Compact representation of an elliptic curve point
draft-jivsov-ecc-compact-00

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Network Workign Group                                          A. Jivsov
Internet-Draft                                      Symantec Corporation
Intended status: Informational                         December 10, 2012
Expires: June 13, 2013

           Compact representation of an elliptic curve point
                      draft-jivsov-ecc-compact-00

Abstract

   This document defines a format for efficient storage representation
   of an elliptic curve point over prime fields, suitable for use with
   any IETF format or protocol.

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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Conventions used in this document  . . . . . . . . . . . . . .  3
   3.  Overview of the compact representation in IETF protocols . . .  3
   4.  The definition of the compact representation . . . . . . . . .  4
     4.1.  Encoding and decoding of an elliptic curve point . . . . .  5
     4.2.  The algorithms to generate a key pair  . . . . . . . . . .  5
       4.2.1.  The black box key generation algorithm . . . . . . . .  6
       4.2.2.  The deterministic key generation algorithm . . . . . .  6
     4.3.  The efficient square root algorithm for p=4*k+3  . . . . .  7
   5.  Interoperability considerations  . . . . . . . . . . . . . . .  7
   6.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . .  8
   7.  Security Considerations  . . . . . . . . . . . . . . . . . . .  8
   8.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     8.1.  Normative References . . . . . . . . . . . . . . . . . . . 10
     8.2.  Informative References . . . . . . . . . . . . . . . . . . 10
   Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 11

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Internet-Draft    Compact representation of an EC point    December 2012

1.  Introduction

   The National Security Agency (NSA) of the United States specifies
   elliptic curve cryptography (ECC) for use in its [SuiteB] set of
   algorithms.  The NIST elliptic curves over the prime fields
   [FIPS-186], which include [SuiteB] curves, or the Brainpool curves
   [RFC5639] are the examples of curves over prime fields.

   This document provides an efficient format for compact representation
   of a point on an elliptic curve over a prime field.  It is intended
   as an open format that other IETF protocols can rely on to minimize
   space required to store an ECC point.  This document complements the
   [RFC6090] with the on-the-wire definition of an ECC point.

   One of the benefits of the ECC is the small size of field elements.
   The compact representation reduces the encoded size of an ECC element
   in half, which can be a substantial saving in cases such as
   encryption of a short message sent to multiple recipients.

2.  Conventions used in this document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].

3.  Overview of the compact representation in IETF protocols

   IETF protocols often use the [SEC1] representation of a point on an
   elliptic curve, which is a sequence of the following fields:

   Field  Description
   ------ --------------------------------------------------------------
   B0     {02, 03, 04}, where 02 or 03 represent a compressed point (x
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