Hybrid PQ/T Key Encapsulation Mechanisms

1.1. 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 this document is provide a small set of techniques for constructing hybrid KEMs designed to achieve specific security properties given conforming component algorithms, that should be suitable for the vast majority of use cases.¶

3.1. Key encapsulation mechanisms

Key encapsulation mechanisms (KEMs) are cryptographic schemes that consist of three algorithms:¶

• KeyGen() -> (pk, sk): A probabilistic key generation algorithm, which generates a public encapsulation key pk and a secret decapsulation key sk.¶

• Encaps(pk) -> (ct, shared_secret): A probabilistic encapsulation algorithm, which takes as input a public encapsulation key pk and outputs a ciphertext ct and shared secret shared_secret.¶

• Decaps(sk, ct) -> shared_secret: A decapsulation algorithm, which takes as input a secret decapsulation key sk and ciphertext ct and outputs a shared secret shared_secret.¶

4.1. Hybrid Security

Informally, hybrid KEMs are secure if the KDF is secure, and if any one of the components KEMs is secure: this is the 'hybrid' property.¶

4.2. IND-CCA security

Also known as IND-CCA2 security for general public key encryption, for KEMs that encapsulate a new random 'message' each time.¶

The notion of INDistinguishability against Chosen-Ciphertext Attacks (IND-CCA) [RS92] is now widely accepted as the standard security notion for asymmetric encryption schemes. IND-CCA security requires that no efficient adversary can recognize which of two messages is encrypted in a given ciphertext, even if the two candidate messages are chosen by the adversary himself.¶

4.3. Ciphertext second preimage resistant (C2PRI) security / ciphertext collision resistance (CCR)

The notion where, even if a KEM has broken IND-CCA security (either due to construction, implementation, or other), its internal structure, based on the Fujisaki-Okamoto transform, guarantees that it is impossible to find a second ciphertext that decapsulates to the same shared secret K: this notion is known as ciphertext second preimage resistance (C2SPI) for KEMs [XWING]. The same notion has also been described as chosen ciphertext resistance elsewhere [CDM23].¶

4.4. Binding properties

5.1. XOF

Extendable-output function (XOF). A function on bit strings in which the output can be extended to any desired length. Ought to satisfy the following properties as long as the specified output length is sufficiently long to prevent trivial attacks:¶

1. (One-way) It is computationally infeasible to find any input that maps to any new pre-specified output.¶

2. (Collision-resistant) It is computationally infeasible to find any two distinct inputs that map to the same output.¶

MUST provide the bit-security required to source input randomness for PQ/T components from a seed that is expanded to a output length, of which a subset is passed to the component key generation algorithms.¶

5.2. Key Derivation Function KDF

A secure key derivation function (KDF) that is modeled as a secure pseudorandom function (PRF) in the standard model [GHP2018] and independent random oracle in the random oracle model (ROM).¶

5.3. Post-Quantum KEM

An IND-CCA KEM that is resilient against post-quantum attacks. It fulfills the scheme API in {kems}.¶

5.4. Nominal Diffie-Hellman Group

The traditional DH-KEM construction depends on an abelian group of order order. We represent this group as the object G that additionally defines helper functions described below. The group operation for G is addition + with identity element I. For any elements A and B of the group G, A + B = B + A is also a member of G. Also, for any A in G, there exists an element -A such that A + (-A) = (-A) + A = I. For convenience, we use - to denote subtraction, e.g., A - B = A + (-B). Integers, taken modulo the group order order, are called scalars; arithmetic operations on scalars are implicitly performed modulo order. Scalar multiplication is equivalent to the repeated application of the group operation on an element A with itself r-1 times, denoted as ScalarMult(A, r). We denote the sum, difference, and product of two scalars using the +, -, and * operators, respectively. (Note that this means + may refer to group element addition or scalar addition, depending on the type of the operands.) For any element A, ScalarMult(A, order) = I. We denote B as a fixed generator of the group. Scalar base multiplication is equivalent to the repeated application of the group operation on B with itself r-1 times, this is denoted as ScalarBaseMult(r). The set of scalars corresponds to GF(order), which we refer to as the scalar field. It is assumed that group element addition, negation, and equality comparison can be efficiently computed for arbitrary group elements.¶

