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Versions: 00 01

Network Working Group                                          R. Barnes
Internet-Draft                                                     Cisco
Intended status: Informational                              K. Bhargavan
Expires: September 12, 2019                                        Inria
                                                          March 11, 2019


                      Hybrid Public Key Encryption
                       draft-barnes-cfrg-hpke-01

Abstract

   This document describes a scheme for hybrid public-key encryption
   (HPKE).  This scheme provides authenticated public key encryption of
   arbitrary-sized plaintexts for a recipient public key.  HPKE works
   for any Diffie-Hellman group and has a strong security proof.  We
   provide instantiations of the scheme using standard and efficient
   primitives.

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 September 12, 2019.

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
   to this document.  Code Components extracted from this document must
   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  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Requirements Notation . . . . . . . . . . . . . . . . . . . .   3
   3.  Security Properties . . . . . . . . . . . . . . . . . . . . .   3
   4.  Notation  . . . . . . . . . . . . . . . . . . . . . . . . . .   3
   5.  Cryptographic Dependencies  . . . . . . . . . . . . . . . . .   3
     5.1.  DH-Based KEM  . . . . . . . . . . . . . . . . . . . . . .   5
   6.  Hybrid Public Key Encryption  . . . . . . . . . . . . . . . .   5
     6.1.  Encryption to a Public Key  . . . . . . . . . . . . . . .   6
     6.2.  Authentication using a Pre-Shared Key . . . . . . . . . .   7
     6.3.  Authentication using an Asymmetric Key  . . . . . . . . .   8
     6.4.  Encryption and Decryption . . . . . . . . . . . . . . . .   9
   7.  Ciphersuites  . . . . . . . . . . . . . . . . . . . . . . . .  10
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  11
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  11
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  11
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  11
     10.2.  Informative References . . . . . . . . . . . . . . . . .  12
   Appendix A.  Possible TODOs . . . . . . . . . . . . . . . . . . .  13
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  13

1.  Introduction

   Hybrid public-key encryption (HPKE) is a substantially more efficient
   solution than traditional public key encryption techniques such as
   those based on RSA or ElGamal.  Encrypted messages convey a single
   ciphertext and authentication tag alongside a short public key, which
   may be further compressed.  The key size and computational complexity
   of elliptic curve cryptographic primitives for authenticated
   encryption therefore make it compelling for a variety of use case.
   This type of public key encryption has many applications in practice,
   for example, in PGP [RFC6637] and in the developing Messaging Layer
   Security protocol [I-D.ietf-mls-protocol].

   Currently, there are numerous competing and non-interoperable
   standards and variants for hybrid encryption, including ANSI X9.63
   [ANSI], IEEE 1363a [IEEE], ISO/IEC 18033-2 [ISO], and SECG SEC 1
   [SECG].  Lack of a single standard makes selection and deployment of
   a compatible, cross-platform and ecosystem solution difficult to
   define.  This document defines an HPKE scheme that provides a subset
   of the functions provided by the collection of schemes above, but
   specified with sufficient clarity that they can be interoperably
   implemented and formally verified.




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2.  Requirements Notation

   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
   BCP14 [RFC2119] [RFC8174]  when, and only when, they appear in all
   capitals, as shown here.

3.  Security Properties

   As a hybrid authentication encryption algorithm, we desire security
   against (adaptive) chosen ciphertext attacks (IND-CCA2 secure).  The
   HPKE variants described in this document achieve this property under
   the Random Oracle model assuming the gap Computational Diffie Hellman
   (CDH) problem is hard [S01].

4.  Notation

   The following terms are used throughout this document to describe the
   operations, roles, and behaviors of HPKE:

   o  Initiator (I): Sender of an encrypted message.

   o  Responder (R): Receiver of an encrypted message.

   o  Ephemeral (E): A fresh random value meant for one-time use.

   o  "(skX, pkX)": A KEM key pair used in role X; "skX" is the private
      key and "pkX" is the public key

   o  "pk(sk)": The public key corresponding to a private key

   o  "len(x)": The one-octet length of the octet string "x"

   o  "+": Concatenation of octet strings; "0x01 + 0x02 = 0x0102"

   o  "*": Repetition of an octet string; "0x01 * 4 = 0x01010101"

   o  "^": XOR of octet strings; "0xF0F0 ^ 0x1234 = 0xE2C4"

