Hybrid ECDHE-SIDH Key Exchange for TLS

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Last updated 2018-11-09 (latest revision 2018-11-05)
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Network Working Group                                          F. Kiefer
Internet-Draft                                                   Mozilla
Intended status: Experimental                             K. Kwiatkowski
Expires: May 10, 2019                                         Cloudflare
                                                       November 06, 2018

                 Hybrid ECDHE-SIDH Key Exchange for TLS


   This draft specifies a TLS key exchange that combines the post-
   quantum key exchange, Supersingular elliptic curve isogenie diffie-
   hellman (SIDH), with elliptic curve Diffie-Hellman (ECDHE) key

Status of This Memo

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   This Internet-Draft will expire on May 10, 2019.

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1.  Introduction

   Supersingular elliptic curve isogenie diffie-hellman (SIDH) has been
   proposed [SIDH] as a diffie-hellman like key-exchange protocol secure
   against quantum computers.  Because there's not enough confidence in
   the security of SIDH yet it should only be used in combination with a
   classical key-exchange scheme.

   This document defines a way to combine [eSIDH] with the ECDHE key
   exchanges defined in [RFC7748] for the TLS 1.3 [RFC8446] key-

   "x25519" is combined with "sidh503" and "x448" is combined with

1.1.  Performance Considerations

   Both handshake partners have to compute the SIDH values in addition
   to the ECDHE values, which requires additional time for computation.
   The handshake messages also get larger because the SIDH values are
   added (see Section 4 for details).

1.2.  Notation

   x25519 and x448 denote the ECDHE algorithms defined over the
   respective curve from [RFC7748].  sidh503 and sidh751 denote the SIDH
   algorithms defined using a prime of bit-length "503" and "751"

1.3.  Terminology

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

2.  Hybrid SIDH-ECDHE Key Exchange

   A hybrid key exchange takes the output of two separate key exchanges
   and mixes the results in a secure way.

   The ECDHE and SIDH shared secrets are calculated independently.  The
   shared secret for ECDHE-SIDH is then the concatenation of the ECDHE
   and the SIDH shared secrets.  For x25519sidh503 for example this is

   secret = x25519_secret || sidh_secret

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   The HKDF-Extract step used by TLS is relied on to combine entropy
   from both secrets.

2.1.  ECDHE shared secret calculation

   The ECDHE shared secret calculation is performed as described in
   Section 7.4.2 of [RFC8446].

2.2.  SIDH Key Exchange

   This document uses primes p503 and p751 defined in [eSIDH] and [SIKE]
   for sidh503 and sidh751.  See [SIKE] for details on how to compute
   key-exchange messages and the shared secret.  Optimised versions of
   the algorithms mentioned here might be used.

2.2.1.  Field Element Representation

   Each element ("c=a+b*i") of the underlying quadratic field GF(p^2) is
   encoded as an array of bytes in little-endian order, i.e., the least
   significant octet appears first, where each element "a,b" from GF(p)
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