The ristretto255 Group
draft-irtf-cfrg-ristretto255-00

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Last updated 2020-05-04
Replaces draft-hdevalence-cfrg-ristretto
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Crypto Forum Research Group                                H. de Valence
Internet-Draft                                                          
Intended status: Informational                                  J. Grigg
Expires: 3 November 2020                                                
                                                           G. Tankersley
                                                                        
                                                             F. Valsorda
                                                                        
                                                            I. Lovecruft
                                                              2 May 2020

                         The ristretto255 Group
                    draft-irtf-cfrg-ristretto255-00

Abstract

   This memo specifies a prime-order group, ristretto255, suitable for
   safely implementing higher-level and complex cryptographic protocols.
   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

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

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   This Internet-Draft will expire on 3 November 2020.

Copyright Notice

   Copyright (c) 2020 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
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
   license-info) in effect on the date of publication of this document.

de Valence, et al.       Expires 3 November 2020                [Page 1]
Internet-Draft                ristretto255                      May 2020

   Please review these documents carefully, as they describe your rights
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Notation and Conventions Used In This Document  . . . . . . .   3
   3.  The group abstraction . . . . . . . . . . . . . . . . . . . .   4
   4.  ristretto255  . . . . . . . . . . . . . . . . . . . . . . . .   5
     4.1.  Internal utility functions and constants  . . . . . . . .   5
       4.1.1.  Negative field elements . . . . . . . . . . . . . . .   6
       4.1.2.  Constant time operations  . . . . . . . . . . . . . .   6
       4.1.3.  Square root of a ratio of field elements  . . . . . .   7
     4.2.  External ristretto255 functions . . . . . . . . . . . . .   7
       4.2.1.  Decode  . . . . . . . . . . . . . . . . . . . . . . .   8
       4.2.2.  Encode  . . . . . . . . . . . . . . . . . . . . . . .   8
       4.2.3.  Equals  . . . . . . . . . . . . . . . . . . . . . . .   9
       4.2.4.  One-way map . . . . . . . . . . . . . . . . . . . . .  10
     4.3.  Scalar field  . . . . . . . . . . . . . . . . . . . . . .  11
   5.  API Considerations  . . . . . . . . . . . . . . . . . . . . .  11
   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  12
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .  12
   8.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  12
   9.  Normative References  . . . . . . . . . . . . . . . . . . . .  12
   10. 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
     A.4.  Square root of a ratio of field elements  . . . . . . . .  16
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  17

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
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