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ACE Working Group                                            G. Selander
Internet-Draft                                               J. Mattsson
Intended status: Standards Track                            F. Palombini
Expires: March 22, 2019                                      Ericsson AB
                                                      September 18, 2018


               Ephemeral Diffie-Hellman Over COSE (EDHOC)
                    draft-selander-ace-cose-ecdhe-10

Abstract

   This document specifies Ephemeral Diffie-Hellman Over COSE (EDHOC), a
   very compact, and lightweight authenticated Diffie-Hellman key
   exchange with ephemeral keys that can be used over any layer.  EDHOC
   provides mutual authentication, perfect forward secrecy, and identity
   protection.  EDHOC uses CBOR and COSE, allowing reuse of existing
   libraries.

Status of This Memo

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

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   This Internet-Draft will expire on March 22, 2019.

Copyright Notice

   Copyright (c) 2018 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
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   include Simplified BSD License text as described in Section 4.e of



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   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Terminology and Requirements Language . . . . . . . . . .   4
   2.  Background  . . . . . . . . . . . . . . . . . . . . . . . . .   4
   3.  EDHOC Overview  . . . . . . . . . . . . . . . . . . . . . . .   6
     3.1.  Ephemeral Public Keys . . . . . . . . . . . . . . . . . .   7
     3.2.  Key Derivation  . . . . . . . . . . . . . . . . . . . . .   8
   4.  EDHOC Authenticated with Asymmetric Keys  . . . . . . . . . .   9
     4.1.  Overview  . . . . . . . . . . . . . . . . . . . . . . . .   9
     4.2.  EDHOC Message 1 . . . . . . . . . . . . . . . . . . . . .  11
     4.3.  EDHOC Message 2 . . . . . . . . . . . . . . . . . . . . .  13
     4.4.  EDHOC Message 3 . . . . . . . . . . . . . . . . . . . . .  17
   5.  EDHOC Authenticated with Symmetric Keys . . . . . . . . . . .  19
     5.1.  Overview  . . . . . . . . . . . . . . . . . . . . . . . .  19
     5.2.  EDHOC Message 1 . . . . . . . . . . . . . . . . . . . . .  20
     5.3.  EDHOC Message 2 . . . . . . . . . . . . . . . . . . . . .  22
     5.4.  EDHOC Message 3 . . . . . . . . . . . . . . . . . . . . .  24
   6.  Error Handling  . . . . . . . . . . . . . . . . . . . . . . .  26
     6.1.  EDHOC Error Message . . . . . . . . . . . . . . . . . . .  26
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  27
     7.1.  The Well-Known URI Registry . . . . . . . . . . . . . . .  27
     7.2.  Media Types Registry  . . . . . . . . . . . . . . . . . .  27
     7.3.  CoAP Content-Formats Registry . . . . . . . . . . . . . .  28
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  28
     8.1.  Security Properties . . . . . . . . . . . . . . . . . . .  28
     8.2.  Cryptographic Considerations  . . . . . . . . . . . . . .  29
     8.3.  Unprotected Data  . . . . . . . . . . . . . . . . . . . .  29
     8.4.  Denial-of-Service . . . . . . . . . . . . . . . . . . . .  30
     8.5.  Implementation Considerations . . . . . . . . . . . . . .  30
     8.6.  Other Documents Referencing EDHOC . . . . . . . . . . . .  31
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  31
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  31
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  32
     9.3.  URIs  . . . . . . . . . . . . . . . . . . . . . . . . . .  34
   Appendix A.  Use of CBOR, CDDL and COSE in EDHOC  . . . . . . . .  34
     A.1.  CBOR and CDDL . . . . . . . . . . . . . . . . . . . . . .  34
     A.2.  COSE  . . . . . . . . . . . . . . . . . . . . . . . . . .  36
   Appendix B.  Test Vectors . . . . . . . . . . . . . . . . . . . .  38
   Appendix C.  EDHOC PSK Chaining . . . . . . . . . . . . . . . . .  38
   Appendix D.  EDHOC with CoAP and OSCORE . . . . . . . . . . . . .  38
     D.1.  Transferring EDHOC in CoAP  . . . . . . . . . . . . . . .  38
     D.2.  Deriving an OSCORE context from EDHOC . . . . . . . . . .  39
   Appendix E.  Message Sizes  . . . . . . . . . . . . . . . . . . .  40
     E.1.  Message Sizes RPK . . . . . . . . . . . . . . . . . . . .  40



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     E.2.  Message Sizes Certificates  . . . . . . . . . . . . . . .  42
     E.3.  Message Sizes PSK . . . . . . . . . . . . . . . . . . . .  42
     E.4.  Summary . . . . . . . . . . . . . . . . . . . . . . . . .  43
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  43
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  44

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 protocol needs to
   work on 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].

   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 mutually authenticated key exchange
   protocol providing perfect forward secrecy and identity protection.
   EDHOC uses CBOR and COSE, allowing reuse of existing libraries.
   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
   can be derived using the EDHOC-Exporter interface.  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].  Compared to the TLS 1.3 handshake with ECDH
   [RFC8446], the number of bytes in EDHOC is less than 1/3 when PSK
   authentication is used and less than 1/2 when RPK authentication is
   used, see Appendix E.

   The ECDH exchange and the key derivation follow [SIGMA], NIST SP-
   800-56A [SP-800-56A], and HKDF [RFC5869].  CBOR



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   [I-D.ietf-cbor-7049bis] and COSE [RFC8152] are used to implement
   these standards.

   This paper 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 asymmetric key
   authentication, Section 5 specifies EDHOC with symmetric key
   authentication, Section 6 specifies the EDHOC error message, and
   Appendix B provides a wealth of test vectors to ease implementation
   and ensure interoperability.

1.1.  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].

   This document uses the Concise Data Definition Language (CDDL)
   [I-D.ietf-cbor-cddl] to express CBOR data structures
   [I-D.ietf-cbor-7049bis].  The use of the CDDL unwrap operator "~" is
   extended to unwrapping of byte strings.  It is the inverse of "bstr
   .cbor" that wraps a data item in a bstr, i.e. ~ bstr .cbor T = T.
   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 TLS 1.3, EDHOC is
   built on a variant of the SIGMA protocol which provide identity
   protection of the initiator (SIGMA-I), and like 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 1.










