Design issues for hybrid key exchange in TLS 1.3

This document categorizes various design decisions one could make when implementing hybrid key exchange in TLS 1.3, with the goal of fostering discussion, providing options for short-term prototypes/experiments, and serving as a basis for eventual standardization. This document does not propose specific post-quantum mechanisms; see for more on the scope of this document. Comments are solicited and should be addressed to the TLS working group mailing list at tls@ietf.org and/or the author(s).

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 mechanisms based on different cryptographic assumptions (for example, 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 mechanisms remains unbroken. We use the term “component” algorithms to refer to the algorithms that are being combined in a hybrid key exchange. 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.

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 (but not all) of the 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 / elliptic curve Diffie–Hellman, and thus we do not necessarily have as much confidence in their fundamental security, or the concrete security level of specific parameterizations. Early adopters eager for post-quantum security may want to use hybrid key exchange to have the potential of post-quantum security 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.) Moreover, it is possible that even by the end of the NIST Post-Quantum Cryptography Standardization Project, and for a period of time thereafter, conservative users may not have full confidence in some algorithms. As such, there may be users for whom hybrid key exchange is an appropriate step prior to an eventual transition to next-generation algorithms.

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, nor algorithm identifiers nor encoding mechanisms for next-generation algorithms. (The outcomes of the NIST Post-Quantum Cryptography Standardization Project will inform this choice.) Authentication using next-generation algorithms. (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. But session authentication cannot be retroactively broken.)

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: Hybrid-aware client, hybrid-aware server: These parties should establish a hybrid shared secret. 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). 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 / ciphertext sizes for post-quantum algorithms range from hundreds of bytes to over one hundred kilobytes, so this impact can be substantially. 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. No duplicate information: Attempting to negotiate hybrid key exchange should not mean having to send multiple public keys of the same type.

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.

We identify four distinct axes along which one can make choices when integrating hybrid key exchange into TLS 1.3: How to negotiate the use of hybridization in general and component algorithms specifically? How many component algorithms can be combined? How should multiple key shares (public keys / ciphertexts) be conveyed? How should multiple shared secrets be combined? The remainder of this document outlines various options we have identified for each of these choices. Immediately below we provide a summary list. Options are labelled with a short code in parentheses to provide easy cross-referencing. (Neg) How to negotiate the use of hybridization in general and component algorithms specifically? (Neg-Ind) Negotiating component algorithms individually (Neg-Ind-1) Traditional algorithms in ClientHello supported_groups extension, next-gen algorithms in another extension (Neg-Ind-2) Both types of algorithms in supported_groups with external mapping to tradition/next-gen. (Neg-Ind-3) Both types of algorithms in supported_groups separated by a delimiter. (Neg-Comb) Negotiating component algorithms as a combination (Neg-Comb-1) Standardize NamedGroup identifiers for each desired combination. (Neg-Comb-2) Use placeholder identifiers in supported_groups with an extension defining the combination corresponding to each placeholder. (Neg-Comb-3) List combinations by inserting grouping delimiters into supported_groups list. (Num) How many component algorithms can be combined? (Num-2) Two. (Num-2+) Two or more. (Shares) How should multiple key shares (public keys / ciphertexts) be conveyed? (Shares-Concat) Concatenate each combination of key shares. (Shares-Multiple) Send individual key shares for each algorithm. (Shares-Ext-Additional) Use an extension to convey key shares for component algorithms. (Comb) How should multiple shared secrets be combined? (Comb-Concat) Concatenate the shared secrets then use directly in the TLS 1.3 key schedule. (Comb-XOR) XOR the shared secrets then use directly in the TLS 1.3 key schedule. (Comb-Chain) Extend the TLS 1.3 key schedule so that there is a stage of the key schedule for each shared secret. (Comb-AltInput) Use the second shared secret in an alternate (otherwise unused) input in the TLS 1.3 key schedule.

Recall that in TLS 1.3, the key exchange mechanism is negotiated via the supported_groups extension. The NamedGroup enum is a list of standardized groups for Diffie–Hellman key exchange, such as secp256r1, x25519, and ffdhe2048. The client, in its ClientHello message, lists its supported mechanisms in the supported_groups extension. The client also optionally includes the public key of one or more of these groups in the key_share extension as a guess of which mechanisms the server might accept in hopes of reducing the number of round trips. If the server is willing to use one of the client’s requested mechanisms, it responds with a key_share extension containing its public key for the desired mechanism. If the server is not willing to use any of the client’s requested mechanisms, the server responds with a HelloRetryRequest message that includes an extension indicating its preferred mechanism.

