Design issues for hybrid key exchange in TLS 1.3
draft-stebila-tls-hybrid-design-00

The information below is for an old version of the document
Document Type Active Internet-Draft (individual)
Authors Douglas Steblia  , Shay Gueron 
Last updated 2019-03-11
Replaced by draft-ietf-tls-hybrid-design
Stream (None)
Formats pdf htmlized (tools) htmlized bibtex
Stream Stream state (No stream defined)
Consensus Boilerplate Unknown
RFC Editor Note (None)
IESG IESG state I-D Exists
Telechat date
Responsible AD (None)
Send notices to (None)
Network Working Group                                         D. Stebila
Internet-Draft                                    University of Waterloo
Intended status: Informational                                 S. Gueron
Expires: September 12, 2019                U. Haifa, Amazon Web Services
                                                          March 11, 2019

            Design issues for hybrid key exchange in TLS 1.3
                   draft-stebila-tls-hybrid-design-00

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.

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 September 12, 2019.

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
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must

Stebila & Gueron       Expires September 12, 2019               [Page 1]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   3
     1.2.  Motivation for use of hybrid key exchange . . . . . . . .   4
     1.3.  Scope . . . . . . . . . . . . . . . . . . . . . . . . . .   4
     1.4.  Goals . . . . . . . . . . . . . . . . . . . . . . . . . .   5
     1.5.  Related work  . . . . . . . . . . . . . . . . . . . . . .   6
   2.  Overview  . . . . . . . . . . . . . . . . . . . . . . . . . .   7
   3.  Design options  . . . . . . . . . . . . . . . . . . . . . . .   9
     3.1.  (Neg) How to negotiate hybridization and component
           algorithms? . . . . . . . . . . . . . . . . . . . . . . .   9
       3.1.1.  Key exchange negotiation in TLS 1.3 . . . . . . . . .   9
       3.1.2.  (Neg-Ind) Negotiating component algorithms
               individually  . . . . . . . . . . . . . . . . . . . .   9
       3.1.3.  (Neg-Comb) Negotiating component algorithms as a
               combination . . . . . . . . . . . . . . . . . . . . .  10
       3.1.4.  Benefits and drawbacks  . . . . . . . . . . . . . . .  11
     3.2.  (Num) How many component algorithms to combine? . . . . .  12
       3.2.1.  (Num-2) Two . . . . . . . . . . . . . . . . . . . . .  12
       3.2.2.  (Num-2+) Two or more  . . . . . . . . . . . . . . . .  12
       3.2.3.  Benefits and Drawbacks  . . . . . . . . . . . . . . .  12
     3.3.  (Shares) How to convey key shares?  . . . . . . . . . . .  12
       3.3.1.  (Shares-Concat) Concatenate key shares  . . . . . . .  13
       3.3.2.  (Shares-Multiple) Send multiple key shares  . . . . .  13
       3.3.3.  (Shares-Ext-Additional) Extension carrying additional
               key shares  . . . . . . . . . . . . . . . . . . . . .  13
       3.3.4.  Benefits and Drawbacks  . . . . . . . . . . . . . . .  13
     3.4.  (Comb) How to use keys? . . . . . . . . . . . . . . . . .  14
       3.4.1.  (Comb-Concat) Concatenate keys then KDF . . . . . . .  14
       3.4.2.  (Comb-XOR) XOR keys then KDF  . . . . . . . . . . . .  15
       3.4.3.  (Comb-Chain) Chain of KDF applications for each key .  15
       3.4.4.  (Comb-AltInput) Second shared secret in an alternate
               KDF input . . . . . . . . . . . . . . . . . . . . . .  16
       3.4.5.  Benefits and Drawbacks  . . . . . . . . . . . . . . .  17
   4.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  18
   5.  Security Considerations . . . . . . . . . . . . . . . . . . .  18
     5.1.  Active security . . . . . . . . . . . . . . . . . . . . .  18
     5.2.  Resumption  . . . . . . . . . . . . . . . . . . . . . . .  19
     5.3.  Failures  . . . . . . . . . . . . . . . . . . . . . . . .  19
   6.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  19
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  19
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .  19
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  19

Stebila & Gueron       Expires September 12, 2019               [Page 2]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  22

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 does not propose specific post-quantum mechanisms; see
   Section 1.3 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.  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.

Stebila & Gueron       Expires September 12, 2019               [Page 3]
Internet-Draft          stebila-tls-hybrid-design             March 2019

1.2.  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
   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.

1.3.  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.)

Stebila & Gueron       Expires September 12, 2019               [Page 4]
Internet-Draft          stebila-tls-hybrid-design             March 2019

1.4.  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
      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

Stebila & Gueron       Expires September 12, 2019               [Page 5]
Internet-Draft          stebila-tls-hybrid-design             March 2019

         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.

   o  *No duplicate information:* Attempting to negotiate hybrid key
      exchange should not mean having to send multiple public keys of
      the same type.

1.5.  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].

