University of Waterloo

dstebila@uwaterloo.ca

Cisco Systems

sfluhrer@cisco.com

University of Haifa and Amazon Web Services

shay.gueron@gmail.com

Internet-Draft Hybrid key exchange refers to using multiple key exchange algorithms simultaneously and combining the result with the goal of providing security even if all but one of the component algorithms is broken. It is motivated by transition to post-quantum cryptography. This document provides a construction for hybrid key exchange in the Transport Layer Security (TLS) protocol version 1.3. Discussion of this work is encouraged to happen on the TLS IETF mailing list tls@ietf.org or on the GitHub repository which contains the draft: https://github.com/dstebila/draft-ietf-tls-hybrid-design.

Introduction This document gives a construction for hybrid key exchange in TLS 1.3. The overall design approach is a simple, "concatenation"-based approach: each hybrid key exchange combination should be viewed as a single new key exchange method, negotiated and transmitted using the existing TLS 1.3 mechanisms. This document does not propose specific post-quantum mechanisms; see for more on the scope of this document.

Revision history

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

Earlier versions of this document categorized various design decisions one could make when implementing hybrid key exchange in TLS 1.3.

• Since draft-ietf-tls-hybrid-design-03:
  • Some wording changes
  • Remove design considerations appendix
• draft-ietf-tls-hybrid-design-03:
  • Remove specific code point examples and requested codepoint range for hybrid private use
  • Change "Open questions" to "Discussion"
  • Some wording changes
• draft-ietf-tls-hybrid-design-02:
  • Bump to version -02 to avoid expiry
• draft-ietf-tls-hybrid-design-01:
  • Forbid variable-length secret keys
  • Use fixed-length KEM public keys/ciphertexts
• draft-ietf-tls-hybrid-design-00:
  • Allow key_exchange values from the same algorithm to be reused across multiple KeyShareEntry records in the same ClientHello.
• draft-stebila-tls-hybrid-design-03:
  • Add requirement for KEMs to provide protection against key reuse.
  • Clarify FIPS-compliance of shared secret concatenation method.
• draft-stebila-tls-hybrid-design-02:
  • Design considerations from draft-stebila-tls-hybrid-design-00 and draft-stebila-tls-hybrid-design-01 are moved to the appendix.
  • A single construction is given in the main body.
• draft-stebila-tls-hybrid-design-01:
  • Add (Comb-KDF-1) and (Comb-KDF-2) options.
  • Add two candidate instantiations.
• draft-stebila-tls-hybrid-design-00: Initial version.

Terminology For the purposes of this document, it is helpful to be able to divide cryptographic algorithms into two classes:

• "Traditional" algorithms: Algorithms which are widely deployed today, but which may be deprecated in the future. In the context of TLS 1.3 in 2019, examples of traditional key exchange algorithms include elliptic curve Diffie-Hellman using secp256r1 or x25519, or finite-field Diffie-Hellman.
• "Next-generation" (or "next-gen") algorithms: Algorithms which are not yet widely deployed, but which may eventually be widely deployed. An additional facet of these algorithms may be that we have less confidence in their security due to them being relatively new or less studied. This includes "post-quantum" algorithms.

"Hybrid" key exchange, in this context, means the use of two (or more) key exchange algorithms based on different cryptographic assumptions, e.g., one traditional algorithm and one next-gen algorithm, with the purpose of the final session key being secure as long as at least one of the component key exchange algorithms remains unbroken. We use the term "component" algorithms to refer to the algorithms combined in a hybrid key exchange. We note that some authors prefer the phrase "composite" to refer to the use of multiple algorithms, to distinguish from "hybrid public key encryption" in which a key encapsulation mechanism and data encapsulation mechanism are combined to create public key encryption. The primary motivation of this document is preparing for post-quantum algorithms. However, it is possible that public key cryptography based on alternative mathematical constructions will be required independent of the advent of a quantum computer, for example because of a cryptanalytic breakthrough. As such we opt for the more generic term "next-generation" algorithms rather than exclusively "post-quantum" algorithms. Note that TLS 1.3 uses the phrase "groups" to refer to key exchange algorithms - for example, the supported_groups extension - since all key exchange algorithms in TLS 1.3 are Diffie-Hellman-based. As a result, some parts of this document will refer to data structures or messages with the term "group" in them despite using a key exchange algorithm that is not Diffie-Hellman-based nor a group.