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      Party U                                                 Party V
         |                          X_U                          |
         +------------------------------------------------------>|
         |                                                       |
         |  X_V, AE( K_2; ID_CRED_V, Sig(V; CRED_V, X_U, X_V) )  |
         |<------------------------------------------------------+
         |                                                       |
         |    AE( K_3; ID_CRED_U, Sig(U; CRED_U, X_V, X_U) )     |
         +------------------------------------------------------>|
         |                                                       |

    Figure 1: 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  X_U and X_V are the ECDH ephemeral public keys of U and V,
      respectively.

   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  AE(K; P) denotes authenticated encryption of plaintext P using the
      key K derived from the shared secret.  The authenticated
      encryption MUST NOT be replaced by plain encryption, see
      Section 8.

   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  An Authenticated Encryption with Additional Data (AEAD) algorithm
      is used.

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

   o  Negotiation of key derivation, encryption, and signature
      algorithms:



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      *  U proposes one or more algorithms of the following kinds in
         order of preference:

         +  HKDF

         +  AEAD

         +  Signature verification

         +  Signature generation

      *  V selects the first supported algorithm of each kind

   o  Verification of common preferred ECDH curve:

      *  U lists supported ECDH curves in order of preference

      *  V verifies that the ECDH curve of the ephemeral key is the
         first supported curve

   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 and
   COSE libraries.  EDHOC does not put any requirement on the lower
   layers and can therefore also be used e.g. in environments without
   IP.

   To simplify implementation, the use of CBOR and COSE in EDHOC is
   summarized in Appendix A.

3.  EDHOC Overview

   EDHOC consists of three messages (message_1, message_2, message_3)
   that maps directly to the three messages in SIGMA-I, plus an EDHOC
   error message.  All EDHOC messages consists of a sequence of CBOR
   encoded data items, where the first data item is an int specifying
   the message type (MSG_TYPE).  The messages may be viewed as a CBOR
   encoding of an indefinite-length array without the first and last
   byte, see Appendix A.1.

   While EDHOC uses the COSE_Key, COSE_Sign1, and COSE_Encrypt0
   structures, only a subset of the parameters are included in the EDHOC
   messages.  After creating EDHOC message_3, Party U can derive
   symmetric application keys, and application protected data can



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   therefore be sent in parallel with EDHOC message_3.  The application
   may protect data using the negotiated algorithms (AEAD, HKDF, etc.)
   and the connection identifiers (C_U, C_V).  EDHOC may be used with
   the media type application/edhoc defined in Section 7.

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

                       Figure 2: EDHOC message flow

   The EDHOC message exchange may be authenticated using pre-shared keys
   (PSK), raw public keys (RPK), or public key certificates.  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
   asymmetric key authentication, the difference being that information
   is only MACed, not signed.

   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, while Protected Application Data
   (PAD_3) may be send in message_3.

3.1.  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
   a subset of the parameters are included in the EDHOC messages.  The
   curve X25519 is mandatory to implement.  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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3.2.  Key Derivation

   Key and IV derivation SHALL be performed as specified in Section 11
   of [RFC8152] with the following input:

   o  The KDF SHALL be the HKDF [RFC5869] in the ECDH-SS w/ HKDF
      negotiated during the message exchange (HKDF_V).

   o  The secret (Section 11.1 of [RFC8152]) SHALL be the ECDH shared
      secret as defined in Section 12.4.1 of [RFC8152].

   o  The salt (Section 11.1 of [RFC8152]) SHALL be the PSK when EDHOC
      is authenticated with symmetric keys, and the empty byte string
      when EDHOC is authenticated with asymmetric keys.  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 fields in the context information COSE_KDF_Context
      (Section 11.2 of [RFC8152]) SHALL have the following values:

      *  AlgorithmID is an int or tstr, see below

      *  PartyUInfo = PartyVInfo = ( null, null, null )

      *  keyDataLength is a uint, see below

      *  protected SHALL be a zero length bstr

      *  other is a bstr and SHALL be aad_2, aad_3, or exchange_hash;
         see below

      *  SuppPrivInfo is omitted

   where exchange_hash, in non-CDDL notation, is:

   exchange_hash = H( bstr .cborseq [ aad_3, CIPHERTEXT_3 ] )

   where H() is the hash function in HKDF_V, which takes a CBOR byte
   string (bstr) as input and produces a CBOR byte string as output.
   The use of '.cborseq' is exemplified in Appendix A.1.

   We define EDHOC-Key-Derivation to be the function which produces the
   output as described in [RFC5869] and [RFC8152] depending on the
   variable input AlgorithmID, keyDataLength, and other:

   output = EDHOC-Key-Derivation(AlgorithmID, keyDataLength, other)



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   For message_i the key, called K_i, SHALL be derived using other =
   aad_i, where i = 2 or 3.  The key SHALL be derived using AlgorithmID
   set to the integer value of the negotiated AEAD (AEAD_V), and
   keyDataLength equal to the key length of AEAD_V.

   If the AEAD algorithm uses an IV, then IV_i for message_i SHALL be
   derived using other = aad_i, where i = 2 or 3.  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 AEAD_V.

3.2.1.  EDHOC-Exporter Interface

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

   EDHOC-Exporter(label, length) = EDHOC-Key-Derivation(label, 8 *
   length, exchange_hash)

   The output of the EDHOC-Exporter function SHALL be derived using
   other = exchange_hash, AlgorithmID = label, and keyDataLength = 8 *
   length, 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.  An example use of the EDHOC-
   Exporter is given in Appendix D.2).

4.  EDHOC Authenticated with Asymmetric Keys

4.1.  Overview

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

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

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

   where ID_CRED_x, for x = U or V, is encoded in a COSE map, see
   Appendix A.2.  In the following we give some examples of possible
   COSE map labels.

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

   o  kid : ID_CRED_x, for x = U or V.




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   Public key certificates can be identified in different ways, for
   example (see [I-D.schaad-cose-x509]):

   o  by a hash value;

      *  x5t : ID_CRED_x, for x = U or V,

   o  by a URL;

      *  x5u : ID_CRED_x, for x = U or V,

   o  by a certificate chain;

      *  x5chain : ID_CRED_x, for x = U or V,

   o  or by a bag of certificates.

      *  x5bag : ID_CRED_x, for x = U or V.

   In the latter two examples, ID_CRED_U and ID_CRED_V contains the
   actual credential used for authentication.  ID_CRED_U and ID_CRED_V
   do not need to uniquely identify the public authentication key, but
   doing so is recommended as the recipient may otherwise have to try
   several public 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, see
   Section 4.4.1 and Section 4.3.1.  Party U and Party V MAY use
   different type of credentials, e.g. one uses RPK and the other uses
   certificate.  Party U and Party V MAY use different signature
   algorithms.

   EDHOC with asymmetric key authentication is illustrated in Figure 3.

















