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Versions: 00 01
Network Working Group D. Stebila
Internet-Draft University of Waterloo
Intended status: Informational S. Fluhrer
Expires: January 9, 2020 Cisco Systems
S. Gueron
U. Haifa, Amazon Web Services
July 08, 2019
Design issues for hybrid key exchange in TLS 1.3
draft-stebila-tls-hybrid-design-01
Abstract
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,
and is motivated by transition to post-quantum cryptography. This
document categorizes various design considerations for using hybrid
key exchange in the Transport Layer Security (TLS) protocol version
1.3 and outlines two concrete instantiations for consideration.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on January 9, 2020.
Copyright Notice
Copyright (c) 2019 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
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carefully, as they describe your rights and restrictions with respect
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Revision history . . . . . . . . . . . . . . . . . . . . 3
1.2. Terminology . . . . . . . . . . . . . . . . . . . . . . . 4
1.3. Motivation for use of hybrid key exchange . . . . . . . . 4
1.4. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5. Goals . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6. Related work . . . . . . . . . . . . . . . . . . . . . . 7
2. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3. Design options . . . . . . . . . . . . . . . . . . . . . . . 10
3.1. (Neg) How to negotiate hybridization and component
algorithms? . . . . . . . . . . . . . . . . . . . . . . . 10
3.1.1. Key exchange negotiation in TLS 1.3 . . . . . . . . . 10
3.1.2. (Neg-Ind) Negotiating component algorithms
individually . . . . . . . . . . . . . . . . . . . . 10
3.1.3. (Neg-Comb) Negotiating component algorithms as a
combination . . . . . . . . . . . . . . . . . . . . . 11
3.1.4. Benefits and drawbacks . . . . . . . . . . . . . . . 12
3.2. (Num) How many component algorithms to combine? . . . . . 13
3.2.1. (Num-2) Two . . . . . . . . . . . . . . . . . . . . . 13
3.2.2. (Num-2+) Two or more . . . . . . . . . . . . . . . . 13
3.2.3. Benefits and Drawbacks . . . . . . . . . . . . . . . 13
3.3. (Shares) How to convey key shares? . . . . . . . . . . . 13
3.3.1. (Shares-Concat) Concatenate key shares . . . . . . . 13
3.3.2. (Shares-Multiple) Send multiple key shares . . . . . 14
3.3.3. (Shares-Ext-Additional) Extension carrying additional
key shares . . . . . . . . . . . . . . . . . . . . . 14
3.3.4. Benefits and Drawbacks . . . . . . . . . . . . . . . 14
3.4. (Comb) How to use keys? . . . . . . . . . . . . . . . . . 14
3.4.1. (Comb-Concat) Concatenate keys . . . . . . . . . . . 15
3.4.2. (Comb-KDF-1) KDF keys . . . . . . . . . . . . . . . . 16
3.4.3. (Comb-KDF-2) KDF keys . . . . . . . . . . . . . . . . 17
3.4.4. (Comb-XOR) XOR keys . . . . . . . . . . . . . . . . . 18
3.4.5. (Comb-Chain) Chain of KDF applications for each key . 18
3.4.6. (Comb-AltInput) Second shared secret in an alternate
KDF input . . . . . . . . . . . . . . . . . . . . . . 19
3.4.7. Benefits and Drawbacks . . . . . . . . . . . . . . . 20
3.4.8. Open questions . . . . . . . . . . . . . . . . . . . 21
4. Candidate instantiations . . . . . . . . . . . . . . . . . . 21
4.1. Candidate Instantiation 1 . . . . . . . . . . . . . . . . 21
4.1.1. ClientHello extension supported_groups . . . . . . . 22
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4.1.2. ClientHello extension hybrid_extension . . . . . . . 22
4.1.3. ClientHello extension key_share . . . . . . . . . . . 23
4.1.4. ServerHello extension KeyShareServerHello . . . . . . 23
4.1.5. Key schedule . . . . . . . . . . . . . . . . . . . . 24
4.2. Candidate Instantiation 2 . . . . . . . . . . . . . . . . 25
4.2.1. ClientHello extension supported_groups . . . . . . . 26
4.2.2. ClientHello extension KeyShareClientHello . . . . . . 26
4.2.3. ServerHello extension KeyShareServerHello . . . . . . 27
4.2.4. Key schedule . . . . . . . . . . . . . . . . . . . . 27
4.3. Comparing Candidate Instantiation 1 and 2 . . . . . . . . 27
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 27
6. Security Considerations . . . . . . . . . . . . . . . . . . . 27
6.1. Active security . . . . . . . . . . . . . . . . . . . . . 28
6.2. Resumption . . . . . . . . . . . . . . . . . . . . . . . 28
6.3. Failures . . . . . . . . . . . . . . . . . . . . . . . . 28
7. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 28
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 29
8.1. Normative References . . . . . . . . . . . . . . . . . . 29
8.2. Informative References . . . . . . . . . . . . . . . . . 29
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 32
1. Introduction
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 also includes two concrete instantiations for
consideration, following two different approaches; it is not our
intention that both be standardized.
