The ristretto255 and decaf448 Groups
draft-irtf-cfrg-ristretto255-decaf448-00

Document Type Active Internet-Draft (cfrg RG)
Authors Henry de Valence  , Jack Grigg  , George Tankersley  , Filippo Valsorda  , Isis Lovecruft  , Mike Hamburg 
Last updated 2020-10-05
Replaces draft-irtf-cfrg-ristretto255
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Crypto Forum Research Group                                H. de Valence
Internet-Draft                                                          
Intended status: Informational                                  J. Grigg
Expires: 8 April 2021                                                   
                                                           G. Tankersley
                                                                        
                                                             F. Valsorda
                                                                        
                                                            I. Lovecruft
                                                                        
                                                              M. Hamburg
                                                          5 October 2020

                  The ristretto255 and decaf448 Groups
                draft-irtf-cfrg-ristretto255-decaf448-00

Abstract

   This memo specifies two prime-order groups, ristretto255 and
   decaf448, 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.  Likewise, the
   decaf448 group can be implemented using edwards448.

Status of This Memo

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

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on 8 April 2021.

Copyright Notice

   Copyright (c) 2020 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

de Valence, et al.        Expires 8 April 2021                  [Page 1]
Internet-Draft            ristretto255-decaf448             October 2020

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

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Notation and Conventions Used In This Document  . . . . . . .   4
     2.1.  Negative field elements . . . . . . . . . . . . . . . . .   4
     2.2.  Constant time operations  . . . . . . . . . . . . . . . .   4
   3.  The group abstraction . . . . . . . . . . . . . . . . . . . .   5
   4.  ristretto255  . . . . . . . . . . . . . . . . . . . . . . . .   6
     4.1.  Internal constants  . . . . . . . . . . . . . . . . . . .   6
     4.2.  Square root of a ratio of field elements  . . . . . . . .   7
     4.3.  External ristretto255 functions . . . . . . . . . . . . .   8
       4.3.1.  Decode  . . . . . . . . . . . . . . . . . . . . . . .   8
       4.3.2.  Encode  . . . . . . . . . . . . . . . . . . . . . . .   9
       4.3.3.  Equals  . . . . . . . . . . . . . . . . . . . . . . .  10
       4.3.4.  One-way map . . . . . . . . . . . . . . . . . . . . .  11
     4.4.  Scalar field  . . . . . . . . . . . . . . . . . . . . . .  12
   5.  decaf448  . . . . . . . . . . . . . . . . . . . . . . . . . .  12
     5.1.  Internal constants  . . . . . . . . . . . . . . . . . . .  13
     5.2.  Square root of a ratio of field elements  . . . . . . . .  13
     5.3.  External decaf448 functions . . . . . . . . . . . . . . .  14
       5.3.1.  Decode  . . . . . . . . . . . . . . . . . . . . . . .  14
       5.3.2.  Encode  . . . . . . . . . . . . . . . . . . . . . . .  15
       5.3.3.  Equals  . . . . . . . . . . . . . . . . . . . . . . .  15
       5.3.4.  One-way map . . . . . . . . . . . . . . . . . . . . .  16
     5.4.  Scalar field  . . . . . . . . . . . . . . . . . . . . . .  17
   6.  API Considerations  . . . . . . . . . . . . . . . . . . . . .  17
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  17
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  18
   9.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  18
   10. Normative References  . . . . . . . . . . . . . . . . . . . .  18
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