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Party U                                                          Party V
|                        C_U, X_U, ALG_1, UAD_1                        |
+--------------------------------------------------------------------->|
|                               message_1                              |
|                                                                      |
|C_U, C_V, X_V, ALG_2, AE(K_2; ID_CRED_V, Sig(V; CRED_V, aad_2), UAD_2)|
|<---------------------------------------------------------------------+
|                               message_2                              |
|                                                                      |
|         S_V, AE(K_3; ID_CRED_U, Sig(U; CRED_U, aad_3), PAD_3)        |
+--------------------------------------------------------------------->|
|                               message_3                              |

            Figure 3: EDHOC with asymmetric key authentication.

4.1.1.  Mandatory to Implement Algorithms

   For EDHOC authenticated with asymmetric keys, the COSE algorithms
   ECDH-SS + HKDF-256, AES-CCM-64-64-128, and Ed25519 are mandatory to
   implement.

4.2.  EDHOC Message 1

4.2.1.  Formatting of Message 1

   message_1 SHALL be a sequence of CBOR data items (see Appendix A.1)
   as defined below

   message_1 = (
     MSG_TYPE : int,
     C_U : bstr,
     ECDH-Curves_U : algs,
     ECDH-Curve_U : uint,
     X_U : bstr,
     HKDFs_U : algs,
     AEADs_U : algs,
     SIGs_V : algs,
     SIGs_U : algs,
     ? UAD_1 : bstr
   )

   alg : int / tstr

   algs = alg / [ 2* alg ]

   where:

   o  MSG_TYPE = 1



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   o  C_U - variable length connection identifier

   o  ECDH-Curves_U - EC curves for ECDH which Party U supports, in
      order of decreasing preference.  If a single algorithm is
      conveyed, it is placed in an int or text string, if multiple
      algorithms are conveyed, an array is used.

   o  ECDH-Curve_U - a single chosen algorithm from ECDH-Curves_U (zero-
      based index, i.e. 0 for the first or only, 1 for the second, etc.)

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

   o  HKDFs_U - supported ECDH-SS w/ HKDF algorithms, in order of
      decreasing preference

   o  AEADs_U - supported AEAD algorithms, in order of decreasing
      preference

   o  SIGs_V - signature algorithms, with which Party U supports
      verification, in order of decreasing preference.

   o  SIGs_U - signature algorithms, with which Party U supports
      signing, in order of decreasing preference.

   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 algorithms and the order of preference MUST NOT be
      changed based on previous error messages.  However, the lists sent
      to Party V (ECDH-Curves_U, HKDFs_U, AEADs_U, SIGs_V, SIGs_U) MAY
      be truncated such that curves/algorithms 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 curves/algorithms which are more preferred than
      the least preferred curve in the list MUST be included in the
      list.

   o  Determine the curve ECDH-Curve_U 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 an ECDH curve that U
      supports, then U SHALL use that curve (which implies that
      ECDH_Curves_U in message_1 SHALL include that curve).  Otherwise
      the first curve in ECDH-Curves_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 indicated by ECDH-Curve_U.  Let X_U
      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.  Party U MUST be able to retrieve the protocol state
      using the connection identifier C_U and optionally other
      information such as the 5-tuple.  The connection identifier MAY be
      used with protocols for which EDHOC establishes application keys,
      in which case C_U SHALL be different from the concurrently used
      identifiers of that protocol.

   o  Format message_1 as the sequence of CBOR data items specified in
      Section 4.2.1 and encode it to a byte string (see Appendix A.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 at least one of each kind of the proposed algorithms
      are supported.

   o  Verify that the ECDH curve indicated by ECDH-Curve_U is supported,
      and that no prior curve in ECDH-Curves_U is supported.

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

   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 6, and the protocol
   MUST be discontinued.  If V does not support the curve ECDH-Curve_U,
   but supports another ECDH curves in ECDH-Curves_U, then ALGs_V MUST
   include the first supported ECDH curve in ECDH-Curves_U.  If V does
   not support any of the algorithms of one kind (ECDH-Curves_U,
   HKDFs_U, AEADs_U, SIGs_V, or SIGs_U), then ALGs_V MUST include one or
   more supported algorithms of that kind.

4.3.  EDHOC Message 2

4.3.1.  Formatting of Message 2

   message_2 SHALL be a sequence of CBOR data items (see Appendix A.1)
   as defined below




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   message_2 = (
     data_2,
     CIPHERTEXT_2 : bstr
   )

   data_2 = (
     MSG_TYPE : int,
     C_U : bstr / nil,
     C_V : bstr,
     X_V : bstr,
     HKDF_V : uint,
     AEAD_V : uint,
     SIG_V : uint,
     SIG_U : uint
   )

   aad_2 : bstr

   where aad_2, in non-CDDL notation, is:

   aad_2 = H( bstr .cborseq [ message_1, data_2 ] )

   where:

   o  MSG_TYPE = 2

   o  C_V - variable length connection identifier

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

   o  HKDF_V - the first supported algorithm from HKDFs_U

   o  AEAD_V - the first supported algorithm from AEADs_U

   o  SIG_V - the first supported algorithm from SIGs_V with which Party
      V signs

   o  SIG_U - the first supported algorithm from SIGs_U with which Party
      U signs

   o  H() - the hash function in HKDF_V, which takes a CBOR byte string
      (bstr) as input and produces a CBOR byte string as output.  The
      use of '.cborseq' is exemplified in Appendix A.1.








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4.3.2.  Party V Processing of Message 2

   Party V SHALL compose message_2 as follows:

   o  Generate an ephemeral ECDH key pair as specified in Section 5 of
      [SP-800-56A] using the curve indicated by ECDH-Curve_U.  Let X_V
      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.  Party V MUST be able to retrieve the protocol state
      using the connection identifier C_V and optionally other
      information such as the 5-tuple.  The connection identifier MAY be
      used with protocols for which EDHOC establishes application keys,
      in which case C_V SHALL be different from the concurrently used
      identifiers of that protocol.  To reduce message overhead, party V
      can set the message field C_U in message_2 to null (still storing
      the actual value of C_U) if there is an external correlation
      mechanism (e.g. the Token in CoAP) that enables Party U to
      correlate message_1 and message_2.

   o  Select HKDF_V, AEAD_V, SIG_V, and SIG_U as the first supported
      algorithms in HKDFs_U, AEADs_U, SIGs_V, and SIGs_U.

   o  Compute COSE_Sign1 as defined in Section 4.4 of [RFC8152], using
      algorithm SIG_V, the private authentication key of Party V, and
      the following parameters (further clarifications in
      Appendix A.2.2).  The unprotected header MAY contain parameters
      (e.g. 'alg').