This document does not propose specific post-quantum mechanisms; see
Section 1.4 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).
1.1. Revision history
o draft-00: Initial version.
o draft-01:
* Add (Comb-KDF-1) (Section 3.4.2) and (Comb-KDF-2)
(Section 3.4.3) options.
* Add Candidate Instantiation 1 (Section 4.1).
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* Add Candidate Instantiation 2 (Section 4.2).
1.2. Terminology
For the purposes of this document, it is helpful to be able to divide
cryptographic algorithms into two classes:
o "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.
o "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.
1.3. Motivation for use of hybrid key exchange
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
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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.
1.4. Scope
This document focuses on hybrid ephemeral key exchange in TLS 1.3
[TLS13]. It intentionally does not address:
o 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 [NIST] will inform this choice.)
o 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.)
1.5. 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:
o *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
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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.
o *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 [BCNS15], [CECPQ1], [FRODO] for
preliminary results about performance characteristics.
o *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 [BCNS15], [FRODO] 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.
o *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.
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o *No duplicate information:* Attempting to negotiate hybrid key
exchange should not mean having to send multiple public keys of
the same type.
1.6. 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].
For the current status of the NIST Post-Quantum Cryptography
Standardization Project, see [NIST]. For additional perspectives on
the general transition from classical to post-quantum cryptography,
see for example [ETSI] and [HOFFMAN], among others.
There have been several Internet-Drafts describing mechanisms for
embedding post-quantum and/or hybrid key exchange in TLS:
o Internet-Drafts for TLS 1.2: [WHYTE12]
o Internet-Drafts for TLS 1.3: [KIEFER], [SCHANCK], [WHYTE13]
There have been several prototype implementations for post-quantum
and/or hybrid key exchange in TLS:
o Experimental implementations in TLS 1.2: [BCNS15], [CECPQ1],
[FRODO], [OQS-102]
o Experimental implementations in TLS 1.3: [CECPQ2], [OQS-111]
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 [EXTERN-PSK].
Considering other IETF standards, there is work on post-quantum
preshared keys in IKEv2 [IKE-PSK] and a framework for hybrid key
exchange in IKEv2 [IKE-HYBRID]. The 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
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preserving security properties. [GIACON] and [BINDEL] examined
combining multiple key encapsulation mechanisms.
2. Overview
We identify four distinct axes along which one can make choices when
integrating hybrid key exchange into TLS 1.3:
1. How to negotiate the use of hybridization in general and
component algorithms specifically?
2. How many component algorithms can be combined?
3. How should multiple key shares (public keys / ciphertexts) be
conveyed?
4. 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.
1. (Neg) (Section 3.1) How to negotiate the use of hybridization in
general and component algorithms specifically?
* (Neg-Ind) (Section 3.1.2) Negotiating component algorithms
individually
+ (Neg-Ind-1) (Section 3.1.2.1) Traditional algorithms in
"ClientHello" "supported_groups" extension, next-gen
algorithms in another extension
+ (Neg-Ind-2) (Section 3.1.2.2) Both types of algorithms in
"supported_groups" with external mapping to tradition/next-
gen.
+ (Neg-Ind-3) (Section 3.1.2.3) Both types of algorithms in
"supported_groups" separated by a delimiter.
* (Neg-Comb) (Section 3.1.3) Negotiating component algorithms as
a combination
+ (Neg-Comb-1) (Section 3.1.3.1) Standardize "NamedGroup"
identifiers for each desired combination.
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+ (Neg-Comb-2) (Section 3.1.3.2) Use placeholder identifiers
in "supported_groups" with an extension defining the
combination corresponding to each placeholder.