This document uses types Element and Scalar to denote elements of the group G and its set of scalars, respectively. We denote Scalar(x) as the conversion of integer input x to the corresponding Scalar value with the same numeric value. For example, Scalar(1) yields a Scalar representing the value 1. We denote equality comparison of these types as == and assignment of values by =. When comparing Scalar values, e.g., for the purposes of sorting lists of Scalar values, the least nonnegative representation mod order is used.¶

We now detail a number of member functions that can be invoked on G.¶

• Order(): Outputs the order of G (i.e., order).¶

• Identity(): Outputs the identity Element of the group (i.e., I).¶

• RandomScalar(): Outputs a random Scalar element in GF(order), i.e., a random scalar in [0, order - 1].¶

• ScalarMult(A, k): Outputs the scalar multiplication between Element A and Scalar k.¶

• ScalarBaseMult(k): Outputs the scalar multiplication between Scalar k and the group generator B.¶

• SerializeElement(A): Maps an Element A to a canonical byte array buf of fixed length Ne. This function raises an error if A is the identity element of the group.¶

• DeserializeElement(buf): Attempts to map a byte array buf to an Element A, and fails if the input is not the valid canonical byte representation of an element of the group. This function raises an error if deserialization fails or if A is the identity element of the group.¶

• SerializeScalar(s): Maps a Scalar s to a canonical byte array buf of fixed length Ns.¶

• DeserializeScalar(buf): Attempts to map a byte array buf to a Scalar s. This function raises an error if deserialization fails.¶

6.1. label

ASCII-encoded bytes that provide oracle cloning [BDG2020] in the security game via domain separation. The IND-CCA security of hybrid KEMs often relies on the KDF function KDF to behave as an independent random oracle, which the inclusion of the label achieves via domain separation [GHP2018].¶

By design, the calls to KDF in these constructions and usage anywhere else in higher level protoocl use separate input domains unless intentionally duplicating the 'label' per concrete instance with fixed paramters. This justifies modeling them as independent functions even if instantiated by the same KDF. This domain separation is achieved by using prefix-free sets of label values. Recall that a set is prefix-free if no element is a prefix of another within the set.¶

Length diffentiation is sometimes used to achieve domain separation but as a technique it is [brittle and prone to misuse][BDG2020] in practice so we favor the use of an explicit post-fix label.¶

7.1. Common security requirements

7.2. Key Generation

We specify a common generic key generation scheme for all generic constructions. This requires the component key generation algorithns to accept the sufficient random seed, possibly according to their parameter set.¶

### Key derivation {#derive-key-pair}¶

7.3. 'Kitchen Sink' construction:

As indicated by the name, the KitchenSink construction puts 'the whole transcript' through the KDF. This relies on the minimum security properties of its component algorithms at the cost of more bytes needing to be processed by the KDF.¶

def KitchenSink-KEM.SharedSecret(pq_SS, trad_SS, pq_CT, pq_PK, trad_CT, trad_PK):
    return KDF(concat(pq_SS, trad_SS, pq_CT, pq_PK, trad_CT, trad_PK, label))

7.4. 'QSF' construction

Inspired by the generic QSF (Quantum Superiority Fighter) framework in [XWING], which leverages the security properties of a KEM like ML-KEM and an inlined instance of DH-KEM, to elide other public data like the PQ ciphertext and encapsulation key from the KDF input:¶

def QSF-KEM.SharedSecret(pq_SS, trad_SS, trad_CT, trad_PK):
    return KDF(concat(pq_SS, trad_SS, trad_CT, trad_PK, label))

8.1. QSF-SHA3-256-ML-KEM-768-P-256

Also known as [XWING] but with P-256 instead of X25519.¶

• label: QSF-SHA3-256-ML-KEM-768-P-256¶

• XOF: [SHAKE-256][FIPS202]¶

• KDF: [SHA3-256][FIPS202]¶

• PQ KEM: ML-KEM-768 [FIPS203]¶

• Group: [P-256][FIPS186] (secp256r1) [ANSIX9.62], where Ne = 33 and Ns = 32.¶

This instantiation uses P-256 for the Group.¶

• Group: P-256¶

  • Order(): Return 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551.¶

  • Identity(): As defined in [ANSIX9.62].¶

  • RandomScalar(): Implemented by returning a uniformly random Scalar in the range [0, G.Order() - 1]. Refer to Section 9 for implementation guidance.¶

