Internet Engineering Task Force (IETF) D. Stebila
Request for Comments: 9954 University of Waterloo
Category: Informational S. Fluhrer
ISSN: 2070-1721 Cisco Systems
S. Gueron
U. Haifa & Meta
April 2026
Hybrid Key Exchange in TLS 1.3
Abstract
Hybrid key exchange refers to using multiple key exchange algorithms
simultaneously and combining the result with the goal of providing
security even if a way is found to defeat the encryption for all but
one of the component algorithms. It is motivated by the transition
to post-quantum cryptography. This document provides a construction
for hybrid key exchange in the Transport Layer Security (TLS)
protocol version 1.3.
Status of This Memo
This document is not an Internet Standards Track specification; it is
published for informational purposes.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Not all documents
approved by the IESG are candidates for any level of Internet
Standard; see Section 2 of RFC 7841.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
https://www.rfc-editor.org/info/rfc9954.
Copyright Notice
Copyright (c) 2026 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
(https://trustee.ietf.org/license-info) in effect on the date of
publication of this document. Please review these documents
carefully, as they describe your rights and restrictions with respect
to this document. Code Components extracted from this document must
include Revised BSD License text as described in Section 4.e of the
Trust Legal Provisions and are provided without warranty as described
in the Revised BSD License.
Table of Contents
1. Introduction
1.1. Terminology
1.2. Motivation for Use of Hybrid Key Exchange
1.3. Scope
1.4. Goals
2. Key Encapsulation Mechanisms
3. Construction for Hybrid Key Exchange
3.1. Negotiation
3.2. Transmitting Public Keys and Ciphertexts
3.3. Shared Secret Calculation
4. Discussion
5. IANA Considerations
6. Security Considerations
7. References
7.1. Normative References
7.2. Informative References
Appendix A. Related Work
Acknowledgements
Authors' Addresses
1. 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, method that should be negotiated and
transmitted using the existing TLS 1.3 mechanisms.
This document does not propose specific post-quantum mechanisms; see
Section 1.3 for more on the scope of this document.
1.1. 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.
For the purposes of this document, it is helpful to divide
cryptographic algorithms into two classes:
* "Traditional" algorithms: Algorithms that are widely deployed
today but may be deprecated in the future. In the context of TLS
1.3, examples of traditional key exchange algorithms include
Elliptic Curve Diffie-Hellman (ECDH) using secp256r1 or x25519 or
finite field Diffie-Hellman.
* "Next-generation" (or "next-gen") algorithms: Algorithms that are
not yet widely deployed but may eventually be widely deployed. An
additional facet of these algorithms may be is that the cryptographic
community has may have less confidence in their security due to them
being relatively new or less studied. This includes "post-quantum" "post-
quantum" algorithms.
In this context, "hybrid" key exchange means the use of two (or more)
key exchange algorithms based on different cryptographic assumptions,
e.g., one traditional algorithm and one next-generation 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.
When one of the algorithms is traditional and one is post-quantum,
this is a Post-Quantum Traditional Hybrid Scheme [PQUIP-TERM]; while
this is the initial use case for this document, the document is not
limited to this case. This document uses the term "component"
algorithms to refer to the algorithms combined in a hybrid key
exchange.
Some researchers prefer the term "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.
It is intended that the component algorithms within a hybrid key
exchange are to be performed, that is, negotiated and transmitted,
within the TLS 1.3 handshake. Any out-of-band method of exchanging
keying material is considered out-of-scope.
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 desired to
mitigate risks independent of the advent of a quantum computer, for
example, because of a cryptanalytic breakthrough. As such, this
document opts for the more generic term "next-generation" algorithms
rather than exclusively "post-quantum" algorithms.
Note that TLS 1.3 uses the term "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 neither Diffie-Hellman-based nor a group.
1.2. 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, US National Institute of Standards and
Technology (NIST) 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; 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 to the threat of retroactive decryption (also known
as "harvest-now-decrypt-later"): 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 traditional 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. Users should consider the confidence they have in each
hybrid component to assess that the hybrid system meets the desired
motivation.
1.3. Scope
This document focuses on hybrid ephemeral key exchange in TLS 1.3
[TLS13]. 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.
* Authentication using next-generation algorithms. While quantum
computers could retroactively decrypt previous sessions, session
authentication cannot be retroactively broken.