In these three approaches, the parties negotiate which traditional algorithm and which next-gen algorithm to use independently. The NamedGroup enum is extended to include algorithm identifiers for each next-gen algorithm.

The client advertises two lists to the server: one list containing its supported traditional mechanisms (e.g. via the existing ClientHello supported_groups extension), and a second list containing its supported next-generation mechanisms (e.g., via an additional ClientHello extension). A server could then select one algorithm from the traditional list, and one algorithm from the next-generation list. (This is the approach in .)

The client advertises a single list to the server which contains both its traditional and next-generation mechanisms (e.g., all in the existing ClientHello supported_groups extension), but with some external table provides a standardized mapping of those mechanisms as either “traditional” or “next-generation”. A server could then select two algorithms from this list, one from each category.

The client advertises a single list to the server delimited into sublists: one for its traditional mechanisms and one for its next-generation mechanisms, all in the existing ClientHello supported_groups extension, with a special code point serving as a delimiter between the two lists. For example, supported_groups = secp256r1, x25519, delimiter, nextgen1, nextgen4.

In these three approaches, combinations of key exchange mechanisms appear as a single monolithic block; the parties negotiate which of several combinations they wish to use.

The NamedGroup enum is extended to include algorithm identifiers for each combination of algorithms desired by the working group. There is no “internal structure” to the algorithm identifiers for each combination, they are simply new code points assigned arbitrarily. The client includes any desired combinations in its ClientHello supported_groups list, and the server picks one of these. This is the approach in and .

The NamedGroup enum is extended to include algorithm identifiers for each next-gen algorithm. Some additional field/extension is used to convey which combinations the parties wish to use. For example, in , there are distinguished NamedGroup called hybrid_marker 0, hybrid_marker 1, hybrid_marker 2, etc. This is complemented by a HybridExtension which contains mappings for each numbered hybrid_marker to the set of component key exchange algorithms (2 or more) for that proposed combination.

The client lists combinations in supported_groups list, using a special delimiter to indicate combinations. For example, supported_groups = combo_delimiter, secp256r1, nextgen1, combo_delimiter, secp256r1, nextgen4, standalone_delimiter, secp256r1, x25519 would indicate that the client’s highest preference is the combination secp256r1+nextgen1, the next highest preference is the combination secp2561+nextgen4, then the single algorithm secp256r1, then the single algorithm x25519. A hybrid-aware server would be able to parse these; a hybrid-unaware server would see unknown, secp256r1, unknown, unknown, secp256r1, unknown, unknown, secp256r1, x25519, which it would be able to process, although there is the potential that every “projection” of a hybrid list that is tolerable to a client does not result in list that is tolerable to the client.

Combinatorial explosion. (Neg-Comb-1) requires new identifiers to be defined for each desired combination. The other 4 options in this section do not. Extensions. (Neg-Ind-1) and (Neg-Comb-2) require new extensions to be defined. The other options in this section do not. New logic. All options in this section except (Neg-Comb-1) require new logic to process negotiation. Matching security levels. (Neg-Ind-1), (Neg-Ind-2), (Neg-Ind-3), and (Neg-Comb-2) allow algorithms of different claimed security level from their corresponding lists to be combined. For example, this could result in combining ECDH secp256r1 (classical security level 128) with NewHope-1024 (classical security level 256). Implementations dissatisfied with a mismatched security levels must either accept this mismatch or attempt to renegotiate. (Neg-Ind-1), (Neg-Ind-2), and (Neg-Ind-3) give control over the combination to the server; (Neg-Comb-2) gives control over the combination to the client. (Neg-Comb-1) only allows standardized combinations, which could be set by TLS working group to have matching security (provided security estimates do not evolve separately). Backwards-compability. TLS 1.3-compliant hybrid-unaware servers should ignore unreocgnized elements in supported_groups (Neg-Ind-2), (Neg-Ind-3), (Neg-Comb-1), (Neg-Comb-2) and unrecognized ClientHello extensions (Neg-Ind-1), (Neg-Comb-2). In (Neg-Ind-3) and (Neg-Comb-3), a server that is hybrid-unaware will ignore the delimiters in supported_groups, and thus might try to negotiate an algorithm individually that is only meant to be used in combination; depending on how such an implementation is coded, it may also encounter bugs when the same element appears multiple times in the list.

Exactly two algorithms can be combined together in hybrid key exchange. This is the approach taken in and .

Two or more algorithms can be combined together in hybrid key exchange. This is the approach taken in .