      *  protected = bstr .cbor { abc : ID_CRED_V }

         +  The use of .cbor is exemplified in Appendix A.1.

      *  payload = CRED_V

      *  external_aad = aad_2

      *  abc - any COSE map label that can identify a public
         authentication key, see Section 4.1

      *  ID_CRED_V - bstr enabling the retrieval of the public
         authentication key of Party V, see Section 4.1

      *  CRED_V - bstr credential containing the public authentication
         key of Party V, see Section 4.1

      Note that only 'protected' and 'signature' of the COSE_Sign1
      object are used in message_2, see next bullet.



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   o  Compute COSE_Encrypt0 as defined in Section 5.3 of [RFC8152], with
      AEAD_V, K_2, IV_2, and the following parameters (further
      clarifications in Appendix A.2.1).  The protected header SHALL be
      empty.  The unprotected header MAY contain parameters (e.g.
      'alg').

      *  plaintext = bstr .cborseq [ ~protected, signature, ? UAD_2 ]

         +  The use of '.cborseq' and '~' is exemplified in
            Appendix A.1.

      *  external_aad = aad_2

      *  UAD_2 = bstr containing opaque unprotected application data

      Note that protected and signature in the plaintext are taken from
      the COSE_Sign1 object, and that that only 'ciphertext' of the
      COSE_Encrypt0 object are used in message_2, see next bullet.

   o  Format message_2 as the sequence of CBOR data items specified in
      Section 4.3.1 and encode it to a byte string (see Appendix A.1).
      CIPHERTEXT_2 is the COSE_Encrypt0 ciphertext.

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 optionally other information such as the 5-tuple.

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

   o  Decrypt and verify COSE_Encrypt0 as defined in Section 5.3 of
      [RFC8152], with AEAD_V, K_2, and IV_2.

   o  Verify COSE_Sign1 as defined in Section 4.4 of [RFC8152], using
      algorithm SIG_V 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 6, and the protocol
   MUST be discontinued.







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4.4.  EDHOC Message 3

4.4.1.  Formatting of Message 3

   message_3 SHALL be a sequence of CBOR data items (see Appendix A.1)
   as defined below

   message_3 = (
     data_3,
     CIPHERTEXT_3 : bstr
   )

   data_3 = (
     MSG_TYPE : int,
     C_V : bstr
   )

   aad_3 : bstr

   where aad_3, in non-CDDL notation, is:

   aad_3 = H( bstr .cborseq [ aad_2, CIPHERTEXT_2, data_3 ] )

   where:

   o  MSG_TYPE = 3

   o  The use of '.cborseq' is exemplified in Appendix A.1.

4.4.2.  Party U Processing of Message 3

   Party U SHALL compose message_3 as follows:

   o  Compute COSE_Sign1 as defined in Section 4.4 of [RFC8152], using
      algorithm SIG_U, the private authentication key of Party U, and
      the following parameters (further clarifications in
      Appendix A.2.2).  The unprotected header MAY contain parameters
      (e.g. 'alg').

      *  protected = bstr .cbor { abc : ID_CRED_U }

         +  The use of .cbor is exemplified in Appendix A.1.

      *  payload = CRED_U

      *  external_aad = aad_3





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      *  abc - any COSE map label that can identify a public
         authentication key, see Section 4.1

      *  ID_CRED_U - bstr enabling the retrieval of the public
         authentication key of Party U, see Section 4.1

      *  CRED_U - bstr credential containing the public authentication
         key of Party U, see Section 4.1

      Note that only 'protected' and 'signature' of the COSE_Sign1
      object are used in message_3, see next bullet.

   o  Compute COSE_Encrypt0 as defined in Section 5.3 of [RFC8152], with
      AEAD_V, K_3, and IV_3 and the following parameters (further
      clarifications in Appendix A.2.1).  The protected header SHALL be
      empty.  The unprotected header MAY contain parameters (e.g.
      'alg').

      *  plaintext = bstr .cborseq [ ~protected, signature, ? PAD_3 ]

         +  The use of '.cborseq' and '~' is exemplified in
            Appendix A.1.

      *  external_aad = aad_2

      *  PAD_3 = bstr containing opaque protected application data

      Note that protected and signature in the plaintext are taken from
      the COSE_Sign1 object, and that only 'ciphertext' of the
      COSE_Encrypt0 object are used in message_3, see next bullet.

   o  Format message_3 as the sequence of CBOR data items specified in
      Section 4.4.1 and encode it to a byte string (see Appendix A.1).
      CIPHERTEXT_3 is the COSE_Encrypt0 ciphertext.

   o  Pass the connection identifiers (C_U, C_V) and the negotiated
      algorithms (AEAD, HDKF, etc.) 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 optionally other information such as the 5-tuple.



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   o  Decrypt and verify COSE_Encrypt0 as defined in Section 5.3 of
      [RFC8152], with AEAD_V, K_3, and IV_3.

   o  Verify COSE_Sign1 as defined in Section 4.4 of [RFC8152], using
      algorithm SIG_U 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 6, and the protocol
   MUST be discontinued.

   o  Pass PAD_3, the connection identifiers (C_U, C_V), and the
      negotiated algorithms (AEAD, HDKF, etc.) 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  Party V SHALL be able to retrieve the PSK using KID.

   KID may optionally contain information about how to retrieve the PSK.
   KID does not need to uniquely identify the PSK, but doing so is
   recommended as the recipient may otherwise have to try several PSKs.

   EDHOC with symmetric key authentication is illustrated in Figure 4.
   AEAD(K; P; A) denotes the output from an AEAD algorithm using key K
   on plaintext P and additional authenticated data A, see [RFC5116].

   Party U                                                       Party V
   |                    C_U, X_U, ALG_1, KID, UAD_1                    |
   +------------------------------------------------------------------>|
   |                             message_1                             |
   |                                                                   |
   |           C_U, C_V, X_V, ALG_2, AEAD(K_2; UAD_2; aad_2)           |
   |<------------------------------------------------------------------+
   |                             message_2                             |
   |                                                                   |
   |                    S_V, AEAD(K_3; PAD_3; aad_3)                   |
   +------------------------------------------------------------------>|
   |                             message_3                             |

            Figure 4: EDHOC with symmetric key authentication.




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5.1.1.  Mandatory to Implement Algorithms

   For EDHOC authenticated with symmetric keys, the COSE algorithms
   ECDH-SS + HKDF-256 and AES-CCM-64-64-128 are mandatory to implement.