+ (Neg-Comb-3) (Section 3.1.3.3) List combinations by
inserting grouping delimiters into "supported_groups" list.
2. (Num) (Section 3.2) How many component algorithms can be
combined?
* (Num-2) (Section 3.2.1) Two.
* (Num-2+) (Section 3.2.2) Two or more.
3. (Shares) (Section 3.3) How should multiple key shares (public
keys / ciphertexts) be conveyed?
* (Shares-Concat) (Section 3.3.1) Concatenate each combination
of key shares.
* (Shares-Multiple) (Section 3.3.2) Send individual key shares
for each algorithm.
* (Shares-Ext-Additional) (Section 3.3.3) Use an extension to
convey key shares for component algorithms.
4. (Comb) (Section 3.4) How should multiple shared secrets be
combined?
* (Comb-Concat) (Section 3.4.1) Concatenate the shared secrets
then use directly in the TLS 1.3 key schedule.
* (Comb-KDF-1) (Section 3.4.2) and (Comb-KDF-2) (Section 3.4.3)
KDF the shared secrets together, then use the output in the
TLS 1.3 key schedule.
* (Comb-XOR) (Section 3.4.4) XOR the shared secrets then use
directly in the TLS 1.3 key schedule.
* (Comb-Chain) (Section 3.4.5) Extend the TLS 1.3 key schedule
so that there is a stage of the key schedule for each shared
secret.
* (Comb-AltInput) (Section 3.4.6) Use the second shared secret
in an alternate (otherwise unused) input in the TLS 1.3 key
schedule.
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3. Design options
3.1. (Neg) How to negotiate hybridization and component algorithms?
3.1.1. Key exchange negotiation in TLS 1.3
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.
3.1.2. (Neg-Ind) Negotiating component algorithms individually
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.
3.1.2.1. (Neg-Ind-1)
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 [SCHANCK].)
3.1.2.2. (Neg-Ind-2)
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
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either "traditional" or "next-generation". A server could then
select two algorithms from this list, one from each category.
3.1.2.3. (Neg-Ind-3)
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".
3.1.3. (Neg-Comb) Negotiating component algorithms as a combination
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.
3.1.3.1. (Neg-Comb-1)
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 [KIEFER] and [OQS-111].
3.1.3.2. (Neg-Comb-2)
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 [WHYTE13], 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.
3.1.3.3. (Neg-Comb-3)
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
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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.
3.1.4. Benefits and drawbacks
*Combinatorial explosion.* (Neg-Comb-1) (Section 3.1.3.1) requires
new identifiers to be defined for each desired combination. The
other 4 options in this section do not.
*Extensions.* (Neg-Ind-1) (Section 3.1.2.1) and (Neg-Comb-2)
(Section 3.1.3.2) 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)
(Section 3.1.3.1) require new logic to process negotiation.
*Matching security levels.* (Neg-Ind-1) (Section 3.1.2.1), (Neg-Ind-
2) (Section 3.1.2.2), (Neg-Ind-3) (Section 3.1.2.3), and (Neg-Comb-2)
(Section 3.1.3.2) 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)
(Section 3.1.2.1), (Neg-Ind-2) (Section 3.1.2.2), and (Neg-Ind-3)
(Section 3.1.2.3) give control over the combination to the server;
(Neg-Comb-2) (Section 3.1.3.2) gives control over the combination to
the client. (Neg-Comb-1) (Section 3.1.3.1) 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)
(Section 3.1.2.2), (Neg-Ind-3) (Section 3.1.2.3), (Neg-Comb-1)
(Section 3.1.3.1), (Neg-Comb-2) (Section 3.1.3.2) and unrecognized
"ClientHello" extensions (Neg-Ind-1) (Section 3.1.2.1), (Neg-Comb-2)
(Section 3.1.3.2). In (Neg-Ind-3) (Section 3.1.2.3) and (Neg-Comb-3)
(Section 3.1.3.3), 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
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encounter bugs when the same element appears multiple times in the
list.
3.2. (Num) How many component algorithms to combine?
3.2.1. (Num-2) Two
Exactly two algorithms can be combined together in hybrid key
exchange. This is the approach taken in [KIEFER] and [SCHANCK].
3.2.2. (Num-2+) Two or more
Two or more algorithms can be combined together in hybrid key
exchange. This is the approach taken in [WHYTE13].