Motivation for use of hybrid key exchange A hybrid key exchange algorithm allows early adopters eager for post-quantum security to have the potential of post-quantum security (possibly from a less-well-studied algorithm) while still retaining at least the security currently offered by traditional algorithms. They may even need to retain traditional algorithms due to regulatory constraints, for example FIPS compliance. Ideally, one would not use hybrid key exchange: one would have confidence in a single algorithm and parameterization that will stand the test of time. However, this may not be the case in the face of quantum computers and cryptanalytic advances more generally. Many (though not all) post-quantum algorithms currently under consideration are relatively new; they have not been subject to the same depth of study as RSA and finite-field or elliptic curve Diffie-Hellman, and thus the security community does not necessarily have as much confidence in their fundamental security, or the concrete security level of specific parameterizations. Moreover, it is possible that after next-generation algorithms are defined, and for a period of time thereafter, conservative users may not have full confidence in some algorithms. Some users may want to accelerate adoption of post-quantum cryptography due the threat of retroactive decryption: if a cryptographic assumption is broken due to the advent of a quantum computer or some other cryptanalytic breakthrough, confidentiality of information can be broken retroactively by any adversary who has passively recorded handshakes and encrypted communications. Hybrid key exchange enables potential security against retroactive decryption while not fully abandoning classical cryptosystems. As such, there may be users for whom hybrid key exchange is an appropriate step prior to an eventual transition to next-generation algorithms.

Scope This document focuses on hybrid ephemeral key exchange in TLS 1.3 . It intentionally does not address:

• Selecting which next-generation algorithms to use in TLS 1.3, or algorithm identifiers or encoding mechanisms for next-generation algorithms. This selection will be based on the recommendations by the Crypto Forum Research Group (CFRG), which is currently waiting for the results of the NIST Post-Quantum Cryptography Standardization Project .
• Authentication using next-generation algorithms. While quantum computers could retroactively decrypt previous sessions, session authentication cannot be retroactively broken.

Goals The primary goal of a hybrid key exchange mechanism is to facilitate the establishment of a shared secret which remains secure as long as as one of the component key exchange mechanisms remains unbroken. In addition to the primary cryptographic goal, there may be several additional goals in the context of TLS 1.3:

• Backwards compatibility: Clients and servers who are "hybrid-aware", i.e., compliant with whatever hybrid key exchange standard is developed for TLS, should remain compatible with endpoints and middle-boxes that are not hybrid-aware. The three scenarios to consider are:
  1. Hybrid-aware client, hybrid-aware server: These parties should establish a hybrid shared secret.
  2. Hybrid-aware client, non-hybrid-aware server: These parties should establish a traditional shared secret (assuming the hybrid-aware client is willing to downgrade to traditional-only).
  3. Non-hybrid-aware client, hybrid-aware server: These parties should establish a traditional shared secret (assuming the hybrid-aware server is willing to downgrade to traditional-only).
  Ideally backwards compatibility should be achieved without extra round trips and without sending duplicate information; see below.
• High performance: Use of hybrid key exchange should not be prohibitively expensive in terms of computational performance. In general this will depend on the performance characteristics of the specific cryptographic algorithms used, and as such is outside the scope of this document. See for preliminary results about performance characteristics.
• Low latency: Use of hybrid key exchange should not substantially increase the latency experienced to establish a connection. Factors affecting this may include the following.
  • The computational performance characteristics of the specific algorithms used. See above.
  • The size of messages to be transmitted. Public key and ciphertext sizes for post-quantum algorithms range from hundreds of bytes to over one hundred kilobytes, so this impact can be substantial. See for preliminary results in a laboratory setting, and for preliminary results on more realistic networks.
  • Additional round trips added to the protocol. See below.
• No extra round trips: Attempting to negotiate hybrid key exchange should not lead to extra round trips in any of the three hybrid-aware/non-hybrid-aware scenarios listed above.
• Minimal duplicate information: Attempting to negotiate hybrid key exchange should not mean having to send multiple public keys of the same type.