  • SerializeElement(A): Implemented using the compressed Elliptic-Curve-Point-to-Octet-String method according to [SEC1], yielding a 33-byte output. Additionally, this function validates that the input element is not the group identity element.¶

  • DeserializeElement(buf): Implemented by attempting to deserialize a 33-byte input string to a public key using the compressed Octet-String-to-Elliptic-Curve-Point method according to [SEC1], and then performs public-key validation as defined in section 3.2.2.1 of [SEC1]. This includes checking that the coordinates of the resulting point are in the correct range, that the point is on the curve, and that the point is not the point at infinity. (As noted in the specification, validation of the point order is not required since the cofactor is 1.) If any of these checks fail, deserialization returns an error.¶

  • SerializeScalar(s): Implemented using the Field-Element-to-Octet-String conversion according to [SEC1].¶

  • DeserializeScalar(buf): Implemented by attempting to deserialize a Scalar from a 32-byte string using Octet-String-to-Field-Element from [SEC1]. This function can fail if the input does not represent a Scalar in the range [0, G.Order() - 1].¶

def expandDecapsulationKey(sk):
  expanded = SHAKE256(sk, 96)
  (pk_M, sk_M) = ML-KEM-768.KeyGen_internal(expanded[0:32], expanded[32:64])
  sk_G = Scalar(expanded[64:96])
  pk_G = ScalarMultBase(sk_G)
  return (sk_M, sk_G, pk_M, pk_G)

def GenerateKeyPair():
  sk = random(32)
  (sk_M, sk_G, pk_M, pk_G) = expandDecapsulationKey(sk)
  return sk, concat(pk_M, pk_G)

def GenerateKeyPairDerand(sk):
  sk_M, sk_G, pk_M, pk_G = expandDecapsulationKey(sk)
  return sk, concat(pk_M, pk_X)

8.2. Shared secret

Given 32-byte strings ss_M, ss_G, and the 33-byte strings ct_G, pk_G, representing the ML-KEM-768 shared secret, P-256 shared secret, P-256 ciphertext (ephemeral public key) and P-256 public key respectively, the 32 byte combined shared secret is given by:¶

def SharedSecret(ss_M, ss_G, ct_G, pk_G):
  return SHA3-256(concat(
    ss_M,
    ss_X,
    ct_G,
    pk_G,
    `label`
  ))

where label is the instance label. In hex label is given by TODO.¶

8.3. Encapsulation

Given an encapsulation key pk, encapsulation proceeds as follows.¶

def Encapsulate(pk):
  pk_M = pk[0:1184]
  pk_G = pk[1184:1217]
  ek_G = RandomScalar()
  ct_G = ScalarMultBase(ek_G)
  ss_G = ScalarMult(ek_G, pk_G)
  (ss_M, ct_M) = ML-KEM-768.Encaps(pk_M)
  ss = SharedSecret(ss_M, ss_G, ct_G, pk_G)
  ct = concat(ct_M, ct_G)
  return (ss, ct)

pk is a 1217 byte X-Wing encapsulation key resulting from GeneratePublicKey()¶

Encapsulate() returns the 32 byte shared secret ss and the 1121 byte ciphertext ct.¶

Note that Encapsulate() may raise an error if the ML-KEM encapsulation does not pass the check of [FIPS203] §7.2.¶

def EncapsulateDerand(pk, eseed):
  pk_M = pk[0:1184]
  pk_G = pk[1184:1217]
  ek_G = eseed[32:65]
  ct_G = ScalarMultBase(ek_G)
  ss_G = ScalarMult(ek_G, pk_G)

  (ss_M, ct_M) = ML-KEM-768.EncapsDerand(pk_M, eseed[0:32])
  ss = SharedSecret(ss_M, ss_G, ct_G, pk_G)
  ct = concat(ct_M, ct_G)
  return (ss, ct)

8.4. Decapsulation

def Decapsulate(ct, sk):
  (sk_M, sk_G, pk_M, pk_G) = expandDecapsulationKey(sk)
  ct_M = ct[0:1088]
  ct_G = ct[1088:1121]
  ss_M = ML-KEM-768.Decapsulate(ct_M, sk_M)
  ss_G = ScalarMult(sk_G, ct_G)
  return SharedSecret(ss_M, ss_G, ct_G, pk_G)

ct is the 1121 byte ciphertext resulting from Encapsulate() sk is a 32 byte decapsulation key resulting from GenerateKeyPair()¶

