The ristretto255 Group
draft-hdevalence-cfrg-ristretto-00

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Crypto Forum Research Group                                H. de Valence
Internet-Draft
Intended status: Informational                                  J. Grigg
Expires: July 24, 2019
                                                           G. Tankersley

                                                             F. Valsorda

                                                            I. Lovecruft
                                                        January 20, 2019

                         The ristretto255 Group
                   draft-hdevalence-cfrg-ristretto-00

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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   Copyright (c) 2019 IETF Trust and the persons identified as the
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   This document is subject to BCP 78 and the IETF Trust's Legal
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   (https://trustee.ietf.org/license-info) in effect on the date of

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   publication of this document.  Please review these documents
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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 . . . . . . . . . . . . . . .   5
       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  . . . . . . . . .  11
     3.4.  Scalar functions  . . . . . . . . . . . . . . . . . . . .  11
   4.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  11
   5.  Security Considerations . . . . . . . . . . . . . . . . . . .  11
   6.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  12
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  12
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .  12
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  12
   Appendix A.  Test vectors . . . . . . . . . . . . . . . . . . . .  13
     A.1.  Multiples of the generator  . . . . . . . . . . . . . . .  13
     A.2.  Invalid encodings . . . . . . . . . . . . . . . . . . . .  13
     A.3.  Group elements from uniform bytestrings . . . . . . . . .  14
   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,

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