Encrypt0 is computed with the following parameters.  Note that
   UAD_2 is omitted.

   o  empty protected header

   o  external_aad = TH_2

   o  empty plaintext, since UAD_2 is omitted

   From the parameters above, the Enc_structure A_2 is computed.







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   A_2 =
   [
     "Encrypt0",
     h'',
     h'164f44d856dd15222fa463f202d9c60be3c69b40f7358d341cdb7b07dee170ca'
   ]

   Which encodes to the following byte string to be used as Additional
   Authenticated Data:

A_2 (CBOR-encoded) (45 bytes)
83 68 45 6e 63 72 79 70 74 30 40 58 20 16 4f 44 d8 56 dd 15 22 2f a4 63 f2
02 d9 c6 0b e3 c6 9b 40 f7 35 8d 34 1c db 7b 07 de e1 70 ca

   The key and nonce used are defined in Appendix B.2.4.1:

   o  key = K_2

   o  nonce = IV_2

   Using the parameters above, the ciphertext CIPHERTEXT_2 can be
   computed:

   CIPHERTEXT_2 (8 bytes)
   ba 38 b9 a3 fc 1a 58 e9

B.2.4.3.  message_2

   From the parameter computed in Appendix B.2.4 and Appendix B.2.4.2,
   message_2 is computed, as the CBOR Sequence of the following items:
   (G_Y, C_V, CIPHERTEXT_2).

  message_2 =
  (
    h'fc3b339367a5225d53a92d380323afd035d7817b6d1be47d946f6b09a9cbdc06',
    h'c2',
    h'ba38b9a3fc1a58e9'
  )

   Which encodes to the following byte string:

message_2 (CBOR Sequence) (45 bytes)
58 20 fc 3b 33 93 67 a5 22 5d 53 a9 2d 38 03 23 af d0 35 d7 81 7b 6d 1b e4
7d 94 6f 6b 09 a9 cb dc 06 41 c2 48 ba 38 b9 a3 fc 1a 58 e9







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B.2.5.  Message 3

   Since TYPE mod 4 equals 1, C_V is not omitted from data_3.

   C_V (1 bytes)
   c2

   Data_3 is constructed, as the CBOR Sequence of the CBOR data item
   above.

   data_3 =
   (
     h'c2'
   )

   data_3 (CBOR Sequence) (2 bytes)
   41 c2

   From data_3, CIPHERTEXT_2 (Appendix B.2.4.2), and TH_2
   (Appendix B.2.4), compute the input to the transcript hash TH_2 =
   H(TH_2 , CIPHERTEXT_2, data_3), as a CBOR Sequence of these 3 data
   items.

( TH_2, CIPHERTEXT_2, data_3 ) (CBOR Sequence) (45 bytes)
58 20 16 4f 44 d8 56 dd 15 22 2f a4 63 f2 02 d9 c6 0b e3 c6 9b 40 f7 35 8d
34 1c db 7b 07 de e1 70 ca 48 ba 38 b9 a3 fc 1a 58 e9 41 c2

   And from there, compute the transcript hash TH_3 = SHA-256(TH_2 ,
   CIPHERTEXT_2, data_3)

TH_3 value (32 bytes)
11 98 aa b3 ed db 61 b8 a1 b1 93 a9 e5 60 2b 5d 5f ea 76 bc 28 52 89 54 81
b5 2b 8a f5 66 d7 fe

   When encoded as a CBOR bstr, that gives:

TH_3 (CBOR-encoded) (34 bytes)
58 20 11 98 aa b3 ed db 61 b8 a1 b1 93 a9 e5 60 2b 5d 5f ea 76 bc 28 52 89
54 81 b5 2b 8a f5 66 d7 fe

B.2.5.1.  Key and Nonce Computation

   The key and nonce for calculating the ciphertext are calculated as
   follows, as specified in Section 3.3.

   HKDF SHA-256 is the HKDF used (as defined by cipher suite 0).

   PRK = HMAC-SHA-256(salt, G_XY)



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   Since this is the symmetric case, salt is the PSK:

   salt (16 bytes)
   a1 1f 8f 12 d0 87 6f 73 6d 2d 8f d2 6e 14 c2 de

   G_XY is the shared secret, and since the curve25519 is used, the ECDH
   shared secret is the output of the X25519 function.