3.2.3. Benefits and Drawbacks
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.
3.3. (Shares) How to convey key shares?
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.
3.3.1. (Shares-Concat) Concatenate 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 [KIEFER], [OQS-111], and
[WHYTE13].
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3.3.2. (Shares-Multiple) Send multiple key shares
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.)
3.3.3. (Shares-Ext-Additional) Extension carrying additional 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 [SCHANCK].
3.3.4. Benefits and Drawbacks
*Backwards compatibility.* (Shares-Multiple) (Section 3.3.2) is fully
backwards compatible with non-hybrid-aware servers. (Shares-Ext-
Additional) (Section 3.3.3) is backwards compatible with non-hybrid-
aware servers provided they ignore unrecognized extensions. (Shares-
Concat) (Section 3.3.1) 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)
(Section 3.3.3) and (Shares-Concat) (Section 3.3.1). (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) (Section 3.3.2)
does not result in duplicate key shares.
3.4. (Comb) How to use keys?
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.
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3.4.1. (Comb-Concat) Concatenate keys
Each party concatenates the shared secrets established by each
component algorithm in an agreed-upon order, then feeds that through
the TLS key schedule. 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:
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(...)
This is the approach used in [KIEFER], [OQS-111], and [WHYTE13].
[GIACON] 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).
[BINDEL] 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,
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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.
3.4.2. (Comb-KDF-1) KDF keys
Each party feeds the shared secrets established by each component
algorithm in an agreed-upon order into a KDF, then feeds that through
the TLS key schedule. In the context of TLS 1.3, this would mean
first applying "HKDF-Extract" to the shared secrets, then using the
output in place of the (EC)DHE input to the second call to "HKDF-
Extract" in the TLS 1.3 key schedule:
0
|
v
PSK -> HKDF-Extract = Early Secret
|
+-----> Derive-Secret(...)
+-----> Derive-Secret(...)
+-----> Derive-Secret(...)
Next-Gen |
| v
(EC)DHE -> HKDF-Extract Derive-Secret(., "derived", "")
| |
v v
output -----> 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(...)
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3.4.3. (Comb-KDF-2) KDF keys
Each party concatenates the shared secrets established by each
component algorithm in an agreed-upon order then feeds that into a
KDF, then feeds the result through the TLS key schedule.
Compared with (Comb-KDF-1) (Section 3.4.2), this method concatenates
the (2 or more) shared secrets prior to input to the KDF, whereas
(Comb-KDF-1) puts the (exactly 2) shared secrets in the two different
input slots to the KDF.
Compared with (Comb-Concat) (Section 3.4.1), this method has an
extract KDF application. While this adds computational overhead,
this may provide a cleaner abstraction of the hybridization mechanism
for the purposes of formal security analysis.
0
|
v
PSK -> HKDF-Extract = Early Secret
|
+-----> Derive-Secret(...)
+-----> Derive-Secret(...)
+-----> Derive-Secret(...)
|
v
concatenated 0
shared |
secret -> HKDF-Extract Derive-Secret(., "derived", "")
^^^^^^ | |
v v
output -----> 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(...)
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3.4.4. (Comb-XOR) XOR keys
Each party XORs the shared secrets established by each component
algorithm (possibly after padding secrets of different lengths), then
feeds that through the TLS key schedule. 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.
[GIACON] 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).
3.4.5. (Comb-Chain) Chain of KDF applications for each key
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:
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0
|
v
PSK -> 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 [SCHANCK].
[BINDEL] 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.
3.4.6. (Comb-AltInput) Second shared secret in an alternate KDF input
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":
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0
|
v
PSK -> 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 [EXTERN-PSK].
3.4.7. Benefits and Drawbacks
*New logic.* While (Comb-Concat) (Section 3.4.1), (Comb-KDF-1)
(Section 3.4.2), and (Comb-KDF-2) (Section 3.4.3) require 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) (Section 3.4.5) 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) (Section 3.4.5) continues that approach.
*Efficiency.* (Comb-KDF-1) (Section 3.4.2), (Comb-KDF-2)
(Section 3.4.3), and (Comb-Chain) (Section 3.4.5) increase the number
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of KDF applications for each component algorithm, whereas (Comb-
Concat) (Section 3.4.1) and (Comb-AltInput) (Section 3.4.6) keep the
number of KDF applications the same (though with potentially longer
inputs).