1.4. Goals
The primary goal of a hybrid key exchange mechanism is to facilitate
the establishment of a shared secret that remains secure as long 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*: 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
middleboxes 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 non-hybrid shared secret (assuming the
hybrid-aware client is willing to downgrade to non-hybrid-
only).
3. Non-hybrid-aware client, hybrid-aware server: These parties
should establish a non-hybrid shared secret (assuming the
hybrid-aware server is willing to downgrade to non-hybrid-
only).
Ideally, backwards compatibility should be achieved without extra
round trips and without sending duplicate information; see below.
* *High performance*: 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 [PST] for preliminary
results about performance characteristics.
* *Low latency*: 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 [PST] for preliminary results in a
laboratory setting and [LANGLEY] for preliminary results on
more realistic networks.
- Additional round trips added to the protocol. See below.
* *No No extra round trips*: trips: Attempting to negotiate hybrid key exchange
should not lead to extra round trips in any of the three
hybrid-aware/non-hybrid-aware hybrid-
aware/non-hybrid-aware scenarios listed above.
* *Minimal Minimal duplicate information*: information: Attempting to negotiate hybrid key
exchange should not mean having to send multiple public keys of
the same type.
The tolerance for lower performance and increased latency due to use
of hybrid key exchange will depend on the context and use case of the
systems and the network involved.
2. 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 and secret key pair can be treated as a long-term key or
reused (see, for example, [KATZ] or [HHK] for definitions of IND-CCA2
and IND-CPA security).
reused. A common design pattern for obtaining security under key
reuse is to apply the Fujisaki-Okamoto (FO) transform [FO] or a
variant thereof [HHK].
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.
See [KATZ] or [HHK] for definitions of IND-CCA2 and IND-CPA security.
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
(1) KeyGen corresponding to selecting an exponent x as the secret key
and computing the public key g^x, (2) encapsulation corresponding to
selecting an exponent y and computing the ciphertext g^y and the
shared secret g^(xy), and (3) decapsulation as corresponding to
computing the shared secret g^(xy). See [HPKE] for more details of
such Diffie-Hellman-
based Diffie-Hellman-based key encapsulation mechanisms. Diffie-Hellman Diffie-
Hellman key exchange, when viewed as a KEM, does not formally satisfy
IND-CCA2 security but is still safe to use for ephemeral key exchange
in TLS 1.3; see, for example, [DOWLING].
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. Finite field
and elliptic curve Diffie-Hellman key exchange methods used in TLS
1.3 satisfy this criteria. For generic KEMs, this means satisfying
IND-CCA2 security or having a transform like the Fujisaki-Okamoto
transform [FO] [HHK] 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.
3. Construction for Hybrid Key Exchange
3.1. 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 or more algorithms. (Note that this is
independent from future documents standardizing solely post-quantum
key exchange methods, which would have to be assigned their own
identifier.)
3.2. Transmitting Public Keys and Ciphertexts
This document takes the relatively simple "concatenation approach":
The messages from the two or more 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; the
representation and length of elements MUST be fixed once the
algorithm is fixed.
Recall that, in TLS 1.3 ([TLS13], Section 4.2.8), a KEM public key or
KEM ciphertext is represented as a KeyShareEntry:
struct {
NamedGroup group;
opaque key_exchange<1..2^16-1>;
} KeyShareEntry;
These are transmitted in the extension_data fields of
KeyShareClientHello and KeyShareServerHello extensions:
struct {
KeyShareEntry client_shares<0..2^16-1>;
} 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
MUST be 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.
Section 4.2.8 of [TLS13] requires that "The key_exchange values for
each KeyShareEntry MUST be generated independently." In the context
of this document, the same algorithm may appear in multiple named
groups; thus, this document relaxes the above requirement to allow
the same key_exchange value for the same algorithm to be reused in
multiple KeyShareEntry records sent within the same ClientHello.