Decapsulate() returns the 32 byte shared secret.¶

8.5. KitchenSink-HKDF-SHA-256-ML-KEM-768-X25519

• label: KitchenSink-HKDF-SHA-256-ML-KEM-768-X25519¶

• XOF: [SHAKE-256][FIPS202]¶

• KDF: HKDF-SHA-256 [HKDF]¶

HKDF is comprised of HKDF-Extract and HKDF-Expand. We compose them as one function here:¶

def LabeledExtract(salt, label, ikm):
  labeled_ikm = concat("Hybrid", suite_id, label, ikm)
  return HDKF-Extract(salt, labeled_ikm)

def LabeledExpand(prk, label, info, L):
  labeled_info = concat(I2OSP(L, 2), "Hybrid", suite_id,
                        label, info)
  return HKDF-Expand(prk, labeled_info, L)


def HKDF(preimage):
  prk = LabeledExtract("", "hybrid_prk", preimage)
  shared_secret = LabeledExpand(prk, "shared_secret", "", 32)
  return shared_secret

• PQ KEM: ML-KEM-768 [FIPS203]¶

• Group: X25519 [X25519]¶

This instantiation uses X25519 for the Group.¶

• Group: Curve25519 [X25519], where Ne = 32 and Ns = 32.¶

  • Order(): Return 2^252 + 0x14def9dea2f79cd65812631a5cf5d3ed (see [RFC7748]).¶

  • Identity(): As defined in [RFC7748].¶

  • RandomScalar(): Implemented by returning a uniformly random Scalar in the range [0, G.Order() - 1]. Refer to Section 9 for implementation guidance.¶

  • SerializeElement(A): Implemented as specified in [RFC7748].¶

  • DeserializeElement(buf): Implemented as specified in [RFC7748].¶

  • SerializeScalar(s): Implemented by outputting the little-endian 32-byte encoding of the Scalar value with the top three bits set to zero.¶

  • DeserializeScalar(buf): Implemented by attempting to deserialize a Scalar from a little-endian 32-byte string. This function can fail if the input does not represent a Scalar in the range [0, G.Order() - 1]. Note that this means the top three bits of the input MUST be zero.¶

def expandDecapsulationKey(sk):
  expanded = SHAKE256(sk, 96)
  (pk_M, sk_M) = ML-KEM-768.KeyGen_internal(expanded[0:32], expanded[32:64])
  sk_G = Scalar(expanded[64:96])
  pk_G = ScalarMultBase(sk_G)
  return (sk_M, sk_G, pk_M, pk_G)

def GenerateKeyPair():
  sk = random(32)
  (sk_M, sk_G, pk_M, pk_G) = expandDecapsulationKey(sk)
  return sk, concat(pk_M, pk_G)

def GenerateKeyPairDerand(sk):
  sk_M, sk_G, pk_M, pk_G = expandDecapsulationKey(sk)
  return sk, concat(pk_M, pk_X)

8.6. Shared secret

Given 32-byte strings ss_M, ss_G, ct_G, pk_G, 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 SharedSecret(ss_M, ss_G, ct_G, pk_G):
  return HKDF(concat(
    ss_M,
    ss_X,
    ct_G,
    pk_G,
    `label`
  ))

where label is the instance label. In hex label is given by TODO.¶

8.7. Encapsulation

Given an encapsulation key pk, encapsulation proceeds as follows.¶

def Encapsulate(pk):
  pk_M = pk[0:1184]
  pk_G = pk[1184:1216]
  ek_G = RandomScalar()
  ct_G = ScalarMultBase(ek_G)
  ss_G = ScalarMult(ek_G, pk_G)
  (ss_M, ct_M) = ML-KEM-768.Encaps(pk_M)
  ss = SharedSecret(ss_M, ss_G, ct_G, pk_G)
  ct = concat(ct_M, ct_G)
  return (ss, ct)

pk is a 1216 byte encapsulation key resulting from GeneratePublicKey()¶

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

Note that Encapsulate() may raise an error if the ML-KEM encapsulation does not pass the check of [FIPS203] §7.2.¶

def EncapsulateDerand(pk, eseed):
  pk_M = pk[0:1184]
  pk_G = pk[1184:1216]
  ek_G = eseed[32:64]
  ct_G = ScalarMultBase(ek_G)
  ss_G = ScalarMult(ek_G, pk_G)