Key encapsulation mechanisms This document models key agreement as key encapsulation mechanisms (KEMs), which consist of three algorithms:

• KeyGen() -> (pk, sk): A probabilistic key generation algorithm, which generates a public key pk and a secret key sk.
• Encaps(pk) -> (ct, ss): A probabilistic encapsulation algorithm, which takes as input a public key pk and outputs a ciphertext ct and shared secret ss.
• Decaps(sk, ct) -> ss: A decapsulation algorithm, which takes as input a secret key sk and ciphertext ct and outputs a shared secret ss, or in some cases a distinguished error value.

The main security property for KEMs is indistinguishability under adaptive chosen ciphertext attack (IND-CCA2), which means that shared secret values should be indistinguishable from random strings even given the ability to have other arbitrary ciphertexts decapsulated. IND-CCA2 corresponds to security against an active attacker, and the public key / secret key pair can be treated as a long-term key or reused. A common design pattern for obtaining security under key reuse is to apply the Fujisaki-Okamoto (FO) transform or a variant thereof . A weaker security notion is indistinguishability under chosen plaintext attack (IND-CPA), which means that the shared secret values should be indistinguishable from random strings given a copy of the public key. IND-CPA roughly corresponds to security against a passive attacker, and sometimes corresponds to one-time key exchange. Key exchange in TLS 1.3 is phrased in terms of Diffie-Hellman key exchange in a group. DH key exchange can be modeled as a KEM, with KeyGen corresponding to selecting an exponent x as the secret key and computing the public key g^x; encapsulation corresponding to selecting an exponent y, computing the ciphertext g^y and the shared secret g^(xy), and decapsulation as computing the shared secret g^(xy). See for more details of such Diffie-Hellman-based key encapsulation mechanisms. TLS 1.3 does not require that ephemeral public keys be used only in a single key exchange session; some implementations may reuse them, at the cost of limited forward secrecy. As a result, any KEM used in the manner described in this document MUST explicitly be designed to be secure in the event that the public key is reused, such as achieving IND-CCA2 security or having a transform like the Fujisaki-Okamoto transform applied. While it is recommended that implementations avoid reuse of KEM public keys, implementations that do reuse KEM public keys MUST ensure that the number of reuses of a KEM public key abides by any bounds in the specification of the KEM or subsequent security analyses. Implementations MUST NOT reuse randomness in the generation of KEM ciphertexts.

Construction for hybrid key exchange

Negotiation Each particular combination of algorithms in a hybrid key exchange will be represented as a NamedGroup and sent in the supported_groups extension. No internal structure or grammar is implied or required in the value of the identifier; they are simply opaque identifiers. Each value representing a hybrid key exchange will correspond to an ordered pair of two algorithms. For example, a future document could specify that one codepoint corresponds to secp256r1+PQALG1, and another corresponds to x25519+PQALG1. (We note that this is independent from future documents standardizing solely post-quantum key exchange methods, which would have to be assigned their own identifier.) Specific values shall be standardized by IANA in the TLS Supported Groups registry.

Transmitting public keys and ciphertexts We take the relatively simple "concatenation approach": the messages from the two algorithms being hybridized will be concatenated together and transmitted as a single value, to avoid having to change existing data structures. The values are directly concatenated, without any additional encoding or length fields; this assumes that the representation and length of elements is fixed once the algorithm is fixed. If concatenation were to be used with values that are not fixed-length, a length prefix or other unambiguous encoding must be used to ensure that the composition of the two values is injective and requires a mechanism different from that specified in this document. Recall that in TLS 1.3 a KEM public key or KEM ciphertext is represented as a KeyShareEntry: ; } KeyShareEntry; ]]> These are transmitted in the extension_data fields of KeyShareClientHello and KeyShareServerHello extensions: ; } KeyShareClientHello; struct { KeyShareEntry server_share; } KeyShareServerHello; ]]> The client's shares are listed in descending order of client preference; the server selects one algorithm and sends its corresponding share. For a hybrid key exchange, the key_exchange field of a KeyShareEntry is the concatenation of the key_exchange field for each of the constituent algorithms. The order of shares in the concatenation is the same as the order of algorithms indicated in the definition of the NamedGroup. For the client's share, the key_exchange value contains the concatenation of the pk outputs of the corresponding KEMs' KeyGen algorithms, if that algorithm corresponds to a KEM; or the (EC)DH ephemeral key share, if that algorithm corresponds to an (EC)DH group. For the server's share, the key_exchange value contains concatenation of the ct outputs of the corresponding KEMs' Encaps algorithms, if that algorithm corresponds to a KEM; or the (EC)DH ephemeral key share, if that algorithm corresponds to an (EC)DH group. requires that ``The key_exchange values for each KeyShareEntry MUST be generated independently.'' In the context of this document, since the same algorithm may appear in multiple named groups, we relax the above requirement to allow the same key_exchange value for the same algorithm to be reused in multiple KeyShareEntry records sent in within the same ClientHello. However, key_exchange values for different algorithms MUST be generated independently.

