Internet DRAFT - draft-connolly-cfrg-xwing-kem

draft-connolly-cfrg-xwing-kem







Crypto Forum                                                 D. Connolly
Internet-Draft                                                 SandboxAQ
Intended status: Informational                                P. Schwabe
Expires: 25 July 2024                        MPI-SP & Radboud University
                                                        B. E. Westerbaan
                                                              Cloudflare
                                                         22 January 2024


            X-Wing: general-purpose hybrid post-quantum KEM
                    draft-connolly-cfrg-xwing-kem-01

Abstract

   This memo defines X-Wing, a general-purpose post-quantum/traditional
   hybrid key encapsulation mechanism (PQ/T KEM) built on X25519 and ML-
   KEM-768.

About This Document

   This note is to be removed before publishing as an RFC.

   The latest revision of this draft can be found at
   https://dconnolly.github.io/draft-connolly-cfrg-xwing-kem/draft-
   connolly-cfrg-xwing-kem.html.  Status information for this document
   may be found at https://datatracker.ietf.org/doc/draft-connolly-cfrg-
   xwing-kem/.

   Discussion of this document takes place on the Crypto Forum Research
   Group mailing list (mailto:cfrg@ietf.org), which is archived at
   https://mailarchive.ietf.org/arch/search/?email_list=cfrg.  Subscribe
   at https://www.ietf.org/mailman/listinfo/cfrg/.

   Source for this draft and an issue tracker can be found at
   https://github.com/dconnolly/draft-connolly-cfrg-xwing-kem.

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
   Task Force (IETF).  Note that other groups may also distribute
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   Internet-Drafts are draft documents valid for a maximum of six months
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Warning: ML-KEM-768 has not been standardised . . . . . .   3
     1.2.  Motivation  . . . . . . . . . . . . . . . . . . . . . . .   3
     1.3.  Design goals  . . . . . . . . . . . . . . . . . . . . . .   3
     1.4.  Not an interactive key-agreement  . . . . . . . . . . . .   4
     1.5.  Not an authenticated KEM  . . . . . . . . . . . . . . . .   4
     1.6.  Comparisons . . . . . . . . . . . . . . . . . . . . . . .   4
       1.6.1.  With HPKE X25519Kyber768Draft00 . . . . . . . . . . .   4
       1.6.2.  With generic combiner . . . . . . . . . . . . . . . .   4
   2.  Requirements Notation . . . . . . . . . . . . . . . . . . . .   5
   3.  Conventions and Definitions . . . . . . . . . . . . . . . . .   5
   4.  Cryptographic Dependencies  . . . . . . . . . . . . . . . . .   5
   5.  X-Wing Construction . . . . . . . . . . . . . . . . . . . . .   6
     5.1.  Encoding and sizes  . . . . . . . . . . . . . . . . . . .   6
     5.2.  Key generation  . . . . . . . . . . . . . . . . . . . . .   7
       5.2.1.  Key derivation  . . . . . . . . . . . . . . . . . . .   7
     5.3.  Combiner  . . . . . . . . . . . . . . . . . . . . . . . .   7
     5.4.  Encapsulation . . . . . . . . . . . . . . . . . . . . . .   8
       5.4.1.  Derandomized  . . . . . . . . . . . . . . . . . . . .   8
     5.5.  Decapsulation . . . . . . . . . . . . . . . . . . . . . .   9
     5.6.  Use in HPKE . . . . . . . . . . . . . . . . . . . . . . .   9
     5.7.  Use in TLS 1.3  . . . . . . . . . . . . . . . . . . . . .  10
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  10
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  10
   8.  TODO  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  11
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  11
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  11



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   Appendix A.  Test vectors # TODO: replace with test vectors that
           re-use ML-KEM, X25519 values  . . . . . . . . . . . . . .  13
   Appendix B.  Acknowledgments  . . . . . . . . . . . . . . . . . .  22
   Appendix C.  Change log . . . . . . . . . . . . . . . . . . . . .  22
     C.1.  Since draft-connolly-cfrg-xwing-kem-00  . . . . . . . . .  22
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  22

1.  Introduction

1.1.  Warning: ML-KEM-768 has not been standardised

   X-Wing uses ML-KEM-768, which has not been standardised yet.  Thus
   X-Wing is not finished, yet, and should not be used, yet.

