Elliptic Curves for Security
draft-irtf-cfrg-curves-01

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Last updated 2015-02-03 (latest revision 2015-01-28)
Replaces draft-agl-cfrgcurve
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CFRG                                                          A. Langley
Internet-Draft                                                    Google
Intended status: Informational                                   R. Salz
Expires: August 1, 2015                              Akamai Technologies
                                                               S. Turner
                                                              IECA, Inc.
                                                        January 28, 2015

                      Elliptic Curves for Security
                       draft-irtf-cfrg-curves-01

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

   This Internet-Draft is submitted in full conformance with the
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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.

   This document is subject to BCP 78 and the IETF Trust's Legal
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Langley, et al.          Expires August 1, 2015                 [Page 1]
Internet-Draft                  cfrgcurve                   January 2015

   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  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Requirements Language . . . . . . . . . . . . . . . . . . . .   3
   3.  Security Requirements . . . . . . . . . . . . . . . . . . . .   3
   4.  Notation  . . . . . . . . . . . . . . . . . . . . . . . . . .   3
   5.  Parameter Generation  . . . . . . . . . . . . . . . . . . . .   4
     5.1.  Edwards Curves  . . . . . . . . . . . . . . . . . . . . .   4
     5.2.  Twisted Edwards Curves  . . . . . . . . . . . . . . . . .   5
   6.  Recommended Curves  . . . . . . . . . . . . . . . . . . . . .   6
   7.  The curve25519 function . . . . . . . . . . . . . . . . . . .   7
     7.1.  Test vectors  . . . . . . . . . . . . . . . . . . . . . .  10
   8.  Diffie-Hellman  . . . . . . . . . . . . . . . . . . . . . . .  11
     8.1.  Test vectors  . . . . . . . . . . . . . . . . . . . . . .  11
   9.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  11
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  12
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  12
     10.2.  Informative References . . . . . . . . . . . . . . . . .  12
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  13

1.  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, various '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 generating
   cryptographic elliptic curves over a given prime field.  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 high practical security in
   cryptographic applications.  The deterministic algorithm operates
   without any input parameters that would permit manipulation of the
   resulting curves.  The selection between curve models is determined
   by choosing the curve form that supports the fastest (currently
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