*Extensibility.* (Comb-AltInput) (Section 3.4.6) 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)
(Section 3.4.1) and (Comb-Chain) (Section 3.4.5) can naturally
accommodate more than 2 component shared secrets since there is no
distinction to how each shared secret is treated. (Comb-AltInput)
(Section 3.4.6) 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.
3.4.8. Open questions
At this point, it is unclear which, if any, of the above methods
preserve FIPS compliance: i.e., if one shared secret is from a FIPS-
compliant method (e.g., ECDH), and another shared secret is from a
non-approved method (e.g., post-quantum), is the result still
considered FIPS compliant? Guidance from NIST on this question would
be helpful. Specifically, are any of these approaches acceptable
under either [NIST-SP-800-56C] or [NIST-SP-800-135]?
4. Candidate instantiations
In this section, we describe two candidate instantiations of hybrid
key exchange in TLS 1.3, based on the design considerations framework
above. It is not our intention that both of these instantations be
standardized; we are providing two for discussion and for comparing
and contrasting the two approaches.
4.1. Candidate Instantiation 1
Candidate Instantiation 1 allows for two or more component algorithms
to be combined (Num-2+) (Section 3.2.2), and negotiates the
combination using markers in the "NamedGroup" list as pointers to an
extension listing the algorithms comprising each possible combination
(Neg-Comb-2) (Section 3.1.3.2) following the approach of [WHYTE13].
The client conveys its multiple key shares individually in the
"client_shares" vector of the "ClientHello" "key_share" extension
(Shares-Multiple) (Section 3.3.2). The server conveys its multiple
key shares concatenated together in its "KeyShareServerHello" struct
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(Shares-Concat) (Section 3.3.1). The shared secrets are combined by
concatenating them then feeding them through a KDF, then feeding the
result into the TLS 1.3 key schedule (Comb-KDF-2) (Section 3.4.3).
4.1.1. ClientHello extension supported_groups
Following [WHYTE13] section 3.1, the "NamedGroup" enum used by the
client to populate the "supported_groups" extension is extended to
include new code points representing markers for hybrid combinations:
enum {
/* existing named groups */
secp256r1 (23),
...,
/* new code points eventually defined for post-quantum algorithms */
...,
/* new code points reserved for hybrid markers */
hybrid_marker00 (0xFD00),
hybrid_marker01 (0xFD01),
...
hybrid_markerFF (0xFDFF),
/* existing reserved code points */
ffdhe_private_use (0x01FC..0x01FF),
ecdhe_private_use (0xFE00..0xFEFF),
(0xFFFF)
} NamedGroup;
"hybrid_marker" code points do not a priori represent any fixed
combination. Instead, during each session establishment, the client
defines what it wants each "hybrid_marker" code point to represent
using the following extension.
4.1.2. ClientHello extension hybrid_extension
Following [WHYTE13] section 3.2.4, a new "ClientHello"
"hybrid_extension" extension is defined. It is defined as follows:
struct {
NamedGroup hybrid_marker;
NamedGroup components<2..10>;
} HybridMapping;
struct {
HybridMapping map<0..255>;
} HybridExtension;
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The "HybridExtension" contains 0 or more "HybridMapping"s. Each
"HybridMapping" corresponds to one of the "hybrid_marker" included in
the "supported_groups" extension, and lists the component algorithms
that are meant to comprise the this hybrid combination, which can be
any of the existing named groups (elliptic curve or finite field),
new code points eventually defined for post-quantum algorithms, or
reserved code points for private use.
4.1.3. ClientHello extension key_share
No syntactical modifications are made to the "KeyShareEntry" or
"KeyShareClientHello" data structures.
Semantically, the client does not send a "KeyShareEntry"
corresponding to any of the "hybrid_marker" code points. Instead,
the client sends "KeyShareEntry" for each of the component algorithms
listed in the "HybridMapping"s.
For example, if the list of "supported_groups" is "secp256r1",
"x25519", "hybrid_marker00", and "hybrid_marker01", where
"hybrid_marker00" comprises "secp256r1" with a fictional post-quantum
algorithm "PQ1", and "hybrid_marker01" comprises "x25519" with "PQ1",
then the client could send three "KeyShareEntry" components: one for
"secp256r1", one for "x25519", and one for "PQ1".