1.2.  Motivation

   There are many choices that can be made when specifying a hybrid KEM:
   the constituent KEMs; their security levels; the combiner; and the
   hash within, to name but a few.  Having too many similar options are
   a burden to the ecosystem.

   The aim of X-Wing is to provide a concrete, simple choice for post-
   quantum hybrid KEM, that should be suitable for the vast majority of
   use cases.

1.3.  Design goals

   By making concrete choices, we can simplify and improve many aspects
   of X-Wing.

   *  Simplicity of definition.  Because all shared secrets and cipher
      texts are fixed length, we do not need to encode the length.
      Using SHA3-256, we do not need HMAC-based construction.  For the
      concrete choice of ML-KEM-768, we do not need to mix in its
      ciphertext, see Section 6.

   *  Security analysis.  Because ML-KEM-768 already assumes QROM, we do
      not need to complicate the analysis of X-Wing by considering
      stronger models.

   *  Performance.  Not having to mix in the ML-KEM-768 ciphertext is a
      nice performance benefit.  Furthermore, by using SHA3-256 in the
      combiner, which matches the hashing in ML-KEM-768, this hash can
      be computed in one go on platforms where two-way Keccak is
      available.






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   We aim for "128 bits" security (NIST PQC level 1).  Although at the
   moment there is no peer-reviewed evidence that ML-KEM-512 does not
   reach this level, we would like to hedge against future cryptanalytic
   improvements, and feel ML-KEM-768 provides a comfortable margin.

   We aim for X-Wing to be usable for most applications, including
   specifically HPKE [RFC9180].

1.4.  Not an interactive key-agreement

   Traditionally most protocols use a Diffie-Hellman (DH) style non-
   interactive key-agreement.  In many cases, a DH key agreement can be
   replaced by the interactive key-agreement afforded by a KEM without
   change in the protocol flow.  One notable example is TLS [HYBRID]
   [XYBERTLS].  However, not all uses of DH can be replaced in a
   straight-forward manner by a plain KEM.

1.5.  Not an authenticated KEM

   In particular, X-Wing is not, borrowing the language of [RFC9180], an
   _authenticated_ KEM.

1.6.  Comparisons

1.6.1.  With HPKE X25519Kyber768Draft00

   X-Wing is most similar to HPKE's X25519Kyber768Draft00 [XYBERHPKE].
   The key differences are:

   *  X-Wing uses the final version of ML-KEM-768.

   *  X-Wing hashes the shared secrets, to be usable outside of HPKE.

   *  X-Wing has a simpler combiner by flattening DHKEM(X25519) into the
      final hash.

   *  X-Wing does not hash in the ML-KEM-768 ciphertext.

   There is also a different KEM called X25519Kyber768Draft00 [XYBERTLS]
   which is used in TLS.  This one should not be used outside of TLS, as
   it assumes the presence of the TLS transcript to ensure non
   malleability.

1.6.2.  With generic combiner

   The generic combiner of [I-D.ounsworth-cfrg-kem-combiners] can be
   instantiated with ML-KEM-768 and DHKEM(X25519).  That achieves
   similar security, but:



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   *  X-Wing is more performant, not hashing in the ML-KEM-768
      ciphertext, and flattening the DHKEM construction, with the same
      level of security.

   *  X-Wing has a fixed 32 byte shared secret, instead of a variable
      shared secret.

   *  X-Wing does not accept the optional counter and fixedInfo
      arguments.

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
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

3.  Conventions and Definitions

   This document is consistent with all terminology defined in
   [I-D.driscoll-pqt-hybrid-terminology].

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

   *  concat(x0, ..., xN): returns the concatenation of byte strings.
      concat(0x01, 0x0203, 0x040506) = 0x010203040506.

   *  random(n): return a pseudorandom byte string of length n bytes
      produced by a cryptographically-secure random number generator.