G_XY (32 bytes)
d5 75 05 50 6d 8f 30 a8 60 a0 63 d0 1b 5b 7a d7 6a 09 4f 70 61 3b 4a e6 6c
5a 90 e5 c2 1f 23 11

   From there, PRK is computed:

PRK (32 bytes)
aa b2 f1 3c cb 1a 4f f7 96 a9 7a 32 a4 d2 fb 62 47 ef 0b 6b 06 da 04 d3 d1
06 39 4b 28 76 e2 8c

   Key K_3 is the output of HKDF-Expand(PRK, info, L).

   info is defined as follows:

info for K_3
[
  10,
  [ null, null, null ],
  [ null, null, null ],
  [ 128, h'', h'1198aab3eddb61b8a1b193a9e5602b5d5fea76bc2852895481b52b8af5
  66d7fe' ]
]

   Which as a CBOR encoded data item is:

info (K_3) (CBOR-encoded) (48 bytes)
84 0a 83 f6 f6 f6 83 f6 f6 f6 83 18 80 40 58 20 11 98 aa b3 ed db 61 b8 a1
b1 93 a9 e5 60 2b 5d 5f ea 76 bc 28 52 89 54 81 b5 2b 8a f5 66 d7 fe

   L is the length of K_3, so 16 bytes.

   From these parameters, K_3 is computed:

   K_3 (16 bytes)
   fe 75 e3 44 27 f8 3a ad 84 16 83 c6 6f a3 8a 62

   Nonce IV_3 is the output of HKDF-Expand(PRK, info, L).

   info is defined as follows:




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info for IV_3
[
  "IV-GENERATION",
  [ null, null, null ],
  [ null, null, null ],
  [ 104, h'', h'1198aab3eddb61b8a1b193a9e5602b5d5fea76bc2852895481b52b8af5
  66d7fe' ]
]

   Which as a CBOR encoded data item is:

info (IV_3) (CBOR-encoded) (61 bytes)
84 6d 49 56 2d 47 45 4e 45 52 41 54 49 4f 4e 83 f6 f6 f6 83 f6 f6 f6 83 18
68 40 58 20 11 98 aa b3 ed db 61 b8 a1 b1 93 a9 e5 60 2b 5d 5f ea 76 bc 28
52 89 54 81 b5 2b 8a f5 66 d7 fe

   L is the length of IV_3, so 13 bytes.

   From these parameters, IV_3 is computed:

   IV_3 (13 bytes)
   60 0a 33 b4 16 de 08 23 52 67 71 ec 8a

B.2.5.2.  Ciphertext Computation

   COSE_Encrypt0 is computed with the following parameters.  Note that
   PAD_2 is omitted.

   o  empty protected header

   o  external_aad = TH_3

   o  empty plaintext, since PAD_2 is omitted

   From the parameters above, the Enc_structure A_3 is computed.

   A_3 =
   [
     "Encrypt0",
     h'',
     h'1198aab3eddb61b8a1b193a9e5602b5d5fea76bc2852895481b52b8af566d7fe'
   ]

   Which encodes to the following byte string to be used as Additional
   Authenticated Data:






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A_3 (CBOR-encoded) (45 bytes)
83 68 45 6e 63 72 79 70 74 30 40 58 20 11 98 aa b3 ed db 61 b8 a1 b1 93 a9
e5 60 2b 5d 5f ea 76 bc 28 52 89 54 81 b5 2b 8a f5 66 d7 fe

   The key and nonce used are defined in Appendix B.2.5.1:

   o  key = K_3

   o  nonce = IV_3

   Using the parameters above, the ciphertext CIPHERTEXT_3 can be
   computed:

   CIPHERTEXT_3 (8 bytes)
   51 29 07 92 61 45 40 04

B.2.5.3.  message_3

   From the parameter computed in Appendix B.2.5 and Appendix B.2.5.2,
   message_3 is computed, as the CBOR Sequence of the following items:
   (C_V, CIPHERTEXT_3).

   message_3 =
   (
     h'c2',
     h'5129079261454004'
   )

   Which encodes to the following byte string:

   message_3 (CBOR Sequence) (11 bytes)
   41 c2 48 51 29 07 92 61 45 40 04

B.2.5.4.  OSCORE Security Context Derivation

   From the previous message exchange, the Common Security Context for
   OSCORE [RFC8613] can be derived, as specified in Section 3.3.1.

