Elliptic Curves for Security
draft-irtf-cfrg-curves-00

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CFRG                                                          A. Langley
Internet-Draft                                                    Google
Intended status: Informational                          January 28, 2015
Expires: August 1, 2015

                      Elliptic Curves for Security
                       draft-irtf-cfrg-curves-00

Abstract

   This memo describes an algorithm for deterministically generating
   parameters for elliptic curves over prime fields offering high
   practical security in cryptographic applications, including Transport
   Layer Security (TLS) and X.509 certificates.  It also specifies a
   specific curve at the ~128-bit security level.

Status of This Memo

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   This Internet-Draft will expire on August 1, 2015.

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   Copyright (c) 2015 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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Langley                  Expires August 1, 2015                 [Page 1]
Internet-Draft                  cfrgcurve                   January 2015

Table of Contents

   1.  Note on authorship  . . . . . . . . . . . . . . . . . . . . .   2
   2.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   3.  Requirements Language . . . . . . . . . . . . . . . . . . . .   3
   4.  Security Requirements . . . . . . . . . . . . . . . . . . . .   3
   5.  Notation  . . . . . . . . . . . . . . . . . . . . . . . . . .   3
   6.  Parameter Generation  . . . . . . . . . . . . . . . . . . . .   4
     6.1.  Edwards Curves  . . . . . . . . . . . . . . . . . . . . .   4
     6.2.  Twisted Edwards Curves  . . . . . . . . . . . . . . . . .   5
     6.3.  Generators  . . . . . . . . . . . . . . . . . . . . . . .   6
   7.  Recommended Curves  . . . . . . . . . . . . . . . . . . . . .   7
   8.  Wire-format of field elements . . . . . . . . . . . . . . . .   8
   9.  Elliptic Curve Diffie-Hellman . . . . . . . . . . . . . . . .   9
     9.1.  Diffie-Hellman protocol . . . . . . . . . . . . . . . . .  11
   10. Test vectors  . . . . . . . . . . . . . . . . . . . . . . . .  11
   11. References  . . . . . . . . . . . . . . . . . . . . . . . . .  12
     11.1.  Normative References . . . . . . . . . . . . . . . . . .  12
     11.2.  Informative References . . . . . . . . . . . . . . . . .  12
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  13

1.  Note on authorship

   This document is a merging of "draft-black-rpgecc-01" (by Benjamin
   Black, Joppe W.  Bos, Craig Costello, Patrick Longa and Michael
   Naehrig) and "draft-turner-thecurve25519function-01" (by Watson Ladd,
   Rich Salz and Sean Turner).  They are the actual authors of the words
   and figures, but authorship also implies support and so are not
   listed as authors until they have confirmed that they support this
   document.  None the less, they deserve any credit for the contents.

2.  Introduction

   Since the initial standardization of elliptic curve cryptography
   (ECC) in [SEC1] there has been significant progress related to both
   efficiency and security of curves and implementations.  Notable
   examples are algorithms protected against certain side-channel
   attacks, different 'special' prime shapes which allow faster modular
   arithmetic, and a larger set of curve models from which to choose.
   There is also concern in the community regarding the generation and
   potential weaknesses of the curves defined in [NIST].

   This memo describes a deterministic algorithm for generation of
   elliptic curves for cryptography.  The constraints in the generation
   process produce curves that support constant-time, exception-free
   scalar multiplications that are resistant to a wide range of side-
   channel attacks including timing and cache attacks, thereby offering
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