4.  Cryptographic Dependencies

   X-Wing relies on the following primitives:

   *  ML-KEM-768 post-quantum key-encapsulation mechanism (KEM) [MLKEM]:

      -  ML-KEM-768.KeyGen(): Randomized algorithm to generate an ML-
         KEM-768 key pair (pk_M, sk_M) of an encapsulation key pk_M and
         decapsulation key sk_M.  Note that ML-KEM-768.KeyGen() returns
         the keys in reverse order of GenerateKeyPair() defined below.

      -  ML-KEM-768.Encaps(pk_M): Randomized algorithm to generate
         (ss_M, ct_M), an ephemeral 32 byte shared key ss_M, and a
         fixed-length encapsulation (ciphertext) of that key ct_M for
         encapsulation key pk_M.




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      -  ML-KEM-768.Decap(ct_M, sk_M): Deterministic algorithm using the
         decapsulation key sk_M to recover the shared key from ct_M.

      To generate deterministic test vectors, we also use

      -  ML-KEM-768.KeyGenDerand(seed): Same as ML-KEM-768.KeyGen(), but
         derandomized as follows. seed is 64 bytes. seed[0:32] is used
         for z (line 1 algorithm 15), and seed[32:64] is used for d
         (line 1 algorithm 12).

      -  ML-KEM-768.EncapsDerand(pk_M, seed): Same as ML-KEM-
         768.Encaps() but derandomized as follows. seed is 32 bytes and
         used for m (line 1 algorithm 16).

   *  X25519 elliptic curve Diffie-Hellman key-exchange defined in
      Section 5 of [RFC7748]:

      -  X25519(k,u): takes 32 byte strings k and u representing a
         Curve25519 scalar and curvepoint respectively, and returns the
         32 byte string representing their scalar multiplication.

      -  X25519_BASE: the 32 byte string representing the standard base
         point of Curve25519.  In hex it is given by
         09000000000000000000000000000000000000000000.

   Note that 9 is the standard basepoint for X25519, cf Section 6.1 of
   [RFC7748].

   *  Symmetric cryptography.

      -  SHAKE128(message, outlen): The extendable-output function (XOF)
         defined in Section 6.2 of [FIPS202].

      -  SHA3-256(message): The hash defined in defined in Section 6.1
         of [FIPS202].

5.  X-Wing Construction

5.1.  Encoding and sizes

   X-Wing encapsulation key, decapsulation key, ciphertexts and shared
   secrets are all fixed length byte strings.

   Decapsulation key (private):  2464 bytes

   Encapsulation key (public):  1216 bytes

   Ciphertext:  1120 bytes



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   Shared secret:  32 bytes

5.2.  Key generation

   An X-Wing keypair (decapsulation key, encapsulation key) is generated
   as follows.

   def GenerateKeyPair():
     (pk_M, sk_M) = ML-KEM-768.KeyGen()
     sk_X = random(32)
     pk_X = X25519(sk_X, X25519_BASE)
     return concat(sk_M, sk_X, pk_X), concat(pk_M, pk_X)

   GenerateKeyPair() returns the 2464 byte secret encapsulation key sk
   and the 1216 byte decapsulation key pk.

5.2.1.  Key derivation

   For testing, it is convenient to have a deterministic version of key
   generation.  An X-Wing implementation MAY provide the following
   derandomized variant of key generation.

   def GenerateKeyPairDerand(seed):
     (pk_M, sk_M) = ML-KEM-768.KeyGenDerand(seed[0:64])
     sk_X = seed[64:96]
     pk_X = X25519(sk_X, X25519_BASE)
     return concat(sk_M, sk_X, pk_X), concat(pk_M, pk_X)

   seed must be 96 bytes.

   GenerateKeyPairDerand() returns the 2464 byte secret encapsulation
   key sk and the 1216 byte decapsulation key pk.

