Combiner function for hybrid key encapsulation mechanisms (Hybrid KEMs)

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Copyright (c) 2023 IETF Trust and the persons identified as the document authors. All rights reserved.¶

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Table of Contents

1. Terminology

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].¶

def kemKeyGen() -> (pk, sk)
def kemEncaps(pk) -> (ct, ss)
def kemDecaps(ct, sk) -> ss

2. Introduction

The need for a KEM combiner function arises in three different contexts within IETF security protocols:¶

1. KEM / PSK hybrids where the output of a KEM is combined with a static pre-shared key.¶
2. Post-quantum / traditional hybrid KEMs where output of a post-quantum KEM is combined with the output of a classical key transport or key exchange algorithm.¶
3. KEM-based authenticated key exchanges (AKEs) where the output of two or more KEMs performed in different directions are combined.¶

This document normalizes a mechanisms for combining the output of two or more KEMs.¶

3. KEM Combiner construction

A KEM combiner is a function that takes in two or more shared secrets SS_i and returns a combined shared secret SS, where all values are byte arrays.¶

SS = kemCombiner(SS_1, SS_2, ..., SS_n)

This document assumes that shared secrets are the output of a KEM, but without loss of generality they MAY also be any other source of cryptographic key material, such as pre-shared keys (PSKs), with PQ/PSK being a quantum-safe migration strategy being made available by some protocols, see for example IKEv2 in [RFC8784].¶

In general it is desirable to use a multi-PRF as a KEM combiner, a function that can be keyed by any input. The following simple yet generic construction can be used in all IETF protocols that need to combine the output of two or more KEMs:¶

KDF(counter || K_1 || ... || K_n || fixedInfo, outputBits)

where:¶

• KDF represents a suitable choice of cryptographic key derivation function,¶
• K_i represent the constant-length input keys,¶
• fixedInfo is some protocol-specific KDF binding,¶
• counter parameter is instantiation-specific and is discussed in Section 4.¶
• outputBits determines the length of the key,¶
• || represents concatenation.¶

In section Section 4 are listed several possible practical instantiations, in compliance with NIST SP-800 56Cr2 [SP800-56C].¶

Each K_i MUST be constant in length, therefore the secret shares SS_i can be used directly only if they are guaranteed to be constant length. For all other cases, it is REQUIRED to hash them first:¶

K_i = H(SS_i)

Any protocols making use of this construction MUST either hash all inputs SS_i, or justify that any un-hashed inputs will always be fixed length.¶

4. Practical instantiations

The KDF MUST be instantiated with one of the following Keccak-based option. Each instance defines a function to be used as KDF, a hash H function to optionally derive the K_i, and a counter.¶

1. KDF = SHA3-256 and H = SHA3-256, with hashSize = 256 bit.¶
2. KDF = SHA3-512 and H = SHA3-512, with hashSize = 512 bit.¶
3. KDF = KMAC128 and H = SHA3-256, with hashSize = 128 bit.¶
4. KDF = KMAC256 and H = SHA3-512, with hashSize = 256 bit.¶

5. IANA Considerations

None.¶

6. Security Considerations

The proposed instantiations in Section 4 are practical multi-PRFs and this specification limits to the use of Keccak-based constructions. The sponge construction was proven to be indifferentiable from a random oracle [SPONGE]. More precisely, for a given capacity c the indifferentiability proof shows that assuming there are no weaknesses found in the Keccak permutation, an attacker has to make an expected number of 2^(c/2) calls to the permutation to tell Keccak from a random oracle. For a random oracle, a difference in only a single bit gives an unrelated, uniformly random output. Hence, to be able to distinguish a key K, derived from shared keys K_i from a random bit string, an adversary has to correctly guess all key shares K_i entirely.¶

Acknowledgements

This document incorporates contributions and comments from a large group of experts. The authors would especially like to acknowledge the expertise and tireless dedication of the following people, who attended many long meetings and generated millions of bytes of electronic mail and VOIP traffic over the past years in pursuit of this document:¶

Douglas Stebila, Nimrod Aviram, Andreas Huelsing, and Stavros Kousidis.¶

We are grateful to all, including any contributors who may have been inadvertently omitted from this list.¶

This document borrows text from similar documents, including those referenced below. Thanks go to the authors of those documents. "Copying always makes things easier and less error prone" - [RFC8411].¶

Authors' Addresses