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Internet Draft                                                   W. Ladd
<draft-ladd-safecurves-00.txt>                              Grad Student
Category: Informational                                      UC Berkeley
Expires 9 July 2014                                        5 January 2014

              Addition Elliptic Curves for IETF protocols
                     <draft-ladd-safecurves-00.txt>

Status of this Memo

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Copyright Notice

   Copyright (c) 2014 IETF Trust and the persons identified as the
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Abstract

   This internet draft contains curves whose Jacobians are groups over



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   which the Decisional Diffie-Hellman problem is hard, and which have
   implementation advantages.

















































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Table of Contents

   1. Introduction ....................................................3
   2. The curves .......................................................

1. Introduction

   This document contains a set of elliptic curves over prime fields
   with many security advantages.

2. The Curves

   Each curve is given by an equation and a basepoint, together with an
   order. All curves are elliptic. Validation information is given at
   [SAFECURVES]. The names given in this document indicate the family.

   Curve25519 is a curve over GF(2^255-19), formula y^2=x^3+486662x^2+x,
   basepoint (9, 147816194475895447910205935684099868872646
   06134616475288964881837755586237401), order 2^252 +
   27742317777372353535851937790883648493.

   E-382 is a curve over GF(2^382-15), formula x^2+y^2=1-6725254x^2y^2,
   basepoint (3914921414754292646847594472454013487047
   137431784830634731377862923477302047857640522480241
   298429278603678181725699, 17), order 2^380 -
   1030303207694556153926491950732314247062623204330168346855

   M-383 is a curve over GF(2^383-187), forumla y^2=x^3+2065150x^2+x,
   basepoint (12,
   473762340189175399766054630037590257683961716725770372563038
   9791524463565757299203154901655432096558642117242906494), order 2^380
   + 166236275931373516105219794935542153308039234455761613271

   Curve383187 is a curve over GF(2^383-187), formula
   y^2=x^3+229969x^2+x, basepoint (5,
   4759238150142744228328102229734187233490253962521130945928672202
   662038422584867624507245060283757321006861735839455), order 2^380 +
   356080847217269887368687156533236720299699248977882517025

   Curve3617 is a curve over GF(2^414-17), formula x^2+y^2=1+3617x^2y^2,
   basepoint
   (17319886477121189177719202498822615443556957307604340815256226
   171904769976866975908866528699294134494857887698432266169206165, 34),
   order 2^411 -
   33364140863755142520810177694098385178984727200411208589594759

   M-511 is a curve over GF(2^511-187), formula y^2 = x^3+530438x^2+x,
   basepoint (5,



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   25004106455650724233689811491392132522115686851736085900709792642
   48275228603899706950518127817176591878667784247582124505430745177
   116625808811349787373477), order 2^508 +
   107247547596357476240445315140681218420707566274348330289655408
   08827675062043

3. Security Considerations

   This entire document discusses methods of implementing cryptography
   securely. The time for an attacker to break the DLP on these curves
   is the square root of the group order with the best known attacks.

   Curves of Edwards form are best when addition is required, those of
   Montgomery form make excellent candidates for Diffie-Hellman key
   agrement on the Kummer surface. Explicit formulas are in the
   Explicit-Formula Database [EFD].

4. IANA Considerations

   IANA should maintain a registry of these curves, calling them
   safecurve-XXXX where XXX is the curve identifier.

5. References

   [SAFECURVES] safecurves.cr.yp.to

   [EFD] http://www.hyperelliptic.org/EFD/g1p/index.html

Author Addresses
   Watson Ladd
   watsonbladd@gmail.com
   Berkeley, CA



















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