5.3.  Combiner

   Given 32 byte strings ss_M, ss_X, ct_X, pk_X, representing the ML-
   KEM-768 shared secret, X25519 shared secret, X25519 ciphertext
   (ephemeral public key) and X25519 public key respectively, the 32
   byte combined shared secret is given by:

   def Combiner(ss_M, ss_X, ct_X, pk_X):
     return SHA3-256(concat(
       XWingLabel,
       ss_M,
       ss_X,
       ct_X,
       pk_X
     ))



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   where XWingLabel is the following 6 byte ASCII string

   XWingLabel = concat(
       "\./",
       "/^\",
   )

5.4.  Encapsulation

   Given an X-Wing encapsulation key pk, encapsulation proceeds as
   follows.

   def Encapsulate(pk):
     pk_M = pk[0:1184]
     pk_X = pk[1184:1216]
     ek_X = random(32)
     ct_X = X25519(ek_X, X25519_BASE)
     ss_X = X25519(ek_X, pk_X)
     (ss_M, ct_M) = ML-KEM-768.Encaps(pk_M)
     ss = Combiner(ss_M, ss_X, ct_X, pk_X)
     ct = concat(ct_M, ct_X)
     return (ss, ct)

   pk is a 1216 byte X-Wing encapsulation key resulting from
   GeneratePublicKey()

   Encapsulate() returns the 32 byte shared secret ss and the 1120 byte
   ciphertext ct.

5.4.1.  Derandomized

   For testing, it is convenient to have a deterministic version of
   encapsulation.  An X-Wing implementation MAY provide the following
   derandomized function.

   def EncapsulateDerand(pk, seed):
     pk_M = pk[0:1184]
     pk_X = pk[1184:1216]
     ek_X = seed[32:64]
     ct_X = X25519(ek_X, X25519_BASE)
     ss_X = X25519(ek_X, pk_X)
     (ss_M, ct_M) = ML-KEM-768.EncapsDerand(pk_M, seed[0:32])
     ss = Combiner(ss_M, ss_X, ct_X, pk_X)
     ct = concat(ct_M, ct_X)
     return (ss, ct)

   pk is a 1216 byte X-Wing encapsulation key resulting from
   GeneratePublicKey() seed MUST be 64 bytes.



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   EncapsulateDerand() returns the 32 byte shared secret ss and the 1120
   byte ciphertext ct.

5.5.  Decapsulation

   def Decapsulate(ct, sk):
     ct_M = ct[0:1088]
     ct_X = ct[1088:1120]
     sk_M = sk[0:2400]
     sk_X = sk[2400:2432]
     pk_X = sk[2432:2464]
     ss_M = ML-KEM-768.Decapsulate(ct_M, sk_M)
     ss_X = X25519(sk_X, ct_X)
     return Combiner(ss_M, ss_X, ct_X, pk_X)

   ct is the 1120 byte ciphertext resulting from Encapsulate() sk is a
   2464 byte X-Wing decapsulation key resulting from GenerateKeyPair()

   Decapsulate() returns the 32 byte shared secret.

5.6.  Use in HPKE

   X-Wing satisfies the HPKE KEM interface as follows.

   The SerializePublicKey, DeserializePublicKey, SerializePrivateKey and
   DeserializePrivateKey are the identity functions, as X-Wing keys are
   fixed-length byte strings, see Section 5.1.

   DeriveKeyPair() is given by

   def DeriveKeyPair(ikm):
     return GenerateKeyPairDerand(SHAKE128(ikm, 96))

   where the HPKE private key and public key are the X-Wing
   decapsulation key and encapsulation key respectively.

   The argument ikm to DeriveKeyPair() SHOULD be at least 32 octets in
   length.  (This is contrary to [RFC9180] which stipulates it should be
   at least Nsk=2432 octets in length.)

   Encap() is Encapsulate() from Section 5.4.

   Decap() is Decapsulate() from Section 5.5.

   X-Wing is not an authenticated KEM: it does not support AuthEncap()
   and AuthDecap(), see Section 1.5.

   Nsecret, Nenc, Npk, and Nsk are defined in Section 7.



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5.7.  Use in TLS 1.3

   For the client's share, the key_exchange value contains the X-Wing
   encapsulation key.

   For the server's share, the key_exchange value contains the X-Wing
   ciphertext.

6.  Security Considerations

   Informally, X-Wing is secure if SHA3 is secure, and either X25519 is
   secure, or ML-KEM-768 is secure.