  (ss_M, ct_M) = ML-KEM-768.EncapsDerand(pk_M, eseed[0:32])
  ss = SharedSecret(ss_M, ss_G, ct_G, pk_G)
  ct = concat(ct_M, ct_G)
  return (ss, ct)

8.8. Decapsulation

def Decapsulate(ct, sk):
  (sk_M, sk_G, pk_M, pk_G) = expandDecapsulationKey(sk)
  ct_M = ct[0:1088]
  ct_G = ct[1088:1120]
  ss_M = ML-KEM-768.Decapsulate(ct_M, sk_M)
  ss_G = ScalarMult(sk_G, ct_G)
  return SharedSecret(ss_M, ss_G, ct_G, pk_G)

ct is the 1120 byte ciphertext resulting from Encapsulate() sk is a 32 byte decapsulation key resulting from GenerateKeyPair()¶

Decapsulate() returns the 32 byte shared secret.¶

8.9. QSF-SHA3-256-ML-KEM-1024-P-384

• label: QSF-SHA3-256-ML-KEM-768-P-256¶

• XOF: [SHAKE-256][FIPS202]¶

• KDF: [SHA3-256][FIPS202]¶

• PQ KEM: ML-KEM-1024 [FIPS203]¶

• Group: [P-384][FIPS186] (secp256r1) [ANSIX9.62], where Ne = 33 and Ns = 32.¶

This instantiation uses P-384 for the Group.¶

• Group: P-384¶

  • Order(): Return 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf 581a0db248b0a77aecec196accc52973¶

  • Identity(): As defined in [ANSIX9.62].¶

  • RandomScalar(): Implemented by returning a uniformly random Scalar in the range [0, G.Order() - 1]. Refer to Section 9 for implementation guidance.¶

  • SerializeElement(A): Implemented using the compressed Elliptic-Curve-Point-to-Octet-String method according to [SEC1], yielding a 61-byte output. Additionally, this function validates that the input element is not the group identity element.¶

  • DeserializeElement(buf): Implemented by attempting to deserialize a 61-byte input string to a public key using the compressed Octet-String-to-Elliptic-Curve-Point method according to [SEC1], and then performs public-key validation as defined in section 3.2.2.1 of [SEC1]. This includes checking that the coordinates of the resulting point are in the correct range, that the point is on the curve, and that the point is not the point at infinity. (As noted in the specification, validation of the point order is not required since the cofactor is 1.) If any of these checks fail, deserialization returns an error.¶

  • SerializeScalar(s): Implemented using the Field-Element-to-Octet-String conversion according to [SEC1].¶

  • DeserializeScalar(buf): Implemented by attempting to deserialize a Scalar from a 48-byte string using Octet-String-to-Field-Element from [SEC1]. This function can fail if the input does not represent a Scalar in the range [0, G.Order() - 1].¶

def expandDecapsulationKey(sk):
  expanded = SHAKE256(sk, 112)
  (pk_M, sk_M) = ML-KEM-1024.KeyGen_internal(expanded[0:32], expanded[32:64])
  sk_G = Scalar(expanded[64:112])
  pk_G = ScalarMultBase(sk_G)
  return (sk_M, sk_G, pk_M, pk_G)

def GenerateKeyPair():
  sk = random(32)
  (sk_M, sk_G, pk_M, pk_G) = expandDecapsulationKey(sk)
  return sk, concat(pk_M, pk_G)

def GenerateKeyPairDerand(sk):
  sk_M, sk_G, pk_M, pk_G = expandDecapsulationKey(sk)
  return sk, concat(pk_M, pk_X)