However, key_exchange values for different algorithms MUST be
generated independently. Explicitly, if the NamedGroup is the hybrid
key exchange MyECDHMyPQKEM, the KeyShareEntry.key_exchange values
MUST be generated in one of the following two ways:
Fully independently:
MyECDHMyPQKEM.KeyGen() = (MyECDH.KeyGen(), MyPQKEM.KeyGen())
KeyShareClientHello {
KeyShareEntry {
NamedGroup: 'MyECDH',
key_exchange: MyECDH.KeyGen()
},
KeyShareEntry {
NamedGroup: 'MyPQKEM',
key_exchange: MyPQKEM.KeyGen()
},
KeyShareEntry {
NamedGroup: 'MyECDHMyPQKEM',
key_exchange: MyECDHMyPQKEM.KeyGen()
},
}
Reusing key_exchange values of the same component algorithm within
the same ClientHello:
myecdh_key_share = MyECDH.KeyGen()
mypqkem_key_share = MyPQKEM.KeyGen()
myecdh_mypqkem_key_share = (myecdh_key_share, mypqkem_key_share)
KeyShareClientHello {
KeyShareEntry {
NamedGroup: 'MyECDH',
key_exchange: myecdh_key_share
},
KeyShareEntry {
NamedGroup: 'MyPQKEM',
key_exchange: mypqkem_key_share
},
KeyShareEntry {
NamedGroup: 'MyECDHMyPQKEM',
key_exchange: myecdh_mypqkem_key_share
},
}
3.3. Shared Secret Calculation
Here, this
This document also takes a simple "concatenation approach": approach" for the
calculation of shared secrets: The two shared secrets are
concatenated together and used as the shared secret in the existing
TLS 1.3 key schedule. Again, this document does not add any
additional structure (length fields) in the concatenation procedure;
for both the traditional groups and post quantum KEMs, the shared
secret output length is fixed for a specific elliptic curve or
parameter set.
In other words, if the NamedGroup is MyECDHMyPQKEM, the shared secret
is calculated as:
concatenated_shared_secret = MyECDH.shared_secret
|| MyPQKEM.shared_secret
and inserted into the TLS 1.3 key schedule in place of the (EC)DHE
shared secret, as shown in Figure 1.
0
|
v
PSK -> 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(...)
Figure 1: Key Schedule for Hybrid Key Exchange
*FIPS compliance of shared secret concatenation.* The
In regard to FIPS compliance, the US National Institute of Standards
and Technology (NIST) documents [NIST-SP-800-56C] and
[NIST-SP-800-135] give 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 an unapproved
algorithm (e.g., post-quantum). [NIST-SP-800-56C] lists simple
concatenation as an approved method for generation of a hybrid shared
secret in which one of the constituent shared secrets is from an
approved method.
4. Discussion
*Larger
Larger public keys and/or ciphertexts.* ciphertexts:
The key_exchange field in the KeyShareEntry struct in Section 3.2
limits public keys and ciphertexts to 2^16-1 bytes. Some post-quantum post-
quantum KEMs have larger public keys and/or ciphertexts; for
example, Classic McEliece's smallest parameter set has a public
key size of 261,120 bytes. bytes [Classic-McEliece]. However, all
defined parameter sets for the Module-Lattice-Based Key
Encapsulation Mechanism (ML-KEM) [NIST-FIPS-203] have public keys
and ciphertexts that fall within the TLS constraints (although
this may result in ClientHello messages larger than a single
packet).
*Duplication
Duplication of key shares.* shares:
Concatenation of public keys in the key_exchange field in the
KeyShareEntry struct as described in Section 3.2 can result in
sending duplicate key shares. For example, if a client wants to
offer support for two combinations, say "SecP256r1MLKEM768" and
"X25519MLKEM768" [ECDHE-MLKEM], it would end up sending two ML-KEM-768 ML-
KEM-768 public keys, since the KeyShareEntry for each combination
contains its own copy of an ML-KEM-768 key. This duplication may
be more problematic for post-quantum algorithms that have larger
public keys. On the other hand, if the client wants to offer, for
example, "SecP256r1MLKEM768" and "secp256r1" (for backwards
compatibility), there is relatively little duplicated data (as the
secp256r1 keys are comparatively small).
5. IANA Considerations
IANA has added this document as a reference for the "TLS Supported
Groups" registry [IANA-TLS].
For hybrid combinations defined per this document, IANA will assign
identifiers in a range that is distinct from the Finite Field Groups
range. In addition, the "Recommended" column SHOULD be "N", and the
"DTLS-OK" column SHOULD be "Y".
6. 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 [GIACON] and [BINDEL] for an
investigation of these issues. Under the assumption that shared
secrets are fixed length once the combination is fixed, the
construction in Section 3.3 corresponds to the dual-PRF combiner of
[BINDEL], which is shown to preserve security under the assumption
that the hash function is a dual-PRF.