5.2.  EDHOC Message 1

5.2.1.  Formatting of Message 1

   message_1 SHALL be a sequence of CBOR data items (see Appendix A.1)
   as defined below

   message_1 = (
     MSG_TYPE : int,
     C_U : bstr,
     ECDH-Curves_U : algs,
     ECDH-Curve_U : uint,
     X_U : bstr,
     HKDFs_U : algs,
     AEADs_U : algs,
     KID : bstr,
     ? UAD_1 : bstr
   )

   alg : int / tstr

   algs = alg / [ 2* alg ]

   where:

   o  MSG_TYPE = 4

   o  C_U - variable length connection identifier

   o  ECDH-Curves_U - EC curves for ECDH which Party U supports, in
      order of decreasing preference.  If a single algorithm is
      conveyed, it is placed in an int or text string, if multiple
      algorithms are conveyed, an array is used.

   o  ECDH-Curve_U - a single chosen algorithm from ECDH-Curves_U (zero-
      based index, i.e. 0 for the first or only, 1 for the second, etc.)

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

   o  HKDFs_U - supported ECDH-SS w/ HKDF algorithms, in order of
      decreasing preference





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   o  AEADs_U - supported AEAD algorithms, in order of decreasing
      preference

   o  KID - bstr enabling the retrieval of the pre-shared key

   o  UAD_1 - bstr containing unprotected opaque application data

5.2.2.  Party U Processing of Message 1

   Party U SHALL compose message_1 as follows:

   o  The supported algorithms and the order of preference MUST NOT be
      changed based on previous error messages.  However, the lists sent
      to Party V (ECDH-Curves_U, HKDFs_U, AEADs_U) MAY be truncated such
      that curves/algorithms 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
      curves/algorithms which are more preferred than the least
      preferred curve in the list MUST be included in the list.

   o  Determine the curve ECDH-Curve_U 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 an ECDH curve that U
      supports, then U SHALL use that curve (which implies that
      ECDH_Curves_U in message_1 SHALL include that curve).  Otherwise
      the first curve in ECDH-Curves_U MUST be used.

   o  Generate an ephemeral ECDH key pair as specified in Section 5 of
      [SP-800-56A] using the curve indicated by ECDH-Curve_U.  Let X_U
      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.  Party U MUST be able to retrieve the protocol state
      using the connection identifier C_U and optionally other
      information such as the 5-tuple.  The connection identifier MAY be
      used with protocols for which EDHOC establishes application keys,
      in which case C_U SHALL be different from the concurrently used
      identifiers of that protocol.

   o  Format message_1 as the sequence of CBOR data items specified in
      Section 5.2.1 and encode it to a byte string (see Appendix A.1).

5.2.3.  Party V Processing of Message 1

   Party V SHALL process message_1 as follows:

   o  Decode message_1 (see Appendix A.1).




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   o  Verify that at least one of each kind of the proposed algorithms
      are supported.

   o  Verify that the ECDH curve indicated by ECDH-Curve_U is supported,
      and that no prior curve in ECDH-Curves_U is supported.

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

   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 6, and the protocol
   MUST be discontinued.  If V does not support the curve ECDH-Curve_U,
   but supports another ECDH curves in ECDH-Curves_U, then ALGs_V MUST
   include the first supported ECDH curve in ECDH-Curves_U.  If V does
   not support any of the algorithms of one kind (ECDH-Curves_U,
   HKDFs_U, AEADs_U), then ALGs_V MUST include one or more supported
   algorithms of that kind.

5.3.  EDHOC Message 2

5.3.1.  Formatting of Message 2

   message_2 SHALL be a sequence of CBOR data items (see Appendix A.1)
   as defined below

   message_2 = (
     data_2,
     CIPHERTEXT_2 : bstr
   )

   data_2 = (
     MSG_TYPE : int,
     C_U : bstr / nil,
     C_V : bstr,
     X_V : bstr,
     HKDF_V : uint,
     AEAD_V : uint
   )

   aad_2 : bstr

   where aad_2, in non-CDDL notation, is:

   aad_2 = H( bstr .cborseq [ message_1, data_2 ] )

   where:



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   o  MSG_TYPE = 5

   o  C_V - variable length connection identifier

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

   o  HKDF_V - the first supported algorithm from HKDFs_U

   o  AEAD_V - the first supported algorithm from AEADs_U

   o  H() - the hash function in HKDF_V, which takes a CBOR byte string
      (bstr) as input and produces a CBOR byte string as output.  The
      use of '.cborseq' is exemplified in Appendix A.1.

5.3.2.  Party V Processing of Message 2

   Party V SHALL compose message_2 as follows:

   o  Generate an ephemeral ECDH key pair as specified in Section 5 of
      [SP-800-56A] using the curve indicated by ECDH-Curve_U.  Let X_V
      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.  Party V MUST be able to retrieve the protocol state
      using the connection identifier C_V and optionally other
      information such as the 5-tuple.  The connection identifier MAY be
      used with protocols for which EDHOC establishes application keys,
      in which case C_V SHALL be different from the concurrently used
      identifiers of that protocol.  To reduce message overhead, party V
      can set the message field C_U in message_2 to null (still storing
      the actual value of C_U) if there is an external correlation
      mechanism (e.g. the Token in CoAP) that enables Party U to
      correlate message_1 and message_2.

   o  Select HKDF_V and AEAD_V as the first supported algorithms in
      HKDFs_U and AEADs_U.

   o  Compute COSE_Encrypt0 as defined in Section 5.3 of [RFC8152], with
      AEAD_V, 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 = aad_2

      *  plaintext = h'' / UAD_2

      *  UAD_2 = bstr containing opaque unprotected application data




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      Note that only 'ciphertext' of the COSE_Encrypt0 object are used
      in message_2, see next bullet.

   o  Format message_2 as the sequence of CBOR data items specified in
      Section 5.3.1 and encode it to a byte string (see Appendix A.1).
      CIPHERTEXT_2 is the COSE_Encrypt0 ciphertext.

5.3.3.  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 optionally other information such as the 5-tuple.

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

   o  Decrypt and verify COSE_Encrypt0 as defined in Section 5.3 of
      [RFC8152], with AEAD_V, K_2, and IV_2.

   If any verification step fails, Party U MUST send an EDHOC error
   message back, formatted as defined in Section 6, and the protocol
   MUST be discontinued.

   o  Pass UAD_2 to the application.