   More precisely, if SHA3-256, SHA3-512, SHAKE-128, and SHAKE-256 may
   be modelled as a random oracle, then the IND-CCA security of X-Wing
   is bounded by the IND-CCA security of ML-KEM-768, and the gap-CDH
   security of Curve25519, see [PROOF].

   The security of X-Wing relies crucially on the specifics of the
   Fujisaki-Okamoto transformation used in ML-KEM-768.  In particular,
   the X-Wing combiner cannot be assumed to be secure, when used with
   different KEMs.

7.  IANA Considerations

   This document requests/registers a new entry to the "HPKE KEM
   Identifiers" registry.

   Value:  TBD (please)

   KEM:  X-Wing

   Nsecret:  32

   Nenc:  1120

   Npk:  1216

   Nsk:  2464

   Auth:  no

   Reference:  This document

   Furthermore, this document requests/registers a new entry to the TLS
   Named Group (or Supported Group) registry, according to the
   procedures in Section 6 of [TLSIANA].




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   Value:  TBD (please)

   Description:  X-Wing

   DTLS-OK:  Y

   Recommended:  Y

   Reference:  This document

   Comment:  PQ/T hybrid of X25519 and ML-KEM-768

8.  TODO

   *  Which validation do we want to require?

9.  References

9.1.  Normative References

   [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/rfc/rfc2119>.

   [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/rfc/rfc8174>.

9.2.  Informative References

   [FIPS202]  National Institute of Standards and Technology, "FIPS 202:
              SHA-3 Standard: Permutation-Based Hash and Extendable-
              Output Functions", n.d.,
              <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.202.pdf>.

   [HYBRID]   Stebila, D., Fluhrer, S., and S. Gueron, "Hybrid key
              exchange in TLS 1.3", Work in Progress, Internet-Draft,
              draft-stebila-tls-hybrid-design-03, 12 February 2020,
              <https://datatracker.ietf.org/doc/html/draft-stebila-tls-
              hybrid-design-03>.









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   [I-D.driscoll-pqt-hybrid-terminology]
              D, F., "Terminology for Post-Quantum Traditional Hybrid
              Schemes", Work in Progress, Internet-Draft, draft-
              driscoll-pqt-hybrid-terminology-02, 7 March 2023,
              <https://datatracker.ietf.org/doc/html/draft-driscoll-pqt-
              hybrid-terminology-02>.

   [I-D.ounsworth-cfrg-kem-combiners]
              Ounsworth, M., Wussler, A., and S. Kousidis, "Combiner
              function for hybrid key encapsulation mechanisms (Hybrid
              KEMs)", Work in Progress, Internet-Draft, draft-ounsworth-
              cfrg-kem-combiners-04, 8 July 2023,
              <https://datatracker.ietf.org/doc/html/draft-ounsworth-
              cfrg-kem-combiners-04>.

   [MLKEM]    National Institute of Standards and Technology, "FIPS 203
              (Initial Draft): Module-Lattice-Based Key-Encapsulation
              Mechanism Standard", n.d.,
              <https://csrc.nist.gov/pubs/fips/203/ipd>.

   [PROOF]    Barbosa, M., Connolly, D., Duarte, J., Kaiser, A.,
              Schwabe, P., Varner, K., and B. E. Westerbraan, "X-Wing:
              The Hybrid KEM You’ve Been Looking For", n.d.,
              <https://eprint.iacr.org/2024/039>.

   [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/rfc/rfc7748>.

   [RFC9180]  Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid
              Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180,
              February 2022, <https://www.rfc-editor.org/rfc/rfc9180>.

   [TLSIANA]  Salowey, J. A. and S. Turner, "IANA Registry Updates for
              TLS and DTLS", Work in Progress, Internet-Draft, draft-
              ietf-tls-rfc8447bis-08, 23 January 2024,
              <https://datatracker.ietf.org/doc/html/draft-ietf-tls-
              rfc8447bis-08>.