   First af all, TH_4 is computed: TH_4 = H( TH_3, CIPHERTEXT_3 ), where
   the input to the hash function is the CBOR Sequence of TH_3 and
   CIPHERTEXT_3

( TH_3, CIPHERTEXT_3 )
(CBOR Sequence) (43 bytes)
58 20 11 98 aa b3 ed db 61 b8 a1 b1 93 a9 e5 60 2b 5d 5f ea 76 bc 28 52 89
54 81 b5 2b 8a f5 66 d7 fe 48 51 29 07 92 61 45 40 04





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   And from there, compute the transcript hash TH_4 = SHA-256( TH_3,
   CIPHERTEXT_3 )

TH_4 value (32 bytes)
df 7c 9b 06 f5 dc 0e e8 86 0b 39 6c 78 c5 be b7 57 41 3f a7 b6 a9 cf 28 3d
db 4c d4 c1 fd e4 3c

   When encoded as a CBOR bstr, that gives:

TH_4 (CBOR-encoded) (34 bytes)
58 20 df 7c 9b 06 f5 dc 0e e8 86 0b 39 6c 78 c5 be b7 57 41 3f a7 b6 a9 cf
28 3d db 4c d4 c1 fd e4 3c

   To derive the Master Secret and Master Salt the same HKDF-Expand
   (PRK, info, L) is used, with different info and L.

   For Master Secret:

   L for Master Secret = 16

Info for Master Secret =
[
  "OSCORE Master Secret",
  [ null, null, null ],
  [ null, null, null ],
  [ 128, h'', h'df7c9b06f5dc0ee8860b396c78c5beb757413fa7b6a9cf283ddb4cd4c1
  fde43c' ]
]

   When encoded as a CBOR bstr, that gives:

info (OSCORE Master Secret) (CBOR-encoded) (68 bytes)
84 74 4f 53 43 4f 52 45 20 4d 61 73 74 65 72 20 53 65 63 72 65 74 83 f6 f6
f6 83 f6 f6 f6 83 18 80 40 58 20 df 7c 9b 06 f5 dc 0e e8 86 0b 39 6c 78 c5
be b7 57 41 3f a7 b6 a9 cf 28 3d db 4c d4 c1 fd e4 3c

   Finally, the Master Secret value computed is:

   OSCORE Master Secret (16 bytes)
   8d 36 8f 09 26 2d c5 52 7f e7 19 e6 6c 91 63 75

   For Master Salt:

   L for Master Secret = 8







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Info for Master Salt =
[
  "OSCORE Master Salt",
  [ null, null, null ],
  [ null, null, null ],
  [ 64, h'', h'df7c9b06f5dc0ee8860b396c78c5beb757413fa7b6a9cf283ddb4cd4c1f
  de43c' ]
]

   When encoded as a CBOR bstr, that gives:

info (OSCORE Master Salt) (CBOR-encoded) (66 bytes)
84 72 4f 53 43 4f 52 45 20 4d 61 73 74 65 72 20 53 61 6c 74 83 f6 f6 f6 83
f6 f6 f6 83 18 40 40 58 20 df 7c 9b 06 f5 dc 0e e8 86 0b 39 6c 78 c5 be b7
57 41 3f a7 b6 a9 cf 28 3d db 4c d4 c1 fd e4 3c

   Finally, the Master Secret value computed is:

   OSCORE Master Salt (8 bytes)
   4d b7 06 58 c5 e9 9f b6

   The Client's Sender ID takes the value of C_V:

   Client's OSCORE Sender ID (1 bytes)
   c2

   The Server's Sender ID takes the value of C_U:

   Server's OSCORE Sender ID (1 bytes)
   c1

   The algorithms are those negociated in the cipher suite:

   AEAD Algorithm
   10

   HMAC Algorithm
   5

Acknowledgments

   The authors want to thank Alessandro Bruni, Karthikeyan Bhargavan,
   Martin Disch, Theis Groenbech Petersen, Dan Harkins, Klaus Hartke,
   Russ Housley, Alexandros Krontiris, Ilari Liusvaara, Karl Norrman,
   Salvador Perez, Eric Rescorla, Michael Richardson, Thorvald Sahl
   Joergensen, Jim Schaad, Carsten Schuermann, Ludwig Seitz, Stanislav
   Smyshlyaev, Valery Smyslov, Rene Struik, and Erik Thormarker for
   reviewing and commenting on intermediate versions of the draft.  We



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   are especially indebted to Jim Schaad for his continuous reviewing
   and implementation of different versions of the draft.

Authors' Addresses

   Goeran Selander
   Ericsson AB

   Email: goran.selander@ericsson.com


   John Preuss Mattsson
   Ericsson AB

   Email: john.mattsson@ericsson.com


   Francesca Palombini
   Ericsson AB

   Email: francesca.palombini@ericsson.com






























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