5.  Cryptographic Dependencies

   HPKE variants rely on the following primitives:

   o  A Key Encapsulation Mechanism (KEM):

      *  GenerateKeyPair(): Generate a key pair (sk, pk)




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      *  Marshal(pk): Produce a fixed-length octet string encoding the
         public key "pk"

      *  Unmarshal(enc): Parse a fixed-length octet string to recover a
         public key

      *  Encap(pk): Generate an ephemeral symmetric key and a fixed-
         length encapsulation of that key that can be decapsulated by
         the holder of the private key corresponding to pk

      *  Decap(enc, sk): Use the private key "sk" to recover the
         ephemeral symmetric key from its encapsulated representation
         "enc"

      *  AuthEncap(pkR, skI) (optional): Same as Encap(), but the
         outputs encode an assurance that the ephemeral shared key is
         known only to the holder of the private key "skI"

      *  AuthDecap(skI, pkR) (optional): Same as Decap(), but the holder
         of the private key "skI" is assured that the ephemeral shared
         key is known only to the holder of the private key
         corresponding to "pkI"

   o  A Key Derivation Function:

      *  Extract(salt, IKM): Extract a pseudorandom key of fixed length
         from input keying material "IKM" and an optional octet string
         "salt"

      *  Expand(PRK, info, L): Expand a pseudorandom key "PRK" using
         optional string "info" into "L" bytes of output keying material

      *  Nh: The output size of the Extract function

   o  An AEAD encryption algorithm [RFC5116]:

      *  Seal(key, nonce, aad, pt): Encrypt and authenticate plaintext
         "pt" with associated data "aad" using secret key "key" and
         nonce "nonce", yielding ciphertext and tag "ct"

      *  Open(key, nonce, aad, ct): Decrypt ciphertext "ct" using
         associated data "aad" with secret key "key" and nonce "nonce",
         returning plaintext message "pt" or the error value "OpenError"

      *  Nk: The length in octets of a key for this algorithm

      *  Nn: The length in octets of a nonce for this algorithm




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   A set of concrete instantiations of these primitives is provided in
   Section 7.  Ciphersuite values are two octets long.

5.1.  DH-Based KEM

   Suppose we are given a Diffie-Hellman group that provides the
   following operations:

   o  GenerateKeyPair(): Generate an ephemeral key pair "(sk, pk)" for
      the DH group in use

   o  DH(sk, pk): Perform a non-interactive DH exchange using the
      private key sk and public key pk to produce a shared secret

   o  Marshal(pk): Produce a fixed-length octet string encoding the
      public key "pk"

   Then we can construct a KEM (which we'll call "DHKEM") in the
   following way:

   def Encap(pkR):
     skE, pkE = GenerateKeyPair()
     zz = DH(skE, pkR)
     enc = Marshal(pkE)
     return zz, enc

   def Decap(enc, skR):
     pkE = Unmarshal(enc)
     return DH(skR, pkE)

   def AuthEncap(pkR, skI):
     skE, pkE = GenerateKeyPair()
     zz = DH(skE, pkR) + DH(skI, pkR)
     enc = Marshal(pkE)
     return zz, enc

   def AuthDecap(enc, skR, pkI):
     pkE = Unmarshal(enc)
     return DH(skR, pkE) + DH(skR, pkI)

   The Marshal and GenerateKeyPair functions are the same as for the
   underlying DH group.

6.  Hybrid Public Key Encryption

   In this section, we define a few HPKE variants.  All cases take a
   plaintext "pt" and a recipient public key "pkR" and produce an
   ciphertext "ct" and an encapsulated key "enc".  These outputs are



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   constructed so that only the holder of the private key corresponding
   to "pkR" can decapsulate the key from "enc" and decrypt the
   ciphertext.  All of the algorithms also take an "info" parameter that
   can be used to influence the generation of keys (e.g., to fold in
   identity information) and an "aad" parameter that provides Additional
   Authenticated Data to the AEAD algorithm in use.