8.10. Shared secret

Given 32-byte string ss_M, the 61-byte strings ss_G, ct_G, pk_G, representing the ML-KEM-1024 shared secret, P-384 shared secret, P-384 ciphertext (ephemeral public key) and P-384 public key respectively, the 32 byte combined shared secret is given by:¶

def SharedSecret(ss_M, ss_G, ct_G, pk_G):
  return SHA3-256(concat(
    ss_M,
    ss_X,
    ct_G,
    pk_G,
    `label`
  ))

where label is the instance label. In hex label is given by TODO.¶

8.11. Encapsulation

Given an encapsulation key pk, encapsulation proceeds as follows.¶

def Encapsulate(pk):
  pk_M = pk[0:1568]
  pk_G = pk[1568:1629]
  ek_G = RandomScalar()
  ct_G = ScalarMultBase(ek_G)
  ss_G = ScalarMult(ek_G, pk_G)
  (ss_M, ct_M) = ML-KEM-1024.Encaps(pk_M)
  ss = SharedSecret(ss_M, ss_G, ct_G, pk_G)
  ct = concat(ct_M, ct_G)
  return (ss, ct)

pk is a 1629 byte X-Wing encapsulation key resulting from GeneratePublicKey()¶

Encapsulate() returns the 32 byte shared secret ss and the 1629 byte ciphertext ct.¶

Note that Encapsulate() may raise an error if the ML-KEM encapsulation does not pass the check of [FIPS203] §7.2.¶

def EncapsulateDerand(pk, eseed):
  pk_M = pk[0:1568]
  pk_G = pk[1568:1629]
  ek_G = eseed[32:80]
  ct_G = ScalarMultBase(ek_G)
  ss_G = ScalarMult(ek_G, pk_G)

  (ss_M, ct_M) = ML-KEM-768.EncapsDerand(pk_M, eseed[0:32])
  ss = SharedSecret(ss_M, ss_G, ct_G, pk_G)
  ct = concat(ct_M, ct_G)
  return (ss, ct)

8.12. Decapsulation

def Decapsulate(ct, sk):
  (sk_M, sk_G, pk_M, pk_G) = expandDecapsulationKey(sk)
  ct_M = ct[0:1568]
  ct_G = ct[1568:1629]
  ss_M = ML-KEM-1024.Decapsulate(ct_M, sk_M)
  ss_G = ScalarMult(sk_G, ct_G)
  return SharedSecret(ss_M, ss_G, ct_G, pk_G)

ct is the 1629 byte ciphertext resulting from Encapsulate() sk is a 32 byte decapsulation key resulting from GenerateKeyPair()¶

Decapsulate() returns the 32 byte shared secret.¶

9.1. Rejection Sampling

Generate a random byte array with Ns bytes, and attempt to map to a Scalar by calling DeserializeScalar in constant time. If it succeeds, return the result. If it fails, try again with another random byte array, until the procedure succeeds. Failure to implement DeserializeScalar in constant time can leak information about the underlying corresponding Scalar.¶

As an optimization, if the group order is very close to a power of 2, it is acceptable to omit the rejection test completely. In particular, if the group order is p, and there is an integer b such that |p - 2^b| is less than 2^(b/2), then RandomScalar can simply return a uniformly random integer of at most b bits.¶

9.2. Wide Reduction

Generate a random byte array with l = ceil(((3 * ceil(log2(G.Order()))) / 2) / 8) bytes, and interpret it as an integer; reduce the integer modulo G.Order() and return the result. See Section 5 of [HASH-TO-CURVE] for the underlying derivation of l.¶

10.1. Fixed-length

Variable-length secrets are generally dangerous. In particular, using key material of variable length and processing it using hash functions may result in a timing side channel. In broad terms, when the secret is longer, the hash function may need to process more blocks internally. In some unfortunate circumstances, this has led to timing attacks, e.g. the Lucky Thirteen [LUCKY13] and Raccoon [RACCOON] attacks.¶

Furthermore, [AVIRAM] identified a risk of using variable-length secrets when the hash function used in the key derivation function is no longer collision-resistant.¶

If concatenation were to be used with values that are not fixed-length, a length prefix or other unambiguous encoding would need to be used to ensure that the composition of the two values is injective and requires a mechanism different from that specified in this document.¶

Therefore, this specification MUST only be used with algorithms which have fixed-length shared secrets (after the variant has been fixed by the algorithm identifier in the NamedGroup negotiation in Section 3.1).¶

11.1. More than two component KEMs

Design team decided to restrict the space to only two components, a traditional and a post-quantum KEM.¶