Restricting the number of component algorithms that can be hybridized to two substantially reduces the generality required. On the other hand, some adopters may want to further reduce risk by employing multiple next-gen algorithms built on different cryptographic assumptions.

In ECDH ephmeral key exchange, the client sends its ephmeral public key in the key_share extension of the ClientHello message, and the server sends its ephmeral public key in the key_share extension of the ServerHello message. For a general key encapsulation mechanism used for ephemeral key exchange, we imagine that that client generates a fresh KEM public key / secret pair for each connection, sends it to the client, and the server responds with a KEM ciphertext. For simplicity and consistency with TLS 1.3 terminology, we will refer to both of these types of objects as “key shares”. In hybrid key exchange, we have to decide how to convey the client’s two (or more) key shares, and the server’s two (or more) key shares.

The client concatenates the bytes representing its two key shares and uses this directly as the key_exchange value in a KeyShareEntry in its key_share extension. The server does the same thing. Note that the key_exchange value can be an octet string of length at most 2^16-1. This is the approach taken in , , and .

The client sends multiple key shares directly in the client_shares vectors of the ClientHello key_share extension. The server does the same. (Note that while the existing KeyShareClientHello struct allows for multiple key share entries, the existing KeyShareServerHello only permits a single key share entry, so some modification would be required to use this approach for the server to send multiple key shares.)

The client sends the key share for its traditional algorithm in the original key_share extension of the ClientHello message, and the key share for its next-gen algorithm in some additional extension in the ClientHello message. The server does the same thing. This is the approach taken in .

Backwards compatibility. (Shares-Multiple) is fully backwards compatible with non-hybrid-aware servers. (Shares-Ext-Additional) is backwards compatible with non-hybrid-aware servers provided they ignore unrecognized extensions. (Shares-Concat) is backwards-compatible with non-hybrid aware servers, but may result in duplication / additional round trips (see below). Duplication versus additional round trips. If a client wants to offer multiple key shares for multiple combinations in order to avoid retry requests, then the client may ended up sending a key share for one algorithm multiple times when using (Shares-Ext-Additional) and (Shares-Concat). (For example, if the client wants to send an ECDH-secp256r1 + McEliece123 key share, and an ECDH-secp256r1 + NewHope1024 key share, then the same ECDH public key may be sent twice. If the client also wants to offer a traditional ECDH-only key share for non-hybrid-aware implementations and avoid retry requests, then that same ECDH public key may be sent another time.) (Shares-Multiple) does not result in duplicate key shares.

Each component key exchange algorithm establishes a shared secret. These shared secrets must be combined in some 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.

Each party concatenates the shared secrets established by each component algorithm in an agreed-upon order, then uses feeds that through a key derivation function. In the context of TLS 1.3, this would mean using the concatenated shared secret in place of the (EC)DHE input to the second call to HKDF-Extract in the TLS 1.3 key schedule:

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(...) ]]> This is the approach used in , , and . analyzes the security of applying a KDF to concatenated KEM shared secrets, but their analysis does not exactly apply here since the transcript of ciphertexts is included in the KDF application (though it should follow relatively straightforwardly). analyzes the security of the (Comb-Concat) approach as abstracted in their dualPRF combiner. They show that, if the component KEMs are IND-CPA-secure (or IND-CCA-secure), then the values output by Derive-Secret are IND-CPA-secure (respectively, IND-CCA-secure). An important aspect of their analysis is that each ciphertext is input to the final PRF calls; this holds for TLS 1.3 since the Derive-Secret calls that derive output keys (application traffic secrets, and exporter and resumption master secrets) include the transcript hash as input.

Each party XORs the shared secrets established by each component algorithm (possibly after padding secrets of different lengths), then uses feeds that through a key derivation function. In the context of TLS 1.3, this would mean using the XORed shared secret in place of the (EC)DHE input to the second call to HKDF-Extract in the TLS 1.3 key schedule. analyzes the security of applying a KDF to the XORed KEM shared secrets, but their analysis does not quite apply here since the transcript of ciphertexts is included in the KDF application (though it should follow relatively straightforwardly).