5.4.  EDHOC Message 3

5.4.1.  Formatting of Message 3

   message_3 SHALL be a sequence of CBOR data items (see Appendix A.1)
   as defined below

   message_3 = (
     data_3,
     CIPHERTEXT_3 : bstr
   )

   data_3 = (
     MSG_TYPE : int,
     C_V : bstr
   )

   aad_3 : bstr

   where aad_3, in non-CDDL notation, is:



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   aad_3 = H( bstr .cborseq [ aad_2, CIPHERTEXT_2, data_3 ] )

   where:

   o  MSG_TYPE = 6

   o  The use of '.cborseq' is exemplified in Appendix A.1.

5.4.2.  Party U Processing of Message 3

   Party U SHALL compose message_3 as follows:

   o  Compute COSE_Encrypt0 as defined in Section 5.3 of [RFC8152], with
      AEAD_V, 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 = aad_3

      *  plaintext = h'' / PAD_3

      *  PAD_3 = bstr containing opaque protected application data

      Note that only 'ciphertext' of the COSE_Encrypt0 object are used
      in message_3, see next bullet.

   o  Format message_3 as the sequence of CBOR data items specified in
      Section 5.4.1 and encode it to a byte string (see Appendix A.1).
      CIPHERTEXT_3 is the COSE_Encrypt0 ciphertext.

   o  Pass the connection identifiers (C_U, C_V) and the negotiated
      algorithms (AEAD, HDKF, etc.) to the application.  The application
      can now derive application keys using the EDHOC-Exporter
      interface.

5.4.3.  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 optionally other information such as the 5-tuple.

   o  Decrypt and verify COSE_Encrypt0 as defined in Section 5.3 of
      [RFC8152], with AEAD_V, K_3, and IV_3.





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   If any verification step fails, Party V MUST send an EDHOC error
   message back, formatted as defined in Section 6, and the protocol
   MUST be discontinued.

   o  Pass PAD_3, the connection identifiers (C_U, C_V), and the
      negotiated algorithms (AEAD, HDKF, etc.) to the application.  The
      application can now derive application keys using the EDHOC-
      Exporter interface.

6.  Error Handling

6.1.  EDHOC Error Message

   This section defines a message format for the EDHOC error message,
   used during the protocol.  An EDHOC error message can be send by both
   parties as a response 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.  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 sequence of CBOR data items (see Appendix A.1) as
   defined below

   error = (
     MSG_TYPE : int,
     ERR_MSG : tstr,
     ? ALGs_V: algs
   )

   alg : int / tstr

   algs = alg / [ 2* alg ]

   where:

   o  MSG_TYPE = 0

   o  ERR_MSG - text string containing the diagnostic payload, defined
      in the same way as in Section 5.5.2 of [RFC7252]

   o  ALGs_V - algorithms that V supports that were not included in
      ECDH-Curve_U, HKDFs_U, AEADs_U, SIGs_V, and SIGs_U.  Note that
      ALG_V contatins the values from the COSE Algorithms registry and
      not indexes.





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7.  IANA Considerations

7.1.  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

7.2.  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

   o  Additional information:

      *  Magic number(s): N/A

      *  File extension(s): N/A

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




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   o  Person & email address to contact for further information: Goeran
      Selander goran.selander@ericsson.com [1]

   o  Intended usage: COMMON

   o  Restrictions on usage: N/A

   o  Author: Goeran Selander goran.selander@ericsson.com [2]

   o  Change Controller: IESG

7.3.  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]]

8.  Security Considerations

8.1.  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 with asymmetric authentication 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 the one that is not derivable from
   routing information in the lower layers.

   Compared to [SIGMA], EDHOC adds an explicit message 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.





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   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 parameters related to the ephemeral
   key, but it enables Party V to verify that the ECDH curve used in the
   protocol is the most preferred curve by U which is supported by both
   U and V.

8.2.  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 aliveness, 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
   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.

8.3.  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 KID, UAD_1, and ERR_MSG in the symmetric case.  Using the
   same KID or UAD_1 in several EDHOC sessions allows passive
   eavesdroppers to correlate the different sessions.  The communicating
   parties may therefore anonymize KID.  Another consideration is that



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   the list of supported algorithms 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 KID, UAD_1, and ERR_MSG in
   the symmetric case.

8.4.  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 their apparent network
   address.

8.5.  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.  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 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 [I-D.ietf-core-object-security]).  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



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   terminate the protocol) or retrieve the wrong security context (which
   also terminates the protocol as the message cannot be verified).

8.6.  Other Documents Referencing EDHOC

   EDHOC has been analyzed in several other documents.  An analysis of
   EDHOC for certificate enrollment was done in [CertEnr], the use of
   EDHOC in LoRaWAN is analyzed in [LoRa1] and [LoRa2], and the use of
   EDHOC in 6TiSCH is described in
   [I-D.ietf-6tisch-dtsecurity-zerotouch-join].

9.  References

9.1.  Normative References

   [I-D.ietf-cbor-7049bis]
              Bormann, C. and P. Hoffman, "Concise Binary Object
              Representation (CBOR)", draft-ietf-cbor-7049bis-02 (work
              in progress), March 2018.

   [I-D.ietf-cbor-cddl]
              Birkholz, H., Vigano, C., and C. Bormann, "Concise data
              definition language (CDDL): a notational convention to
              express CBOR and JSON data structures", draft-ietf-cbor-
              cddl-05 (work in progress), August 2018.

   [I-D.ietf-core-echo-request-tag]
              Amsuess, C., Mattsson, J., and G. Selander, "Echo and
              Request-Tag", draft-ietf-core-echo-request-tag-02 (work in
              progress), June 2018.

   [I-D.ietf-core-object-security]
              Selander, G., Mattsson, J., Palombini, F., and L. Seitz,
              "Object Security for Constrained RESTful Environments
              (OSCORE)", draft-ietf-core-object-security-15 (work in
              progress), August 2018.

   [I-D.schaad-cose-x509]
              Schaad, J., "CBOR Object Signing and Encryption (COSE):
              Headers for carrying and referencing X.509 certificates",
              draft-schaad-cose-x509-02 (work in progress), July 2018.

   [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>.





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   [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>.

   [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>.

   [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>.

   [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>.

   [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>.

9.2.  Informative References

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

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



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   [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. and B. Damm, "6tisch Zero-Touch Secure Join
              protocol", draft-ietf-6tisch-dtsecurity-zerotouch-join-02
              (work in progress), April 2018.

   [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-13
              (work in progress), July 2018.

   [I-D.ietf-ace-oscore-profile]
              Seitz, L., Palombini, F., Gunnarsson, M., and G. Selander,
              "OSCORE profile of the Authentication and Authorization
              for Constrained Environments Framework", draft-ietf-ace-
              oscore-profile-02 (work in progress), June 2018.