11.2. Parameterized output length

Not analyzed as part of any security proofs in the literature, and a complicatation deemed unnecessary.¶

11.3. Protocol-specific labels / info

The concrete instantiations have specific labels, protocol-specific information is out of scope.¶

11.4. Other Component Primitives

There is demand for other hybrid variants that either use different primitives (RSA, NTRU, Classic McEliece, FrodoKEM), parameters, or that use a combiner optimized for a specific use case. Other use cases could be covered in subsequent documents and not included here.¶

12.1. HPKE

TODO¶

13.1. Normative References

[FIPS203]

"Module-lattice-based key-encapsulation mechanism standard", National Institute of Standards and Technology (U.S.), DOI 10.6028/nist.fips.203, August 2024, <https://doi.org/10.6028/nist.fips.203>.

[HASH-TO-CURVE]

Faz-Hernandez, A., Scott, S., Sullivan, N., Wahby, R. S., and C. A. Wood, "Hashing to Elliptic Curves", RFC 9380, DOI 10.17487/RFC9380, August 2023, <https://www.rfc-editor.org/rfc/rfc9380>.

[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>.

[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>.

[RFC8017]

Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch, "PKCS #1: RSA Cryptography Specifications Version 2.2", RFC 8017, DOI 10.17487/RFC8017, November 2016, <https://www.rfc-editor.org/rfc/rfc8017>.

[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>.

13.2. Informative References

[ANSIX9.62]

ANS, "Public Key Cryptography for the Financial Services Industry: the Elliptic Curve Digital Signature Algorithm (ECDSA)", ANS X9.62-2005, November 2005.

[AVIRAM]

Nimrod Aviram, Benjamin Dowling, Ilan Komargodski, Kenny Paterson, Eyal Ronen, and Eylon Yogev, "[TLS] Combining Secrets in Hybrid Key Exchange in TLS 1.3", 1 September 2021, <https://mailarchive.ietf.org/arch/msg/tls/F4SVeL2xbGPaPB2GW_GkBbD_a5M/>.

[BDG2020]

"Separate Your Domains: NIST PQC KEMs, Oracle Cloning and Read-Only Indifferentiability", 2020, <https://eprint.iacr.org/2020/241.pdf>.

[CDM23]

Cremers, C., Dax, A., and N. Medinger, "Keeping Up with the KEMs: Stronger Security Notions for KEMs and automated analysis of KEM-based protocols", 2023, <https://eprint.iacr.org/2023/1933.pdf>.

[FIPS186]

"Digital Signature Standard (DSS)", National Institute of Standards and Technology (U.S.), DOI 10.6028/nist.fips.186-5, February 2023, <https://doi.org/10.6028/nist.fips.186-5>.

[GHP2018]

"KEM Combiners", 2018, <https://eprint.iacr.org/2018/024.pdf>.

[HKDF]

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/rfc/rfc5869>.

[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>.

[KSMW2024]

Kraemer, J., Struck, P., and M. Weishaupl, "Binding Security of Implicitly-Rejecting KEMs and Application to BIKE and HQC", n.d., <https://eprint.iacr.org/2024/1233>.

[LUCKY13]

Al Fardan, N. J. and K. G. Paterson, "Lucky Thirteen: Breaking the TLS and DTLS record protocols", n.d., <https://ieeexplore.ieee.org/iel7/6547086/6547088/06547131.pdf>.

[RACCOON]

Merget, R., Brinkmann, M., Aviram, N., Somorovsky, J., Mittmann, J., and J. Schwenk, "Raccoon Attack: Finding and Exploiting Most-Significant-Bit-Oracles in TLS-DH(E)", September 2020, <https://raccoon-attack.com/>.

[SCHMIEG2024]

Schmieg, S., "Unbindable Kemmy Schmidt: ML-KEM is neither MAL-BIND-K-CT nor MAL-BIND-K-PK", 2024, <https://eprint.iacr.org/2024/523.pdf>.

[SEC1]

"Elliptic Curve Cryptography, Standards for Efficient Cryptography Group, ver. 2", 2009, <https://secg.org/sec1-v2.pdf>.

[X25519]

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>.

[XWING]

"X-Wing: The Hybrid KEM You’ve Been Looking For", 2024, <https://eprint.iacr.org/2024/039.pdf>.