Each party applies a chain of key derivation functions to the shared secrets established by each component algorithm in an agreed-upon order; roughly speaking: F(k1 || F(k2)). In the context of TLS 1.3, this would mean extending the key schedule to have one round of the key schedule applied for each component algorithm’s shared secret:

HKDF-Extract = Early Secret | +-----> Derive-Secret(...) +-----> Derive-Secret(...) +-----> Derive-Secret(...) | v Derive-Secret(., "derived", "") | v traditional_shared_secret -> HKDF-Extract ^^^^^^^^^^^^^^^^^^^^^^^^^ | Derive-Secret(., "derived", "") | v next_gen_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(...) ]]> This is the approach used in . analyzes the security of this approach as abstracted in their nested dual-PRF N combiner, showing a similar result as for the dualPRF combiner that it preserves IND-CPA (or IND-CCA) security. Again their analysis depends on each ciphertext being input to the final PRF (Derive-Secret) calls, which holds for TLS 1.3.

In the context of TLS 1.3, the next-generation shared secret is used in place of a currently unused input in the TLS 1.3 key schedule, namely replacing the 0 “IKM” input to the final HKDF-Extract:

HKDF-Extract = Early Secret | +-----> Derive-Secret(...) +-----> Derive-Secret(...) +-----> Derive-Secret(...) | v Derive-Secret(., "derived", "") | v traditional_shared_secret -> HKDF-Extract = Handshake Secret ^^^^^^^^^^^^^^^^^^^^^^^^^ | +-----> Derive-Secret(...) +-----> Derive-Secret(...) | v Derive-Secret(., "derived", "") | v next_gen_shared_secret -> HKDF-Extract = Master Secret ^^^^^^^^^^^^^^^^^^^^^^ | +-----> Derive-Secret(...) +-----> Derive-Secret(...) +-----> Derive-Secret(...) +-----> Derive-Secret(...) ]]> This approach is not taken in any of the known post-quantum/hybrid TLS drafts. However, it bears some similarities to the approach for using external PSKs in .

New logic. While (Comb-Concat) requires new logic to compute the concatenated shared secret, this value can then be used by the TLS 1.3 key schedule without changes to the key schedule logic. In contrast, (Comb-Chain) requires the TLS 1.3 key schedule to be extended for each extra component algorithm. Philosophical. The TLS 1.3 key schedule already applies a new stage for different types of keying material (PSK versus (EC)DHE), so (Comb-Chain) continues that approach. Efficiency. (Comb-Chain) increases the number of KDF applications for each component algorithm, whereas (Comb-Concat) and (Comb-AltInput) keep the number of KDF applications the same (though with potentially longer inputs). Extensibility. (Comb-AltInput) changes the use of an existing input, which might conflict with other future changes to the use of the input. More than 2 component algorithms. The techniques in (Comb-Concat) and (Comb-Chain) can naturally accommodate more than 2 component shared secrets since there is no distinction to how each shared secret is treated. (Comb-AltInput) would have to make some distinct, since the 2 component shared secrets are used in different ways; for example, the first shared secret is used as the “IKM” input in the 2nd HKDF-Extract call, and all subsequent shared secrets are concatenated to be used as the “IKM” input in the 3rd HKDF-Extract call.

None.

The majority of this document is about security considerations. As noted especially in , 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. While many natural approaches seem to achieve this, there can be subtleties (see for example the introduction of ). The rest of this section highlights a few unresolved questions related to security.

One security consideration that is not yet resolved is whether key encapsulation mechanisms used in TLS 1.3 must be secure against active attacks (IND-CCA), or whether security against passive attacks (IND-CPA) suffices. Existing security proofs of TLS 1.3 (such as , ) are formulated specifically around Diffie–Hellman and use an “actively secure” Diffie–Hellman assumption (PRF Oracle Diffie–Hellman (PRF-ODH)) rather than a “passively secure” DH assumption (e.g. decisional Diffie–Hellman (DDH)), but do not claim that the actively secure notion is required. In the context of TLS 1.2, show that, at least in one formalization, a passively secure assumption like DDH is insufficient (even when signatures are used for mutual authentication). Resolving this issue for TLS 1.3 is an open question.

TLS 1.3 allows for session resumption via a pre-shared key. When a pre-shared key is used during session establishment, an ephemeral key exchange can also be used to enhance forward secrecy. If the original key exchange was hybrid, should an ephemeral key exchange in a resumption of that original key exchange be required to use the same hybrid algorithms?

Some post-quantum key exchange algorithms have non-trivial failure rates: two honest parties may fail to agree on the same shared secret with non-negligible probability. Does a non-negligible failure rate affect the security of TLS? How should such a failure be treated operationally? What is an acceptable failure rate?

These ideas have grown from discussions with many colleagues, including Christopher Wood, Matt Campagna, and authors of the various hybrid Internet-Drafts and implementations cited in this document. 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.