   [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-14 (work in progress), July 2018.

   [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>.

   [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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   [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>.

9.3.  URIs

   [1] mailto:goran.selander@ericsson.com

   [2] mailto:goran.selander@ericsson.com

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 [I-D.ietf-cbor-cddl], 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) [I-D.ietf-cbor-cddl] provides
   a way to express structures for protocol messages and APIs that use
   CBOR.  [I-D.ietf-cbor-cddl] 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
   and maps {} of pairs of data items.  Some examples are given below.
   For a complete specification and more examples, see
   [I-D.ietf-cbor-7049bis] and [I-D.ietf-cbor-cddl].  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
    << 1, 2, null >>    0x430102f6           byte string
    [ 1, 2, null ]      0x830102f6           array
    [_ 1, 2, null ]     0x9f0102f6ff         array (indefinite-length)
    ( 1, 2, null )      0x0102f6             group
    { 4: h'cd' }        0xa10441cd           map
    ------------------------------------------------------------------

   All EDHOC messages consist of a sequence of CBOR encoded data items.
   While an EDHOC message in itself is not a CBOR data item, it may be
   viewed as the CBOR encoding of an indefinite-length array [_
   message_i ] without the first byte (0x9f) and the last byte (0xff),
   for i = 1, 2 and 3.  The same applies to the EDHOC error message.

   The message format specification uses the constructs '.cbor',
   '.cborseq' and '~' enabling conversion between different CDDL types
   matching different CBOR items with different encodings.  Some
   examples are given below.

   An type (e.g. an uint) may be wrapped in a byte string (bstr), and
   back again:

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

   A array, say of an uint and a byte string, may be converted into a
   byte string (bstr):

   CDDL Type                       Diagnostic              Encoded
   --------------------------------------------------------------------
   bstr                            h'cd'                   0x41cd
   [ uint, bstr ]                  [ 24, h'cd' ]           0x82181841cd
   bstr .cborseq [ uint, bstr ]    << 24, h'cd' >>         0x44181841cd
   --------------------------------------------------------------------




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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.

A.2.1.  Encryption and Decryption

   The COSE parameters used in COSE_Encrypt0 (see Section 5.2 of
   [RFC8152]) are constructed as described below.  Note that "i" in
   "K_i", "IV_i" and "aad_i" is a variable with value i = 2 or 3,
   depending on whether the calculation is made over message_2 or
   message_3.

   o  The secret key K_i is a CBOR bstr, generated with the EDHOC-Key-
      Derivation function as defined in Section 3.2.

   o  The initialization vector IV_i is a CBOR bstr, also generated with
      the EDHOC-Key-Derivation function as defined in Section 3.2.

   o  The plaintext is a CBOR bstr.  If the application data (UAD and
      PAD) is omitted, then plaintext = h'' in the symmetric case, and
      plaintext = << ~protected, signature >> in the asymmetric case.
      For instance, if protected = h'a10140' and signature = h'050607'
      (CBOR encoding 0x43050607), then plaintext = h'a1014043050607'.

   o  The external_aad is a CBOR bstr.  It is always set to aad_i.

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

   o  The key K is the value of the key K_i.

   o  The nonce N is the value of the initialization vector IV_i.

   o  The plaintext P is the value of the COSE plaintext.  E.g. if the
      COSE plaintext = h'010203', then P = 0x010203.

   o  The associated data A is the CBOR encoding of:

      [ "Encrypt0", h'', aad_i ]

      This equals the concatenation of 0x8368456e63727970743040 and the
      CBOR encoding of aad_i.  For instance if aad_2 = h'010203' (CBOR
      encoding 0x43010203), then A = 0x8368456e6372797074304043010203.





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A.2.2.  Signing and Verification

   The COSE parameters used in COSE_Sign1 (see Section 4.2 of [RFC8152])
   are constructed as described below.  Note that "i" in "aad_i" is a
   variable with values i = 2 or 3, depending on whether the calculation
   is made over message_2 or message_3.  Note also that "x" in
   "ID_CRED_x" and "CRED_x" is a variable with values x = U or V,
   depending on whether it is the credential of U or of V that is used
   in the relevant protocol message.

   o  The key is the private authentication key of U or V.  This may be
      stored as a COSE_KEY object or as a certificate.

   o  The protected parameter is a map { abc : ID_CRED_x } wrapped in a
      byte string.

   o  The payload is a bstr cointaining the CBOR encoding of a COSE_KEY
      or a single certificate.

   o  external_aad = aad_i.

   COSE constructs the input to the Signature Algorithm as follows:

   o  The key is the private authentication key of U or V.

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

      [ "Signature1", << { abc : ID_CRED_x } >>, aad_i, CRED_x ]

      For instance if abc = 4 (CBOR encoding 0x04), ID_CRED_U = h'1111'
      (CBOR encoding 0x421111), aad_3 = h'222222' (CBOR encoding
      0x43222222), and CRED_U = h'55555555' (CBOR encoding
      0x4455555555), then M =
      0x846a5369676e61747572653145A104421111432222224455555555.

A.2.3.  Key Derivation

   Assuming use of the mandatory-to-implement algorithms HKDF SHA-256
   and AES-CCM-16-64-128, the extract phase of HKDF produces a
   pseudorandom key (PRK) as follows:

   PRK = HMAC-SHA-256( salt, ECDH shared secret )

   where salt = 0x in the asymmetric case and salt = PSK in the
   symmetric case.  As the output length L is smaller than the hash
   function output size, the expand phase of HKDF consists of a single
   HMAC invocation, and K_i and IV_i are therefore the first 16 and 13
   bytes, respectively, of



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

   where | | means byte string concatenation, and info is the CBOR
   encoding of

   COSE_KDF_Context = [
     AlgorithmID,
     [ null, null, null ],
     [ null, null, null ],
     [ keyDataLength, h'', aad_i ]
   ]

   If AES-CCM-16-64-128 then AlgorithmID = 10 and keyDataLength = 128
   for K_i, and AlgorithmID = "IV-GENERATION" (CBOR encoding
   0x6d49562d47454e45524154494f4e) and keyDataLength = 104 for IV_i.
   Hence, if aad_2 = h'aaaa' then

   K_2  = HMAC-SHA-256( PRK, 0x840a83f6f6f683f6f6f68318804042aaaa01 )
   IV_2 = HMAC-SHA-256( PRK, 0x846d49562d47454e45524154494f4e
                                   83f6f6f683f6f6f68318804042aaaa01 )

Appendix B.  Test Vectors

   This appendix provides a wealth of test vectors to ease
   implementation and ensure interoperability.