As noted in Section 2, 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. ML-
KEM has such security properties. However, some other post-quantum
KEMs designed to be IND-CPA-secure (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 [FLUHRER].
*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 ML-KEM.
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 [LUCKY13] and Raccoon [RACCOON] attacks.
Furthermore, [AVIRAM] identifies 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 that
have fixed-length shared secrets (after the variant has been fixed by
the algorithm identifier in the NamedGroup negotiation in
Section 3.1).
7. References
7.1. Normative References
[FO] Fujisaki, E. and T. Okamoto, "Secure Integration of
Asymmetric and Symmetric Encryption Schemes", Journal of
Cryptology, vol. 26, no. 1, pp. 80-101,
DOI 10.1007/s00145-011-9114-1, December 2011,
<https://doi.org/10.1007/s00145-011-9114-1>.
[HHK] Hofheinz, D., Hövelmanns, K., and E. Kiltz, "A Modular
Analysis of the Fujisaki-Okamoto Transformation", Theory
of Cryptography (TCC 2017), Lecture Notes in Computer
Science, vol. 10677, pp. 341-371,
DOI 10.1007/978-3-319-70500-2_12, 2017,
<https://doi.org/10.1007/978-3-319-70500-2_12>.
[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/info/rfc2119>.
[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/info/rfc8174>.
[TLS13] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
<https://www.rfc-editor.org/info/rfc8446>.
7.2. Informative References
[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/>.
[BCNS15] Bos, J., Costello, C., Naehrig, M., and D. Stebila, "Post-
Quantum Key Exchange for the TLS Protocol from the Ring
Learning with Errors Problem", 2015 IEEE Symposium on
Security and Privacy, pp. 553-570, DOI 10.1109/sp.2015.40,
May 2015, <https://doi.org/10.1109/sp.2015.40>.
[BERNSTEIN]
Bernstein, D. J., Ed., Buchmann, J., Ed., and E. Dahmen,
Ed., "Post-Quantum Cryptography", Springer Berlin,
DOI 10.1007/978-3-540-88702-7, 2009,
<https://doi.org/10.1007/978-3-540-88702-7>.
[BINDEL] Bindel, N., Brendel, J., Fischlin, M., Goncalves, B., and
D. Stebila, "Hybrid Key Encapsulation Mechanisms and
Authenticated Key Exchange", Post-Quantum Cryptography
(PQCrypto 2019), Lecture Notes in Computer Science, vol.
11505, pp. 206-226, DOI 10.1007/978-3-030-25510-7_12,
2019, <https://doi.org/10.1007/978-3-030-25510-7_12>.
[CAMPAGNA] Campagna, M. and E. Crockett, "Hybrid Post-Quantum Key
Encapsulation Methods (PQ KEM) for Transport Layer
Security 1.2 (TLS)", Work in Progress, Internet-Draft,
draft-campagna-tls-bike-sike-hybrid-07, 2 September 2021,
<https://datatracker.ietf.org/doc/html/draft-campagna-tls-
bike-sike-hybrid-07>.
[CECPQ1] Braithwaite, M., "Experimenting with Post-Quantum
Cryptography", Google Security Blog, 7 July 2016,
<https://security.googleblog.com/2016/07/experimenting-
with-post-quantum.html>.
[CECPQ2] Langley, A., "CECPQ2", 12 December 2018,
<https://www.imperialviolet.org/2018/12/12/cecpq2.html>.
[Classic-McEliece]
Josefsson, S., "Classic McEliece", Work in Progress,
Internet-Draft, draft-josefsson-mceliece-03, 7 July 2025,
<https://datatracker.ietf.org/doc/html/draft-josefsson-
mceliece-03>.
[DODIS] Dodis, Y. and J. Katz, "Chosen-Ciphertext Security of
Multiple Encryption", Theory of Cryptography (TCC 2005),
Lecture Notes in Computer Science, vol. 3378, pp. 188-209,
DOI 10.1007/978-3-540-30576-7_11, 2005,
<https://doi.org/10.1007/978-3-540-30576-7_11>.
[DOWLING] Dowling, B., Fischlin, M., Günther, F., and D. Stebila, "A
Cryptographic Analysis of the TLS 1.3 Handshake Protocol",
Journal of Cryptology, vol. 34, article 37,
DOI 10.1007/s00145-021-09384-1, July 2021,
<https://doi.org/10.1007/s00145-021-09384-1>.