4.1.4. ServerHello extension KeyShareServerHello
The server responds with a "KeyShareServerHello" struct containing a
single "KeyShareEntry", which contains a single "NamedGroup" value
and an opaque "key_exchange" string.
To complete the negotiation of a hybrid algorithm, the server
responds with the "NamedGroup" value being the "hybrid_marker" code
point correspond to the combination that the server was willing to
agree to.
The "key_exchange" string is the octet representation of the
following struct:
struct {
KeyShareEntry key_share<2..10>;
} HybridKeyShare;
where there is one "key_share" entry for each of the components of
this hybrid combination.
Note that the "key_exchange" string has a maximum length of 2^16-1
octets, which may be insufficient for some post-quantum algorithms or
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for some hybridizations of multiple post-quantum algorithms. It
remains an open question as to whether this length can be increased
without breaking existing TLS 1.3 implementations.
4.1.5. Key schedule
The component algorithm shared secrets are combined by concatenating
them, then applying a key derivation function, the output of which is
then used in the TLS 1.3 key schedule in place of the (EC)DHE shared
secret. The component shared secrets are concatenated in the order
that they appear in the "components" vector of the "HybridMapping"
extension above.
We provide two options for concatenating the shared secrets, and
would like feedback from the working group in which to proceed with.
Each component algorithm's "shared_secret" is defined by the
algorithm itself, for example the DHE or ECDHE shared secrets as
defined in Section 7.4 of [TLS13], or as defined by post-quantum
methods once standardized in their own documents.
*Option 1: Using data structures.* Option 1 uses a full-fledged TLS
1.3 data structure to represent the list of component shared secrets.
As a result, lengths of each shared secret are unambiguously encoded.
struct SharedSecret {
opaque shared_secret<0..2^16-1>;
}
struct {
SharedSecret component<2..10>;
} HybridSharedSecret;
The "concatenated_shared_secret" is then the octet representation of
the "HybridSharedSecret " struct.
*Option 2: Direct concatenation.* Option 2 directly concatenates the
shared secrets. Option 2 should only be considered if the shared
secret for each algorithm is guarantees to be of a fixed length,
which would imply that, once the component algorithms are fixed,
concatenation is bijective.
concatenated_shared_secret = shared_secret0 | shared_secret1 | ...
In either option, the "concatenated_shared_secret" octet string is
used as the IKM argument of HKDF-Extract, with the zero-length string
as the salt argument. THe output of HKDF-Extract is used as the IKM
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argument for HKDF-Extract's calculation of the handshake secret, as
shown below.
0
|
v
PSK -> HKDF-Extract = Early Secret
|
+-----> Derive-Secret(...)
+-----> Derive-Secret(...)
+-----> Derive-Secret(...)
|
v
concatenated 0
shared |
secret -> HKDF-Extract Derive-Secret(., "derived", "")
^^^^^^ | |
v v
output -----> 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(...)
4.2. Candidate Instantiation 2
Candidate Instantiation 2 allows for exactly two component algorithms
to be combined (Num-2) (Section 3.2.1), and uses code points
standardized for each permissible combination. The client
concatenates its multiple key shares together as a distinct entry in
the "client_shares" vector of the "ClientHello" "key_share" extension
(Shares-Concat) (Section 3.3.1). The server does the same. The
shared secrets are combined by concatenating them then feeding them
through a KDF, then feeding the result into the TLS 1.3 key schedule
(Comb-KDF-2) (Section 3.4.3).
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4.2.1. ClientHello extension supported_groups
The "NamedGroup" enum used by the client to populate the
"supported_groups" extension is extended to include new code points
representing each desired combination.
For example,
enum {
/* existing named groups */
secp256r1 (23),
x25519 (0x001D),
...,
/* new code points eventually defined for post-quantum algorithms */
PQ1 (0x????),
PQ2 (0x????),
...,
/* new code points defined for hybrid combinations */
secp256r1_PQ1 (0x????),
secp256r1_PQ2 (0x????),
x25519_PQ1 (0x????),
x25519_PQ2 (0x????),
/* existing reserved code points */
ffdhe_private_use (0x01FC..0x01FF),
ecdhe_private_use (0xFE00..0xFEFF),
(0xFFFF)
} NamedGroup;
4.2.2. ClientHello extension KeyShareClientHello
The client sends a "KeyShareClientHello" struct containing multiple
"KeyShareEntry" values, some of which may correspond to some of the
hybrid combination code points it listed in the "supported_groups"
extension above.