   In addition to the base case of encrypting to a public key, we
   include two authenticated variants, one of which authenticates
   possession of a pre-shared key, and one of which authenticates
   possession of a KEM private key.  The following one-octet values will
   be used to distinguish between modes:

                           +-----------+-------+
                           | Mode      | Value |
                           +-----------+-------+
                           | mode_base | 0x00  |
                           |           |       |
                           | mode_psk  | 0x01  |
                           |           |       |
                           | mode_auth | 0x02  |
                           +-----------+-------+

   All of these cases follow the same basic two-step pattern:

   1.  Set up an encryption context that is shared between the sender
       and the recipient

   2.  Use that context to encrypt or decrypt content

   A "context" encodes the AEAD algorithm and key in use, and manages
   the nonces used so that the same nonce is not used with multiple
   plaintexts.

   The procedures described in this session are laid out in a Python-
   like pseudocode.  The ciphersuite in use is left implicit.

6.1.  Encryption to a Public Key

   The most basic function of an HPKE scheme is to enable encryption for
   the holder of a given KEM private key.  The "SetupBaseI()" and
   "SetupBaseR()" procedures establish contexts that can be used to
   encrypt and decrypt, respectively, for a given private key.

   The the shared secret produced by the KEM is combined via the KDF
   with information describing the key exchange, as well as the explicit
   "info" parameter provided by the caller.




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   Note that the "SetupCore()" method is also used by the other HPKE
   variants describe below.  The value "0*Nh" in the "SetupBase()"
   procedure represents an all-zero octet string of length "Nh".

   def SetupCore(mode, secret, kemContext, info):
     context = ciphersuite + mode +
               len(kemContext) + kemContext +
               len(info) + info
     key = Expand(secret, "hpke key" + context, Nk)
     nonce = Expand(secret, "hpke nonce" + context, Nn)
     return Context(key, nonce)

   def SetupBase(pkR, zz, enc, info):
     kemContext = enc + pkR
     secret = Extract(0\*Nh, zz)
     return SetupCore(mode_base, secret, kemContext, info)

   def SetupBaseI(pkR, info):
     zz, enc = Encap(pkR)
     return SetupBase(pkR, zz, enc, info)

   def SetupBaseR(enc, skR, info):
     zz = Decap(enc, skR)
     return SetupBase(pk(skR), zz, enc, info)

   Note that the context construction in the SetupCore procedure is
   equivalent to serializing a structure of the following form in the
   TLS presentation syntax:

   struct {
       uint16 ciphersuite;
       uint8 mode;
       opaque kemContext<0..255>;
       opaque info<0..255>;
   } HPKEContext;

6.2.  Authentication using a Pre-Shared Key

   This variant extends the base mechansism by allowing the recipient to
   authenticate that the sender possessed a given pre-shared key (PSK).
   We assume that both parties have been provisioned with both the PSK
   value "psk" and another octet string "pskID" that is used to identify
   which PSK should be used.

   The primary differences from the base case are:

   o  The PSK is used as the "salt" input to the KDF (instead of 0)




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   o  The PSK ID is added to the context string used as the "info" input
      to the KDF

   This mechanism is not suitable for use with a low-entropy password as
   the PSK.  A malicious recipient that does not possess the PSK can use
   decryption of a plaintext as an oracle for performing offline
   dictionary attacks.

   def SetupPSK(pkR, psk, pskID, zz, enc, info):
     kemContext = enc + pkR + pskID
     secret = Extract(psk, zz)
     return SetupCore(mode_psk, secret, kemContext, info)

   def SetupPSKI(pkR, psk, pskID, info):
     zz, enc = Encap(pkR)
     return SetupPSK(pkR, psk, pskID, zz, enc, info)

   def SetupPSKR(enc, skR, psk, pskID, info):
     zz = Decap(enc, skR)
     return SetupPSK(pk(skR), psk, pskID, zz, enc, info)

6.3.  Authentication using an Asymmetric Key

   This variant extends the base mechansism by allowing the recipient to
   authenticate that the sender possessed a given KEM private key.  This
   assurance is based on the assumption that "AuthDecap(enc, skR, pkI)"
   produces the correct shared secret only if the encapsulated value
   "enc" was produced by "AuthEncap(pkR, skI)", where "skI" is the
   private key corresponding to "pkI".  In other words, only two people
   could have produced this secret, so if the recipient is one, then the
   sender must be the other.

