| Internet-Draft | xwing | January 2024 |
| Connolly, et al. | Expires 25 July 2024 | [Page] |
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.¶
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.¶
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Copyright (c) 2024 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.¶
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.¶
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.¶
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.¶
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].¶
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.¶
In particular, X-Wing is not, borrowing the language of [RFC9180], an authenticated KEM.¶
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.¶
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:¶
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.¶
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:¶
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.¶
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].¶
X-Wing encapsulation key, decapsulation key, ciphertexts and shared secrets are all fixed length byte strings.¶
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.¶
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.¶
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
))
¶
where XWingLabel is the following 6 byte ASCII string¶
XWingLabel = concat(
"\./",
"/^\",
)
¶
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.¶
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.¶
EncapsulateDerand() returns the 32 byte shared secret ss and the 1120 byte
ciphertext ct.¶
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.¶
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.¶
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.¶
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.¶
This document requests/registers a new entry to the "HPKE KEM Identifiers" registry.¶
TBD (please)¶
X-Wing¶
32¶
1120¶
1216¶
2464¶
no¶
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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a59ec52099d7bfb00a3ccde4084825145f022d89a126519f7904eb7ec4db0b08e70d7d67 bf18e537476b4ce97b2ad1c84c0630ba053a13affff42ecea695c080942df74369a23f93 a1f397f14dce28acbedb6a90e7a0a6423c277254b71be2d887386915e5924e85f1c65218 2f8c0db076364a97d7acaf0f238c912fd56403593a8b2526884737790a887d9a8382fab3 d2967803d0a1e62b610289af4ea26c66ef29c4832a4b48ffa225d5be2401656753a9ed00 c45a057efc666abaecfaeef972643de281f5d6a6ef43ed2fbba963a95c8d36461323d51d 18f92e58e4de1b4edd1d93ba14ea6adc3b8b63e71d0edc92555f3f962e68fbf42a0fc04c b7da107203468589655f1b3b979ccc2efee6f10f0ec631c040e4436b8acaa4716708bf96 d2db8108a36117d10664cb2a3e3af672a10b0de5c2a284e6b9de37533bd181bc14fa0490 35d5050b5526ba59f893a1778103b6e2d946090c0eba049e5c1ad843a3121d539564866a f5647437 ss 1e037823ddbf1875756d86a3374b2d2347d5b7f3c84d229ecc5960523cdaa8b4¶
TODO acknowledge.¶
RFC Editor's Note: Please remove this section prior to publication of a final version of this document.¶
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.¶