The "KeyShareEntry" for a hybrid combination code point contains an
opaque "key_exchange" string which is the octet representation of the
following struct:
struct {
KeyShareEntry key_share<2..10>;
} HybridKeyShare;
where there is one "key_share" entry for each of the components of
this hybrid combination.
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Note that this approach may result in duplication of key shares being
sent; for example, a client wanting to support either the combination
"secp256r1_PQ1" or "x25519_PQ1" would send two "PQ1" key shares.
4.2.3. ServerHello extension KeyShareServerHello
The server responds with a "KeyShareServerHello" struct containing a
single "KeyShareEntry", which contains a single "NamedGroup" value
and an opaque "key_exchange" string. The "key_exchange" string is
the octet representation of the "HybridKeyShare" struct defined
above.
4.2.4. Key schedule
The key schedule is computed as in Candidate Instantiation 1 above.
4.3. Comparing Candidate Instantiation 1 and 2
CI2 requires much less change to negotiation routines - each hybrid
combination is just a new key exchange method, and the concatenation
of key shares and shared secrets can be handled internally to that
method. This comes at the cost, however, of combinatorial explosion
of code points: one code point needs to be standardized for each
desired combination. We have also limited the number of hybrid
algorithms to 2 in CI2 to somewhat limit the explosion of code points
needing to be defined. Concatenating client key shares also risks
sending duplicate key shares, increasing communication sizes.
CI1 requires more change to negotiation routines, since it introduces
new data structures and has an indirect mapping between hybrid
combinations and key shares. Benefits from this approach include
avoiding sending duplicate key shares and not needing to standardize
every possible supported combination. Implementers, however, must do
the work of deciding which combinations of algorithms are meaningful
/ tolerable / desirable from a security perspective, potentially
complicating interoperability.
5. IANA Considerations
If Candidate Instantiation 1 is selected, the TLS Supported Groups
registry will have to be updated to include code points for hybrid
markers.
6. Security Considerations
The majority of this document is about security considerations. As
noted especially in Section 3.4, the shared secrets computed in the
hybrid key exchange should be computed in a way that achieves the
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"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 [GIACON]).
The rest of this section highlights a few unresolved questions
related to security.
6.1. Active 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
[DFGS15], [DOWLING]) 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, [KPW13] 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.
6.2. Resumption
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?
6.3. Failures
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?
7. Acknowledgements
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
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attendees at the Workshop on Post-Quantum Software in Mountain View,
California, in January 2019.
Martin Thomson suggested the (Comb-KDF-1) (Section 3.4.2) approach.
8. References
8.1. Normative References
[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>.
8.2. Informative References
[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, DOI 10.1109/sp.2015.40, May 2015.
[BERNSTEIN]
"Post-Quantum Cryptography", Springer Berlin
Heidelberg book, DOI 10.1007/978-3-540-88702-7, 2009.
[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, <https://eprint.iacr.org/2018/903>.
[CECPQ1] Braithwaite, M., "Experimenting with Post-Quantum
Cryptography", July 2016,
<https://security.googleblog.com/2016/07/
experimenting-with-post-quantum.html>.
[CECPQ2] Langley, A., "CECPQ2", December 2018,
<https://www.imperialviolet.org/2018/12/12/cecpq2.html>.
[DFGS15] Dowling, B., Fischlin, M., Guenther, F., and D. Stebila,
"A Cryptographic Analysis of the TLS 1.3 Handshake
Protocol Candidates", Proceedings of the 22nd ACM SIGSAC
Conference on Computer and Communications Security -
CCS '15, DOI 10.1145/2810103.2813653, 2015.
[DODIS] Dodis, Y. and J. Katz, "Chosen-Ciphertext Security of
Multiple Encryption", Theory of Cryptography pp. 188-209,
DOI 10.1007/978-3-540-30576-7_11, 2005.
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[DOWLING] Dowling, B., "Provable Security of Internet Protocols",
Queensland University of Technology dissertation,
DOI 10.5204/thesis.eprints.108960, n.d..
[ETSI] Campagna, M., Ed. and . others, "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.
[EXTERN-PSK]
Housley, R., "TLS 1.3 Extension for Certificate-based
Authentication with an External Pre-Shared Key", draft-
ietf-tls-tls13-cert-with-extern-psk-02 (work in progress),
May 2019.