Shared secret calculation Here we also take a simple "concatenation approach": the two shared secrets are concatenated together and used as the shared secret in the existing TLS 1.3 key schedule. Again, we do not add any additional structure (length fields) in the concatenation procedure: among all Round 3 finalists and alternate candidates, once the algorithm and variant are specified, the shared secret output length is fixed. In other words, the shared secret is calculated as and inserted into the TLS 1.3 key schedule in place of the (EC)DHE shared secret: HKDF-Extract = Early Secret | +-----> Derive-Secret(...) +-----> Derive-Secret(...) +-----> Derive-Secret(...) | v Derive-Secret(., "derived", "") | v concatenated_shared_secret -> HKDF-Extract = Handshake Secret ^^^^^^^^^^^^^^^^^^^^^^^^^^ | +-----> Derive-Secret(...) +-----> Derive-Secret(...) | v Derive-Secret(., "derived", "") | v 0 -> HKDF-Extract = Master Secret | +-----> Derive-Secret(...) +-----> Derive-Secret(...) +-----> Derive-Secret(...) +-----> Derive-Secret(...) ]]> FIPS-compliance of shared secret concatenation. or give NIST recommendations for key derivation methods in key exchange protocols. Some hybrid combinations may combine the shared secret from a NIST-approved algorithm (e.g., ECDH using the nistp256/secp256r1 curve) with a shared secret from a non-approved algorithm (e.g., post-quantum). lists simple concatenation as an approved method for generation of a hybrid shared secret in which one of the constituent shared secret is from an approved method.

Discussion Larger public keys and/or ciphertexts. The HybridKeyExchange struct in limits public keys and ciphertexts to 2^16-1 bytes; this is bounded by the same (2^16-1)-byte limit on the key_exchange field in the KeyShareEntry struct. Some post-quantum KEMs have larger public keys and/or ciphertexts; for example, Classic McEliece's smallest parameter set has public key size 261,120 bytes. Hence this draft can not accommodate all current NIST Round 3 candidates. Duplication of key shares. Concatenation of public keys in the HybridKeyExchange struct as described in can result in sending duplicate key shares. For example, if a client wanted to offer support for two combinations, say "secp256r1+sikep503" and "x25519+sikep503", it would end up sending two sikep503 public keys, since the KeyShareEntry for each combination contains its own copy of a sikep503 key. This duplication may be more problematic for post-quantum algorithms which have larger public keys. Failures. Some post-quantum key exchange algorithms have non-zero probability of failure, meaning two honest parties may derive different shared secrets. This would cause a handshake failure. All current NIST Round 3 candidates have either 0 or cryptographically small failure rate; if other algorithms are used, implementers should be aware of the potential of handshake failure. Clients can retry if a failure is encountered.

IANA Considerations Identifiers for specific key exchange algorithm combinations will be defined in later documents.