   [XYBERHPKE]
              Westerbaan, B. and C. A. Wood, "X25519Kyber768Draft00
              hybrid post-quantum KEM for HPKE", Work in Progress,
              Internet-Draft, draft-westerbaan-cfrg-hpke-xyber768d00-02,
              4 May 2023, <https://datatracker.ietf.org/doc/html/draft-
              westerbaan-cfrg-hpke-xyber768d00-02>.






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   [XYBERTLS] Westerbaan, B. and D. Stebila, "X25519Kyber768Draft00
              hybrid post-quantum key agreement", Work in Progress,
              Internet-Draft, draft-tls-westerbaan-xyber768d00-03, 24
              September 2023, <https://datatracker.ietf.org/doc/html/
              draft-tls-westerbaan-xyber768d00-03>.

Appendix A.  Test vectors # TODO: replace with test vectors that re-use
             ML-KEM, X25519 values

seed
  7f9c2ba4e88f827d616045507605853ed73b8093f6efbc88eb1a6eacfa66ef263cb1eea9
  88004b93103cfb0aeefd2a686e01fa4a58e8a3639ca8a1e3f9ae57e235b8cc873c23dc62
  b8d260169afa2f75ab916a58d974918835d25e6a435085b2
sk
  24c59d1c7603e7b74bc7aa1bc2cb3a214b3cfaebb63bd85b65408427c498ba394371bb27
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  78d99d23f8235da90791604b4f0a4f7640680f59b633d93dfb84282ba54c674b115684a4
  1bc331b659a61a04883d0c5ebbc0772754a4c33b6a90e52e0678ce06a0453ba8a188b15a
  496bae6a24177b636d12fbb088f2cd9504ac200231473031a31a5c62e46288fb3edb858b



Connolly, et al.          Expires 25 July 2024                 [Page 13]

Internet-Draft                    xwing                     January 2024


  21bc0ea59a212fd1c6dba09e920712d068a2be7abcf4f2a3533443ee1780dd419681a960
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  b97e63e0e41d354274a079d3e6fb2e15
pk
  1bc331b659a61a04883d0c5ebbc0772754a4c33b6a90e52e0678ce06a0453ba8a188b15a
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  b262b8731b9e962976c41152a76c30b502d0425635357b43cd3a3ecef5bc9910bb89ca9e



Connolly, et al.          Expires 25 July 2024                 [Page 14]

Internet-Draft                    xwing                     January 2024


  91ba75e8121d53c2329b5222df12560d242724523ff60b6ead310d99954d483b91383a72
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  6740ce2a32fc5145030145cfb97e63e0e41d354274a079d3e6fb2e15
eseed
  badfd6dfaac359a5efbb7bcc4b59d538df9a04302e10c8bc1cbf1a0b3a5120ea17cda7cf
  ad765f5623474d368ccca8af0007cd9f5e4c849f167a580b14aabdef
ct
  718ad10318b367fc4390f63147fa5250ef61b65384a563f2c7951b2d45881fcf9f446ddd
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  220dc800bcb1ae83d35ffca54a6dabba730764d60b1a4a506206efa380d7d1d89069778b



Connolly, et al.          Expires 25 July 2024                 [Page 15]

Internet-Draft                    xwing                     January 2024


  082bb92396af4547024797797e01c927c78c9f70750ef2002dfe1516baa4f165a3176942
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  b3b0ba04e83f80c1b06b4975f00207b357550d24405189412ea6a83ad56c4873f499fdbd
  c761aa72
ss     2fae7214767890c4703fad953f5e3f91303111498caa135d77cde634151e71b5

seed
  aee7eef47cb0fca9767be1fda69419dfb927e9df07348b196691abaeb580b32def58538b
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  8ac850933c7aff1533b94c834adbb69c6115bad4692d8619
sk
  89722dd1c8829af93f6e5405ecd93a5aaabcb9264aafc363d731bb4f276021b0c0682636
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  f68450f4f4b14bda3af5f129b3e292c6a676aa0b7a045c7251e315ca3707ff23bec349a9
  50d49718560b2ff66cbd49c848b4036c2186a0315c4e6a32f3035207a48651891f50ec6c
  0eb19d13e90457611e0c7ccdf012a3e19412d8c1563f1ab22b39859b27a7bcac72cbf2c8
  3c666deb401e4239603645872b997673b6205d97cdd68b0a782742e62c24ad746261085d
  e3c95f49dbb8172c05f3f2414e63652c3b358d603e867173e03203af06a26bb0bfc0b521