   TODO: This section needs to be updated.

Appendix C.  EDHOC PSK Chaining

   An application using EDHOC may want to derive new PSKs to use for
   authentication in future EDHOC sessions.  In this case, the new PSK
   and KID SHOULD be derived as follows where length is the key length
   (in bytes) of AEAD_V.

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

Appendix D.  EDHOC with CoAP and OSCORE

D.1.  Transferring EDHOC in CoAP

   EDHOC can be transferred as an exchange of CoAP [RFC7252] messages.
   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 8.  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



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   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.
   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 5.

             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 5: Example of transferring EDHOC in CoAP

D.2.  Deriving an OSCORE context from EDHOC

   When EDHOC is used to derive parameters for OSCORE
   [I-D.ietf-core-object-security], the parties must make sure that the
   EDHOC connection identifiers are unique, i.e. C_V MUST NOT be equal
   to C_U.  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




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   o  The AEAD Algorithm is AEAD_V and the HMAC-based Key Derivation
      Function (HKDF) is HKDF_V, as defined in this document

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

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

Appendix E.  Message Sizes

   This appendix gives an estimate of the message sizes of EDHOC with
   different authentication methods.  Note that the examples in this
   appendix are not test vectors, the cryptographic parts are just
   replaced with byte strings of the same length.  All examples are
   given in CBOR diagnostic notation and hexadecimal.

E.1.  Message Sizes RPK

E.1.1.  message_1

   message_1 = (
     1,
     h'c3',
     4,
     0,
     h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d
       1e1f',
     -27,
     10,
     -8,
     -8
   )

   message_1 (44 bytes):
   01 41 C3 04 00 58 20 00 01 02 03 04 05 06 07 08 09 0A 0B 0C
   0D 0E 0F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
   38 1A 0A 27 27

E.1.2.  message_2

   plaintext = <<
     { 4 : 'acdc' },
     h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d
       1e1f202122232425262728292a2b2c2d2e2f303132333435363738393a3b
       3c3d3e3f'
   >>




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   The protected header map is 7 bytes.  The length of plaintext is 73
   bytes so assuming a 64-bit MAC value the length of ciphertext is 81
   bytes.

   message_2 = (
     2,
     null,
     h'c4',
     h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d
       1e1f',
     0,
     0,
     0,
     0,
     h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d
       1e1f202122232425262728292a2b2c2d2e2f303132333435363738393a3b
       3c3d3e3f404142434445464748494a4b4c4d4e4f50'
   )

   message_2 (125 bytes):
   02 F6 41 C4 58 20 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D
   0E 0F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 00 00
   00 00 58 51 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F
   10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22 23
   24 25 26 27 28 29 2A 2B 2C 2D 2E 2F 30 31 32 33 34 35 36 37
   38 39 3A 3B 3C 3D 3E 3F 40 41 42 43 44 45 46 47 48 49 4A 4B
   4C 4D 4E 4F 50

E.1.3.  message_3

   The plaintext and ciphertext in message_3 are assumed to be of equal
   sizes as in message_2.

   message_3 = (
     3,
     h'c3',
     h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d
       1e1f202122232425262728292a2b2c2d2e2f303132333435363738393a3b
       3c3d3e3f404142434445464748494a4b4c4d4e4f50'
   )

   message_3 (86 bytes):
   03 41 C3 58 51 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E
   0F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22
   23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F 30 31 32 33 34 35 36
   37 38 39 3A 3B 3C 3D 3E 3F 40 41 42 43 44 45 46 47 48 49 4A
   4B 4C 4D 4E 4F 50




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E.2.  Message Sizes Certificates

   When the certificates are distributed out-of-band and identified with
   the x5t header and a SHA256/64 hash value, the protected header map
   will be 13 bytes instead of 7 bytes (assuming labels in the range
   -24...23).

   protected = << { TDB1 : [ TDB6, h'0001020304050607' ] } >>

   When the certificates are identified with the x5chain header, the
   message sizes depends on the size of the (truncated) certificate
   chains.  The protected header map will be 3 bytes + the size of the
   certificate chain (assuming a label in the range -24...23).

   protected = << { TDB3 : h'0001020304050607...' } >>

E.3.  Message Sizes PSK

E.3.1.  message_1

   message_1 = (
     4,
     h'c3',
     4,
     0,
     h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d
       1e1f',
     -27,
     10,
     'abba'
   )

   message_1 (47 bytes):
   04 41 C3 04 00 58 20 00 01 02 03 04 05 06 07 08 09 0A 0B 0C
   0D 0E 0F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
   38 1A 0A 44 61 63 64 63

E.3.2.  message_2

   Assuming a 0 byte plaintext and a 64-bit MAC value the ciphertext is
   8 bytes










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   message_2 = (
     5,
     null,
     h'c4',
     h'000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d
       1e1f',
     0,
     0,
     h'0001020304050607'
   )

   message_2 (49 bytes):
   05 F6 41 C4 58 20 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D
   0E 0F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 00 00
   48 61 62 63 64 65 66 67 68

E.3.3.  message_3

   The plaintext and ciphertext in message_3 are assumed to be of equal
   sizes as in message_2.

   message_3 = (
     6,
     h'c3',
     h'0001020304050607'
   )

   message_3 (12 bytes):
   06 41 C3 48 00 01 02 03 04 05 06 07

E.4.  Summary

                 PSK       RPK       x5t     x5chain
   --------------------------------------------------------------------
   message_1      47        44        44        44
   message_2      49       125       131       121 + Certificate chain
   message_3      12        86        92        82 + Certificate chain
   --------------------------------------------------------------------
   Total         108       255       267       247 + Certificate chains

                 Figure 6: Typical message sizes in bytes

Acknowledgments

   The authors want to thank Dan Harkins, Ilari Liusvaara, Jim Schaad,
   and Ludwig Seitz for reviewing intermediate versions of the draft and
   contributing concrete proposals incorporated in this version.  We are




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

   We are also grateful to Theis Groenbech Petersen, Thorvald Sahl
   Joergensen, Alessandro Bruni, and Carsten Schuermann for their work
   on formal analysis of EDHOC.

Authors' Addresses

   Goeran Selander
   Ericsson AB

   Email: goran.selander@ericsson.com


   John Mattsson
   Ericsson AB

   Email: john.mattsson@ericsson.com


   Francesca Palombini
   Ericsson AB

   Email: francesca.palombini@ericsson.com


























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