Security Considerations The shared secrets computed in the hybrid key exchange should be computed in a way that achieves the "hybrid" property: the resulting secret is secure as long as at least one of the component key exchange algorithms is unbroken. See and for an investigation of these issues. Under the assumption that shared secrets are fixed length once the combination is fixed, the construction from corresponds to the dual-PRF combiner of which is shown to preserve security under the assumption that the hash function is a dual-PRF. As noted in , KEMs used in the manner described in this document MUST explicitly be designed to be secure in the event that the public key is reused, such as achieving IND-CCA2 security or having a transform like the Fujisaki-Okamoto transform applied. Some IND-CPA-secure post-quantum KEMs (i.e., without countermeasures such as the FO transform) are completely insecure under public key reuse; for example, some lattice-based IND-CPA-secure KEMs are vulnerable to attacks that recover the private key after just a few thousand samples . Public keys, ciphertexts, and secrets should be constant length. This document assumes that the length of each public key, ciphertext, and shared secret is fixed once the algorithm is fixed. This is the case for all Round 3 finalists and alternate candidates. Note that variable-length secrets are, generally speaking, dangerous. In particular, when using key material of variable length and processing it using hash functions, a timing side channel may arise. 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 and Raccoon attacks. Furthermore, identified a risk of using variable-length secrets when the hash function used in the key derivation function is no longer collision-resistant. 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 ).

Acknowledgements These ideas have grown from discussions with many colleagues, including Christopher Wood, Matt Campagna, Eric Crockett, authors of the various hybrid Internet-Drafts and implementations cited in this document, and members of the TLS working group. The immediate impetus for this document came from discussions with attendees at the Workshop on Post-Quantum Software in Mountain View, California, in January 2019. Daniel J. Bernstein and Tanja Lange commented on the risks of reuse of ephemeral public keys. Matt Campagna and the team at Amazon Web Services provided additional suggestions. Nimrod Aviram proposed restricting to fixed-length secrets.

References Normative References This document specifies version 1.3 of the Transport Layer Security (TLS) protocol. TLS allows client/server applications to communicate over the Internet in a way that is designed to prevent eavesdropping, tampering, and message forgery. This document updates RFCs 5705 and 6066, and obsoletes RFCs 5077, 5246, and 6961. This document also specifies new requirements for TLS 1.2 implementations. Informative References AWS AWS Hybrid key exchange refers to executing two independent key exchanges and feeding the two resulting shared secrets into a Pseudo Random Function (PRF), with the goal of deriving a secret which is as secure as the stronger of the two key exchanges. This document describes new hybrid key exchange schemes for the Transport Layer Security 1.2 (TLS) protocol. The key exchange schemes are based on combining Elliptic Curve Diffie-Hellman (ECDH) with a post-quantum key encapsulation method (PQ KEM) using the existing TLS PRF. This document specifies a TLS 1.3 extension that allows a server to authenticate with a combination of a certificate and an external pre-shared key (PSK). ICANN Quantum computing is the study of computers that use quantum features in calculations. For over 20 years, it has been known that if very large, specialized quantum computers could be built, they could have a devastating effect on asymmetric classical cryptographic algorithms such as RSA and elliptic curve signatures and key exchange, as well as (but in smaller scale) on symmetric cryptographic algorithms such as block ciphers, MACs, and hash functions. There has already been a great deal of study on how to create algorithms that will resist large, specialized quantum computers, but so far, the properties of those algorithms make them onerous to adopt before they are needed. Small quantum computers are being built today, but it is still far from clear when large, specialized quantum computers will be built that can recover private or secret keys in classical algorithms at the key sizes commonly used today. It is important to be able to predict when large, specialized quantum computers usable for cryptanalysis will be possible so that organization can change to post-quantum cryptographic algorithms well before they are needed. This document describes quantum computing, how it might be used to attack classical cryptographic algorithms, and possibly how to predict when large, specialized quantum computers will become feasible. Post-Quantum Post-Quantum Cisco Systems Cisco Systems ISARA Corporation Philips ELVIS-PLUS This document describes how to extend Internet Key Exchange Protocol Version 2 (IKEv2) so that the shared secret exchanged between peers has resistance against quantum computer attacks. The basic idea is to exchange one or more post-quantum key exchange payloads in conjunction with the existing (Elliptic Curve) Diffie-Hellman payload. The possibility of quantum computers poses a serious challenge to cryptographic algorithms deployed widely today. The Internet Key Exchange Protocol Version 2 (IKEv2) is one example of a cryptosystem that could be broken; someone storing VPN communications today could decrypt them at a later time when a quantum computer is available. It is anticipated that IKEv2 will be extended to support quantum-secure key exchange algorithms; however, that is not likely to happen in the near term. To address this problem before then, this document describes an extension of IKEv2 to allow it to be resistant to a quantum computer by using preshared keys. Mozilla Cloudflare This draft specifies a TLS key exchange that combines the post- quantum key exchange, Supersingular elliptic curve isogenie diffie- hellman (SIDH), with elliptic curve Diffie-Hellman (ECDHE) key exchange. n.d. National Institute of Standards and Technology (NIST) n.d. National Institute of Standards and Technology (NIST) National Institute of Standards and Technology (NIST) Open Quantum Safe Project Open Quantum Safe Project Amazon Web Services This document defines a Transport Layer Security (TLS) extension that allows parties to establish an additional shared secret using a second key exchange algorithm and incorporates this shared secret into the TLS key schedule. This document describes the Quantum-Safe Hybrid ciphersuite, a new cipher suite providing modular design for quantum-safe cryptography to be adopted in the handshake for the Transport Layer Security (TLS) protocol version 1.2. In particular, it specifies the use of the NTRUEncrypt encryption scheme in a TLS handshake. Onboard Security Onboard Security Cisco Systems Philips This document describes the Quantum-Safe Hybrid Key Exchange, a mechanism for providing modular design for quantum-safe cryptography to be adopted in the handshake for the Transport Layer Security (TLS) protocol version 1.3. This note describes the eXtended Merkle Signature Scheme (XMSS), a hash-based digital signature system that is based on existing descriptions in scientific literature. This note specifies Winternitz One-Time Signature Plus (WOTS+), a one-time signature scheme; XMSS, a single-tree scheme; and XMSS^MT, a multi-tree variant of XMSS. Both XMSS and XMSS^MT use WOTS+ as a main building block. XMSS provides cryptographic digital signatures without relying on the conjectured hardness of mathematical problems. Instead, it is proven that it only relies on the properties of cryptographic hash functions. XMSS provides strong security guarantees and is even secure when the collision resistance of the underlying hash function is broken. It is suitable for compact implementations, is relatively simple to implement, and naturally resists side-channel attacks. Unlike most other signature systems, hash-based signatures can so far withstand known attacks using quantum computers. Cisco Inria Inria Cloudflare This document describes a scheme for hybrid public-key encryption (HPKE). This scheme provides a variant of public-key encryption of arbitrary-sized plaintexts for a recipient public key. It also includes three authenticated variants, including one which authenticates possession of a pre-shared key, and two optional ones which authenticate possession of a KEM private key. HPKE works for any combination of an asymmetric key encapsulation mechanism (KEM), key derivation function (KDF), and authenticated encryption with additional data (AEAD) encryption function. Some authenticated variants may not be supported by all KEMs. We provide instantiations of the scheme using widely used and efficient primitives, such as Elliptic Curve Diffie-Hellman key agreement, HKDF, and SHA2. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF.