Connolly, et al.          Expires 25 July 2024                 [Page 16]

Internet-Draft                    xwing                     January 2024


  118b6fd99613a160829b04475374b8214859bcc316f4e06a84f264ec3cb513f66b71ac3a
  3d135aa589198cb02113cc17e13a0f15fc1d3d734966c3751a74ac27c781323043e36389
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  9e75e14084b0bc85620499bf468ae161
pk
  3d135aa589198cb02113cc17e13a0f15fc1d3d734966c3751a74ac27c781323043e36389
  dca9a2af6508bdba0260662691426d1d8899cd77736c21b17eb3a31fc118154264e2b10e
  22c506b7803b1f4b25d178b688b641d0943185107eed18b228e8b68753a8d75a77f29b5b
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  4dba1dc3434976f60b59d443bad51e87d974c9f747b76017bd17021c24246a9987db1b31
  8562bf665b41fb153c0ba675cac593b990ce595a7851fa18ea345bf20c3524862532544e
  05e5c69daa0dc4f2b24704338e29144d653657d47a20f39ed2b1174cb3120ed1590e4ac9



Connolly, et al.          Expires 25 July 2024                 [Page 17]

Internet-Draft                    xwing                     January 2024


  32579dc2da9f12f6c07ec7a31963208faa5c758615713965b9d5661860cfe5652d74231d
  2ce9b696ea9e45305a28d84c082709d2238bbc849b6b3cac64b78b532995af6b4ce9880f
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eseed
  f90b0cdf8a7b9c264029ac185b70b83f2801f2f4b3f70c593ea3aeeb613a7f1b1de33fd7
  5081f592305f2e4526edc09631b10958f464d889f31ba010250fda7f
ct
  f98f274dc74db1798915be81f089fbf792116ec03539b6c02cfbe649267f100df0ef51ec
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  cb600cfd6ca0bdf4915a47fe02d71b8fcc27f0f17c78a300c6345ccc2f77a438772f4297
  f7b2160aec93e4c8c72c0dbe67868753c18491861a1c1b96eaae07023436602fbb6f2bfb



Connolly, et al.          Expires 25 July 2024                 [Page 18]

Internet-Draft                    xwing                     January 2024


  161a5f778bb3086c2255423a8c51052833f6b63ed2cc732a7e2c4d36123471b451b64083
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  0208a15c
ss     d482dd1a592f072109a0d8a86991ca6bd5bab25f13e788377fc34506f508ffdd

seed
  1368ec2967fc84ef2ae9aff268e0b1700affc6820b523a3d917135f2dff2ee06bfe72b31
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sk
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  fefb9e2e0916f4d753bb354b1cdb0ec61840ae14a0b0a6b89419cbcd4c2cc9fa8df8da7b
  ef4a829e17b996461b499ca051b5989b17738b158057342454745051e7b01aa5a8971181



Connolly, et al.          Expires 25 July 2024                 [Page 19]

Internet-Draft                    xwing                     January 2024


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  76cdd9add2eba7768b4ac7abb269b07e
pk
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ss     1e037823ddbf1875756d86a3374b2d2347d5b7f3c84d229ecc5960523cdaa8b4

Appendix B.  Acknowledgments

   TODO acknowledge.

Appendix C.  Change log

      *RFC Editor's Note:* Please remove this section prior to
      publication of a final version of this document.

C.1.  Since draft-connolly-cfrg-xwing-kem-00

   *  A copy of the X25519 public key is now included in the X-Wing
      decapsulation (private) key, so that decapsulation does not
      require separate access to the X-Wing public key.  See #2.

Authors' Addresses

   Deirdre Connolly
   SandboxAQ
   Email: durumcrustulum@gmail.com


   Peter Schwabe
   MPI-SP & Radboud University
   Email: peter@cryptojedi.org


   Bas Westerbaan
   Cloudflare
   Email: bas@cloudflare.com



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