[FRODO] Bos, J., Costello, C., Ducas, L., Mironov, I., Naehrig,
M., Nikolaenko, V., Raghunathan, A., and D. Stebila,
"Frodo", Proceedings of the 2016 ACM SIGSAC Conference on
Computer and Communications Security - CCS'16,
DOI 10.1145/2976749.2978425, 2016.
[GIACON] Giacon, F., Heuer, F., and B. Poettering, "KEM Combiners",
Public-Key Cryptography - PKC 2018 pp. 190-218,
DOI 10.1007/978-3-319-76578-5_7, 2018.
[HARNIK] Harnik, D., Kilian, J., Naor, M., Reingold, O., and A.
Rosen, "On Robust Combiners for Oblivious Transfer and
Other Primitives", Lecture Notes in Computer Science pp.
96-113, DOI 10.1007/11426639_6, 2005.
[HOFFMAN] Hoffman, P., "The Transition from Classical to Post-
Quantum Cryptography", draft-hoffman-c2pq-05 (work in
progress), May 2019.
[IKE-HYBRID]
Tjhai, C., Tomlinson, M., grbartle@cisco.com, g., Fluhrer,
S., Geest, D., Garcia-Morchon, O., and V. Smyslov,
"Framework to Integrate Post-quantum Key Exchanges into
Internet Key Exchange Protocol Version 2 (IKEv2)", draft-
tjhai-ipsecme-hybrid-qske-ikev2-03 (work in progress),
January 2019.
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[IKE-PSK] Fluhrer, S., McGrew, D., Kampanakis, P., and V. Smyslov,
"Postquantum Preshared Keys for IKEv2", draft-ietf-
ipsecme-qr-ikev2-08 (work in progress), March 2019.
[KIEFER] Kiefer, F. and K. Kwiatkowski, "Hybrid ECDHE-SIDH Key
Exchange for TLS", draft-kiefer-tls-ecdhe-sidh-00 (work in
progress), November 2018.
[KPW13] Krawczyk, H., Paterson, K., and H. Wee, "On the Security
of the TLS Protocol: A Systematic Analysis", Advances in
Cryptology - CRYPTO 2013 pp. 429-448,
DOI 10.1007/978-3-642-40041-4_24, 2013.
[LANGLEY] Langley, A., "Post-quantum confidentiality for TLS", April
2018, <https://www.imperialviolet.org/2018/04/11/
pqconftls.html>.
[NIELSEN] Nielsen, M. and I. Chuang, "Quantum Computation and
Quantum Information", Cambridge University Press , 2000.
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"Post-Quantum Cryptography", n.d.,
<https://www.nist.gov/pqcrypto>.
[NIST-SP-800-135]
National Institute of Standards and Technology (NIST),
"Recommendation for Existing Application-Specific Key
Derivation Functions", December 2011,
<https://doi.org/10.6028/NIST.SP.800-135r1>.
[NIST-SP-800-56C]
National Institute of Standards and Technology (NIST),
"Recommendation for Key-Derivation Methods in Key-
Establishment Schemes", April 2018,
<https://doi.org/10.6028/NIST.SP.800-56Cr1>.
[OQS-102] Open Quantum Safe Project, "OQS-OpenSSL-1-0-2_stable",
November 2018, <https://github.com/open-quantum-
safe/openssl/tree/OQS-OpenSSL_1_0_2-stable>.
[OQS-111] Open Quantum Safe Project, "OQS-OpenSSL-1-1-1_stable",
November 2018, <https://github.com/open-quantum-
safe/openssl/tree/OQS-OpenSSL_1_1_1-stable>.
[SCHANCK] Schanck, J. and D. Stebila, "A Transport Layer Security
(TLS) Extension For Establishing An Additional Shared
Secret", draft-schanck-tls-additional-keyshare-00 (work in
progress), April 2017.
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[WHYTE12] Schanck, J., Whyte, W., and Z. Zhang, "Quantum-Safe Hybrid
(QSH) Ciphersuite for Transport Layer Security (TLS)
version 1.2", draft-whyte-qsh-tls12-02 (work in progress),
July 2016.
[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", draft-whyte-qsh-
tls13-06 (work in progress), October 2017.
[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 pp. 360-374, DOI 10.1007/978-3-540-24632-9_26, 2004.
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 Amazon Web Services
Email: shay.gueron@gmail.com
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