The ristretto255 Group
draft-hdevalence-cfrg-ristretto-01

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Crypto Forum Research Group                                H. de Valence
Internet-Draft                                                  J. Grigg
Intended status: Informational                             G. Tankersley
Expires: 9 November 2019                                     F. Valsorda
                                                            I. Lovecruft
                                                              8 May 2019

                         The ristretto255 Group
                   draft-hdevalence-cfrg-ristretto-01

Abstract

   This memo specifies a prime-order group, ristretto255, suitable for
   implementing complex cryptographic protocols such as zero-knowledge
   proofs.  The ristretto255 group can be implemented using Curve25519,
   allowing existing Curve25519 implementations to be reused and
   extended to provide a prime-order group.

Status of This Memo

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   This Internet-Draft will expire on 9 November 2019.

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   Copyright (c) 2019 IETF Trust and the persons identified as the
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   Please review these documents carefully, as they describe your rights
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de Valence, et al.       Expires 9 November 2019                [Page 1]
Internet-Draft                ristretto255                      May 2019

   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.  Notation and Conventions Used In This Document  . . . . . . .   4
   3.  ristretto255  . . . . . . . . . . . . . . . . . . . . . . . .   4
     3.1.  Internal utility functions  . . . . . . . . . . . . . . .   5
       3.1.1.  Negative field elements . . . . . . . . . . . . . . .   6
       3.1.2.  Constant time operations  . . . . . . . . . . . . . .   6
       3.1.3.  Square root of a ratio of field elements  . . . . . .   6
     3.2.  External ristretto255 functions . . . . . . . . . . . . .   7
       3.2.1.  DECODE  . . . . . . . . . . . . . . . . . . . . . . .   7
       3.2.2.  ENCODE  . . . . . . . . . . . . . . . . . . . . . . .   8
       3.2.3.  EQUALS  . . . . . . . . . . . . . . . . . . . . . . .   9
       3.2.4.  FROM_UNIFORM_BYTES  . . . . . . . . . . . . . . . . .  10
     3.3.  Operations on internal representations  . . . . . . . . .  10
     3.4.  Scalar field  . . . . . . . . . . . . . . . . . . . . . .  11
   4.  API Considerations  . . . . . . . . . . . . . . . . . . . . .  11
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  12
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  12
   7.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  12
   8.  Normative References  . . . . . . . . . . . . . . . . . . . .  12
   9.  Informative References  . . . . . . . . . . . . . . . . . . .  12
   Appendix A.  Test vectors . . . . . . . . . . . . . . . . . . . .  13
     A.1.  Multiples of the generator  . . . . . . . . . . . . . . .  13
     A.2.  Invalid encodings . . . . . . . . . . . . . . . . . . . .  14
     A.3.  Group elements from uniform bytestrings . . . . . . . . .  15
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  15

1.  Introduction

   Ristretto is a technique for constructing prime order groups with
   non-malleable encodings from non-prime-order elliptic curves.  It
   extends the [Decaf] approach to cofactor elimination to support
   cofactor-8 curves such as Curve25519 [RFC7748].  In particular, this
   allows an existing Curve25519 library to provide a prime-order group
   with only a thin abstraction layer.

   Edwards curves provide a number of implementation benefits for
   cryptography, such as complete addition formulas with no exceptional
   points and the fastest known formulas for curve operations.  However,
   every Edwards curve has a point of order 4, so that the group of
   points on the curve is not of prime order but has a small cofactor.
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