[ECDHE-MLKEM]
Kwiatkowski, K., Kampanakis, P., Westerbaan, B., and D.
Stebila, "Post-quantum hybrid ECDHE-MLKEM Key Agreement
for TLSv1.3", Work in Progress, Internet-Draft, draft-
kwiatkowski-tls-ecdhe-mlkem-03, 24 December 2024,
<https://datatracker.ietf.org/doc/html/draft-kwiatkowski-
tls-ecdhe-mlkem-03>.
ietf-tls-ecdhe-mlkem-04, 8 February 2026,
<https://datatracker.ietf.org/doc/html/draft-ietf-tls-
ecdhe-mlkem-04>.
[ETSI] Campagna, M., Ed., et al., "Quantum Safe Cryptography and
Security: An introduction, benefits, enablers and
challengers", ETSI White Paper No. 8, June 2015,
<https://www.etsi.org/images/files/ETSIWhitePapers/
QuantumSafeWhitepaper.pdf>.
[EVEN] Even, S. and O. Goldreich, "On the Power of Cascade
Ciphers", Advances in Cryptology, pp. 43-50,
DOI 10.1007/978-1-4684-4730-9_4, 1984,
<https://doi.org/10.1007/978-1-4684-4730-9_4>.
[EXTERN-PSK]
Housley, R., "TLS 1.3 Extension for Certificate-Based
Authentication with an External Pre-Shared Key", RFC 8773,
DOI 10.17487/RFC8773, March 2020,
<https://www.rfc-editor.org/info/rfc8773>.
[FLUHRER] Fluhrer, S., "Cryptanalysis of ring-LWE based key exchange
with key share reuse", Cryptology ePrint Archive, Paper
2016/085, 2016, <https://eprint.iacr.org/2016/085>.
[FRODO] Bos, J., Costello, C., Ducas, L., Mironov, I., Naehrig,
M., Nikolaenko, V., Raghunathan, A., and D. Stebila,
"Frodo: Take off the Ring! Practical, Quantum-Secure Key
Exchange from LWE", Proceedings of the 2016 ACM SIGSAC
Conference on Computer and Communications Security, pp.
1006-1018, DOI 10.1145/2976749.2978425, October 2016,
<https://doi.org/10.1145/2976749.2978425>.
[GIACON] Giacon, F., Heuer, F., and B. Poettering, "KEM Combiners",
Public-Key Cryptography (PKC 2018), Lecture Notes in
Computer Science, vol. 10769, pp. 190-218,
DOI 10.1007/978-3-319-76578-5_7, 2018,
<https://doi.org/10.1007/978-3-319-76578-5_7>.
[HARNIK] Harnik, D., Kilian, J., Naor, M., Reingold, O., and A.
Rosen, "On Robust Combiners for Oblivious Transfer and
Other Primitives", Advances in Cryptology (EUROCRYPT
2005), Lecture Notes in Computer Science, vol. 3494, pp.
96-113, DOI 10.1007/11426639_6, 2005,
<https://doi.org/10.1007/11426639_6>.
[HPKE] Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid
Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180,
February 2022, <https://www.rfc-editor.org/info/rfc9180>.
[IANA-TLS] IANA, "TLS Supported Groups",
<https://www.iana.org/assignments/tls-parameters>.
[IKE-HYBRID]
Tjhai, C., Tomlinson, M., Bartlett, G., Fluhrer, S., Van
Geest, D., Garcia-Morchon, O., and V. Smyslov, "Framework
to Integrate Post-quantum Key Exchanges into Internet Key
Exchange Protocol Version 2 (IKEv2)", Work in Progress,
Internet-Draft, draft-tjhai-ipsecme-hybrid-qske-ikev2-04,
9 July 2019, <https://datatracker.ietf.org/doc/html/draft-
tjhai-ipsecme-hybrid-qske-ikev2-04>.
[IKE-PSK] Fluhrer, S., Kampanakis, P., McGrew, D., and V. Smyslov,
"Mixing Preshared Keys in the Internet Key Exchange
Protocol Version 2 (IKEv2) for Post-quantum Security",
RFC 8784, DOI 10.17487/RFC8784, June 2020,
<https://www.rfc-editor.org/info/rfc8784>.