Related work Quantum computing and post-quantum cryptography in general are outside the scope of this document. For a general introduction to quantum computing, see a standard textbook such as . For an overview of post-quantum cryptography as of 2009, see . For the current status of the NIST Post-Quantum Cryptography Standardization Project, see . For additional perspectives on the general transition from classical to post-quantum cryptography, see for example and , among others. There have been several Internet-Drafts describing mechanisms for embedding post-quantum and/or hybrid key exchange in TLS:

• Internet-Drafts for TLS 1.2: ,
• Internet-Drafts for TLS 1.3: , ,

There have been several prototype implementations for post-quantum and/or hybrid key exchange in TLS:

• Experimental implementations in TLS 1.2: , , , ,
• Experimental implementations in TLS 1.3: , ,

These experimental implementations have taken an ad hoc approach and not attempted to implement one of the drafts listed above. Unrelated to post-quantum but still related to the issue of combining multiple types of keying material in TLS is the use of pre-shared keys, especially the recent TLS working group document on including an external pre-shared key . Considering other IETF standards, there is work on post-quantum preshared keys in IKEv2 and a framework for hybrid key exchange in IKEv2 . The XMSS hash-based signature scheme has been published as an informational RFC by the IRTF . In the academic literature, initiated the study of combining multiple symmetric encryption schemes; , , and examined combining multiple public key encryption schemes, and coined the term "robust combiner" to refer to a compiler that constructs a hybrid scheme from individual schemes while preserving security properties. and examined combining multiple key encapsulation mechanisms.