   The primary differences from the base case are:

   o  The calls to "Encap" and "Decap" are replaced with calls to
      "AuthEncap" and "AuthDecap".

   o  The initiator public key is added to the context string used as
      the "info" input to the KDF

   Obviously, this variant can only be used with a KEM that provides
   "AuthEncap()" and "AuthDecap()" procuedures.

   This mechanism authenticates only the key pair of the initiator, not
   any other identity.  If an application wishes to authenticate some
   other identity for the sender (e.g., an email address or domain
   name), then this identity should be included in the "info" parameter
   to avoid unknown key share attacks.



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   def SetupAuth(pkR, pkI, zz, enc, info):
     kemContext = enc + pkR + pkI
     secret = Extract(0*Nh, zz)
     return SetupCore(mode_auth, secret, kemContext, info)

   def SetupAuthI(pkR, skI, info):
     zz, enc = AuthEncap(pkR, skI)
     return SetupAuth(pkR, pk(skI), zz, enc, info)

   def SetupAuthR(enc, skR, pkI, info):
     zz = AuthDecap(enc, skR, pkI)
     return SetupAuth(pk(skR), pkI, zz, enc, info)

6.4.  Encryption and Decryption

   HPKE allows multiple encryption operations to be done based on a
   given setup transaction.  Since the public-key operations involved in
   setup are typically more expensive than symmetric encryption or
   decryption, this allows applications to "amortize" the cost of the
   public-key operations, reducing the overall overhead.

   In order to avoid nonce reuse, however, this decryption must be
   stateful.  Each of the setup procedures above produces a context
   object that stores the required state:

   o  The AEAD algorithm in use

   o  The key to be used with the AEAD algorithm

   o  A base nonce value

   o  A sequence number (initially 0)

   All of these fields except the sequence number are constant.  The
   sequence number is used to provide nonce uniqueness: The nonce used
   for each encryption or decryption operation is the result of XORing
   the base nonce with the current sequence number, encoded as a big-
   endian integer of the same length as the nonce.  Implementations MAY
   use a sequence number that is shorter than the nonce (padding on the
   left with zero), but MUST return an error if the sequence number
   overflows.

   Each encryption or decryption operation increments the sequence
   number for the context in use.  A given context SHOULD be used either
   only for encryption or only for decryption.






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   It is up to the application to ensure that encryptions and
   decryptions are done in the proper sequence, so that the nonce values
   used for encryption and decryption line up.

   def Context.Nonce(seq):
     encSeq = encode\_big\_endian(seq, len(self.nonce))
     return self.nonce ^ encSeq

   def Context.Seal(aad, pt):
     ct = Seal(self.key, self.Nonce(self.seq), aad, pt)
     self.seq += 1
     return ct

   def Context.Open(aad, ct):
     pt = Open(self.key, self.Nonce(self.seq), aad, pt)
     if pt == OpenError:
       return OpenError
     self.seq += 1
     return pt

7.  Ciphersuites

   The HPKE variants as presented will function correctly for any
   combination of primitives that provides the functions described
   above.  In this section, we provide specific instantiations of these
   primitives for standard groups, including: Curve25519, Curve448
   [RFC7748], and the NIST curves P-256 and P-512.

      +--------+-------------------+-------------+------------------+
      | Value  | KEM               | KDF         | AEAD             |
      +--------+-------------------+-------------+------------------+
      | 0x0001 | DHKEM(P-256)      | HKDF-SHA256 | AES-GCM-128      |
      |        |                   |             |                  |
      | 0x0002 | DHKEM(P-256)      | HKDF-SHA256 | ChaCha20Poly1305 |
      |        |                   |             |                  |
      | 0x0002 | DHKEM(Curve25519) | HKDF-SHA256 | AES-GCM-128      |
      |        |                   |             |                  |
      | 0x0002 | DHKEM(Curve25519) | HKDF-SHA256 | ChaCha20Poly1305 |
      |        |                   |             |                  |
      | 0x0001 | DHKEM(P-521)      | HKDF-SHA512 | AES-GCM-256      |
      |        |                   |             |                  |
      | 0x0002 | DHKEM(P-521)      | HKDF-SHA512 | ChaCha20Poly1305 |
      |        |                   |             |                  |
      | 0x0002 | DHKEM(Curve448)   | HKDF-SHA512 | AES-GCM-256      |
      |        |                   |             |                  |
      | 0x0002 | DHKEM(Curve448)   | HKDF-SHA512 | ChaCha20Poly1305 |
      +--------+-------------------+-------------+------------------+