[KATZ] Katz, J. and Y. Lindell, "Introduction to Modern
Cryptography", Third Edition, CRC Press, 2021.
[KIEFER] Kiefer, F. and K. Kwiatkowski, "Hybrid ECDHE-SIDH Key
Exchange for TLS", Work in Progress, Internet-Draft,
draft-kiefer-tls-ecdhe-sidh-00, 5 November 2018,
<https://datatracker.ietf.org/doc/html/draft-kiefer-tls-
ecdhe-sidh-00>.
[LANGLEY] Langley, A., "Post-quantum confidentiality for TLS", 11
April 2018, <https://www.imperialviolet.org/2018/04/11/
pqconftls.html>.
[LUCKY13] Al Fardan, N. and K. Paterson, "Lucky Thirteen: Breaking
the TLS and DTLS Record Protocols", 2013 IEEE Symposium on
Security and Privacy, pp. 526-540, DOI 10.1109/sp.2013.42,
May 2013, <https://doi.org/10.1109/sp.2013.42>.
[NIELSEN] Nielsen, M. A. and I. L. Chuang, "Quantum Computation and
Quantum Information", Cambridge University Press, 2000.
[NIST] NIST, "Post-Quantum Cryptography",
<https://www.nist.gov/pqcrypto>.
[NIST-FIPS-203]
NIST, "Module-Lattice-Based Key-Encapsulation Mechanism
Standard", NIST FIPS 203, DOI 10.6028/NIST.FIPS.203,
August 2024, <https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.203.pdf>.
[NIST-SP-800-135]
Dang, Q., "Recommendation for Existing Application-
Specific Key Derivation Functions", NIST SP 800-135r1,
DOI 10.6028/nist.sp.800-135r1, December 2011,
<https://doi.org/10.6028/nist.sp.800-135r1>.
[NIST-SP-800-56C]
Barker, E., Chen, L., and R. Davis, "Recommendation for
Key-Derivation Methods in Key-Establishment Schemes", NIST
SP 800-56Cr2, DOI 10.6028/nist.sp.800-56cr2, August 2020,
<https://doi.org/10.6028/nist.sp.800-56cr2>.
[OQS-102] "OQS-OpenSSL-1-0-2_stable", commit 537b2f9, 31 January
2020, <https://github.com/open-quantum-safe/openssl/tree/
OQS-OpenSSL_1_0_2-stable>.
[OQS-111] "OQS-OpenSSL-1-1-1_stable", commit 5f49b7a, 8 January
2025, <https://github.com/open-quantum-safe/openssl/tree/
OQS-OpenSSL_1_1_1-stable>.
[OQS-PROV] "OQS Provider for OpenSSL 3", commit 573fb25, 8 January
2026,
<https://github.com/open-quantum-safe/oqs-provider/>.
[PQUIP-TERM]
Driscoll, F., Parsons, M., and B. Hale, "Terminology for
Post-Quantum Traditional Hybrid Schemes", RFC 9794,
DOI 10.17487/RFC9794, June 2025,
<https://www.rfc-editor.org/info/rfc9794>.
[PST] Paquin, C., Stebila, D., and G. Tamvada, "Benchmarking
Post-quantum Cryptography in TLS", Post-Quantum
Cryptography (PQCrypto 2020), Lecture Notes in Computer
Science, vol. 12100, pp. 72-91,
DOI 10.1007/978-3-030-44223-1_5, 2020,
<https://doi.org/10.1007/978-3-030-44223-1_5>.
[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/>.
[RFC9370] Tjhai, CJ., Tomlinson, M., Bartlett, G., Fluhrer, S., Van
Geest, D., Garcia-Morchon, O., and V. Smyslov, "Multiple
Key Exchanges in the Internet Key Exchange Protocol
Version 2 (IKEv2)", RFC 9370, DOI 10.17487/RFC9370, May
2023, <https://www.rfc-editor.org/info/rfc9370>.
[S2N] Hopkins, A. and M. Campagna, "Post-quantum TLS now
supported in AWS KMS", AWS Security Blog, 4 November 2019,
<https://aws.amazon.com/blogs/security/post-quantum-tls-
now-supported-in-aws-kms/>.