Stebila & Gueron       Expires September 12, 2019               [Page 6]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   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
   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.

Stebila & Gueron       Expires September 12, 2019               [Page 7]
Internet-Draft          stebila-tls-hybrid-design             March 2019

          +  (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.

          +  (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-XOR) (Section 3.4.2) XOR the shared secrets then use
          directly in the TLS 1.3 key schedule.

       *  (Comb-Chain) (Section 3.4.3) Extend the TLS 1.3 key schedule
          so that there is a stage of the key schedule for each shared
          secret.

Stebila & Gueron       Expires September 12, 2019               [Page 8]
Internet-Draft          stebila-tls-hybrid-design             March 2019

       *  (Comb-AltInput) (Section 3.4.4) Use the second shared secret
          in an alternate (otherwise unused) input in the TLS 1.3 key
          schedule.

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].)

Stebila & Gueron       Expires September 12, 2019               [Page 9]
Internet-Draft          stebila-tls-hybrid-design             March 2019

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
   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.

Stebila & Gueron       Expires September 12, 2019              [Page 10]
Internet-Draft          stebila-tls-hybrid-design             March 2019

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
   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)

Stebila & Gueron       Expires September 12, 2019              [Page 11]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   (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
   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.

Stebila & Gueron       Expires September 12, 2019              [Page 12]
Internet-Draft          stebila-tls-hybrid-design             March 2019

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].

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

Stebila & Gueron       Expires September 12, 2019              [Page 13]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   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.

3.4.1.  (Comb-Concat) Concatenate keys then KDF

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

                                       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(...)

Stebila & Gueron       Expires September 12, 2019              [Page 14]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   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,
   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-XOR) XOR keys then KDF

   Each party XORs the shared secrets established by each component
   algorithm (possibly after padding secrets of different lengths), then
   uses feeds that through a key derivation function.  In the context of
   TLS 1.3, this would mean using the XORed shared secret in place of
   the (EC)DHE input to the second call to "HKDF-Extract" in the TLS 1.3
   key schedule.

   [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).

3.4.3.  (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:

Stebila & Gueron       Expires September 12, 2019              [Page 15]
Internet-Draft          stebila-tls-hybrid-design             March 2019

                                       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.

3.4.4.  (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":

Stebila & Gueron       Expires September 12, 2019              [Page 16]
Internet-Draft          stebila-tls-hybrid-design             March 2019

                                       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].

3.4.5.  Benefits and Drawbacks

   *New logic.* While (Comb-Concat) (Section 3.4.1) requires new logic
   to compute the concatenated shared secret, this value can then be
   used by the TLS 1.3 key schedule without changes to the key schedule
   logic.  In contrast, (Comb-Chain) (Section 3.4.3) 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 3.4.3) continues that approach.

   *Efficiency.* (Comb-Chain) (Section 3.4.3) increases the number of
   KDF applications for each component algorithm, whereas (Comb-Concat)

Stebila & Gueron       Expires September 12, 2019              [Page 17]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   (Section 3.4.1) and (Comb-AltInput) (Section 3.4.4) keep the number
   of KDF applications the same (though with potentially longer inputs).

   *Extensibility.* (Comb-AltInput) (Section 3.4.4) 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 3.4.3) can naturally
   accommodate more than 2 component shared secrets since there is no
   distinction to how each shared secret is treated.  (Comb-AltInput)
   (Section 3.4.4) 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.

4.  IANA Considerations

   None.

5.  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
   "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.

5.1.  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

Stebila & Gueron       Expires September 12, 2019              [Page 18]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   used for mutual authentication).  Resolving this issue for TLS 1.3 is
   an open question.

5.2.  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?

5.3.  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?

6.  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
   attendees at the Workshop on Post-Quantum Software in Mountain View,
   California, in January 2019.

7.  References

7.1.  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>.

7.2.  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.

Stebila & Gueron       Expires September 12, 2019              [Page 19]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   [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.

   [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-00 (work in progress),
              February 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.

Stebila & Gueron       Expires September 12, 2019              [Page 20]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   [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-04 (work in
              progress), August 2018.

   [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.

   [IKE-PSK]  Fluhrer, S., McGrew, D., Kampanakis, P., and V. Smyslov,
              "Postquantum Preshared Keys for IKEv2", draft-ietf-
              ipsecme-qr-ikev2-07 (work in progress), January 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.

   [NIST]     National Institute of Standards and Technology (NIST),
              "Post-Quantum Cryptography", n.d.,
              <https://www.nist.gov/pqcrypto>.

   [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>.

Stebila & Gueron       Expires September 12, 2019              [Page 21]
Internet-Draft          stebila-tls-hybrid-design             March 2019

   [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.

   [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 Steblia
   University of Waterloo

   Email: dstebila@uwaterloo.ca

   Shay Gueron
   University of Haifa and Amazon Web Services

   Email: shay.gueron@gmail.com

Stebila & Gueron       Expires September 12, 2019              [Page 22]