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   For the NIST curves P-256 and P-521, the Marshal function of the DH
   scheme produces the normal (non-compressed) representation of the
   public key, according to [SECG].  When these curves are used, the
   recipient of an HPKE ciphertext MUST validate that the ephemeral
   public key "pkE" is on the curve.  The relevant validation procedures
   are defined in [keyagreement]

   For the CFRG curves Curve25519 and Curve448, the Marshal function is
   the identity function, since these curves already use fixed-length
   octet strings for public keys.

   The values "Nk" and "Nn" for the AEAD algorithms referenced above are
   as follows:

                      +------------------+----+----+
                      | AEAD             | Nk | Nn |
                      +------------------+----+----+
                      | AES-GCM-128      | 16 | 12 |
                      |                  |    |    |
                      | AES-GCM-256      | 32 | 12 |
                      |                  |    |    |
                      | ChaCha20Poly1305 | 32 | 12 |
                      +------------------+----+----+

8.  Security Considerations

   [[ TODO ]]

9.  IANA Considerations

   [[ OPEN ISSUE: Should the above table be in an IANA registry? ]]

10.  References

10.1.  Normative References

   [ANSI]     "Public Key Cryptography for the Financial Services
              Industry -- Key Agreement and Key Transport Using Elliptic
              Curve Cryptography", n.d..

   [IEEE]     "IEEE 1363a, Standard Specifications for Public Key
              Cryptography - Amendment 1 -- Additional Techniques",
              n.d..

   [ISO]      "ISO/IEC 18033-2, Information Technology - Security
              Techniques - Encryption Algorithms - Part 2 -- Asymmetric
              Ciphers", n.d..




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   [keyagreement]
              Barker, E., Chen, L., Roginsky, A., and M. Smid,
              "Recommendation for Pair-Wise Key Establishment Schemes
              Using Discrete Logarithm Cryptography", National Institute
              of Standards and Technology report,
              DOI 10.6028/nist.sp.800-56ar2, May 2013.

   [MAEA10]   "A Comparison of the Standardized Versions of ECIES",
              n.d., <http://sceweb.sce.uhcl.edu/yang/teaching/
              csci5234WebSecurityFall2011/Chaum-blind-signatures.PDF>.

   [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>.

   [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>.

   [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>.

   [S01]      "A Proposal for an ISO Standard for Public Key Encryption
              (verison 2.1)", n.d.,
              <http://www.shoup.net/papers/iso-2_1.pdf>.

   [SECG]     "Elliptic Curve Cryptography, Standards for Efficient
              Cryptography Group, ver. 2", n.d.,
              <http://www.secg.org/download/aid-780/sec1-v2.pdf>.

10.2.  Informative References

   [I-D.ietf-mls-protocol]
              Barnes, R., Millican, J., Omara, E., Cohn-Gordon, K., and
              R. Robert, "The Messaging Layer Security (MLS) Protocol",
              draft-ietf-mls-protocol-03 (work in progress), January
              2019.

   [RFC6637]  Jivsov, A., "Elliptic Curve Cryptography (ECC) in
              OpenPGP", RFC 6637, DOI 10.17487/RFC6637, June 2012,
              <https://www.rfc-editor.org/info/rfc6637>.




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Appendix A.  Possible TODOs

   The following extensions might be worth specifying:

   o  Multiple recipients - It might be possible to add some
      simplifications / assurances for the case where the same value is
      being encrypted to multiple recipients.

   o  Test vectors - Obviously, we can provide decryption test vectors
      in this document.  In order to provide known-answer tests, we
      would have to introduce a non-secure deterministic mode where the
      ephemeral key pair is derived from the inputs.  And to do that
      safely, we would need to augment the decrypt function to detect
      the deterministic mode and fail.

   o  A reference implementation in hacspec or similar

Authors' Addresses

   Richard L. Barnes
   Cisco

   Email: rlb@ipv.sx


   Karthik Bhargavan
   Inria

   Email: karthikeyan.bhargavan@inria.fr






















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