[SCHANCK] Schanck, J. M. and D. Stebila, "A Transport Layer Security
(TLS) Extension For Establishing An Additional Shared
Secret", Work in Progress, Internet-Draft, draft-schanck-
tls-additional-keyshare-00, 17 April 2017,
<https://datatracker.ietf.org/doc/html/draft-schanck-tls-
additional-keyshare-00>.
[WHYTE12] Schanck, J. M., Whyte, W., and Z. Zhang, "Quantum-Safe
Hybrid (QSH) Ciphersuite for Transport Layer Security
(TLS) version 1.2", Work in Progress, Internet-Draft,
draft-whyte-qsh-tls12-02, 22 July 2016,
<https://datatracker.ietf.org/doc/html/draft-whyte-qsh-
tls12-02>.
[WHYTE13] Whyte, W., Zhang, Z., Fluhrer, S., and O. Garcia-Morchon,
"Quantum-Safe Hybrid (QSH) Key Exchange for Transport
Layer Security (TLS) version 1.3", Work in Progress,
Internet-Draft, draft-whyte-qsh-tls13-06, 3 October 2017,
<https://datatracker.ietf.org/doc/html/draft-whyte-qsh-
tls13-06>.
[XMSS] Huelsing, A., Butin, D., Gazdag, S., Rijneveld, J., and A.
Mohaisen, "XMSS: eXtended Merkle Signature Scheme",
RFC 8391, DOI 10.17487/RFC8391, May 2018,
<https://www.rfc-editor.org/info/rfc8391>.
[ZHANG] Zhang, R., Hanaoka, G., Shikata, J., and H. Imai, "On the
Security of Multiple Encryption or CCA-security+CCA-
security=CCA-security?", Public Key Cryptography (PKC
2004), Lecture Notes in Computer Science, vol. 2947, pp.
360-374, DOI 10.1007/978-3-540-24632-9_26, 2004,
<https://doi.org/10.1007/978-3-540-24632-9_26>.
Appendix A. 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 [NIELSEN]. For an
overview of post-quantum cryptography as of 2009, see [BERNSTEIN];
while not containing more recent advances, it still provides a
helpful introduction. For the current status of the NIST Post-
Quantum Cryptography Standardization Project, see [NIST]. For
additional perspectives on the general transition from traditional to
post-quantum cryptography, see for example [ETSI], among others.
There have been several Internet-Drafts describing mechanisms for
embedding post-quantum and/or hybrid key exchange in TLS:
* TLS 1.2: [WHYTE12], [CAMPAGNA]
* TLS 1.3: [KIEFER], [SCHANCK], [WHYTE13]
There have been several prototype implementations for post-quantum
and/or hybrid key exchange in TLS:
* TLS 1.2: [BCNS15], [CECPQ1], [FRODO], [OQS-102], [S2N]
* TLS 1.3: [CECPQ2], [OQS-111], [OQS-PROV], [PST]
These experimental implementations have taken an ad hoc approach and
not attempted to implement one of the Internet-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 [EXTERN-PSK].
Considering other IETF standards, there is work
[RFC9370] on post-quantum pre-
shared keys the multiple key exchanges in the Internet Key Exchange
Protocol Version 2 (IKEv2)
[IKE-PSK] and has been published as a framework for hybrid key exchange Proposed Standard,
and other IETF work includes post-quantum preshared keys in IKEv2
[IKE-HYBRID].
[IKE-PSK]. The eXtended Merkle Signature Scheme (XMSS) hash-based
signature scheme has been published as an Informational RFC by the
IRTF [XMSS].
In the academic literature, [EVEN] initiated the study of combining
multiple symmetric encryption schemes; [ZHANG], [DODIS], and [HARNIK]
examined combining multiple public key encryption schemes; and
[HARNIK] coined the term "robust combiner" to refer to a compiler
that constructs a hybrid scheme from individual schemes while
preserving security properties. [GIACON] and [BINDEL] examined
combining multiple key encapsulation mechanisms.
Acknowledgements
The ideas in this document have grown from discussions with many
colleagues, including Christopher Wood, Matt Campagna, Eric Crockett,
Deirdre Connolly, authors of the various hybrid documents 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.
Authors' Addresses
Douglas Stebila
University of Waterloo
Email: dstebila@uwaterloo.ca
Scott Fluhrer
Cisco Systems
Email: sfluhrer@cisco.com
Shay Gueron
University of Haifa and Meta
Email: shay.gueron@gmail.com