Overview

PSEC-KEM (Provably Secured Elliptic Curve Encryption with Key Encapsulation mechanism) is an algorithm designed by NTT Laboratories, Japan in 1999. PSEC-KEM is provably secured under the computational Diffie-Hellman assumption on the elliptic curves and is an efficient integration of both asymmetric and symmetric key cryptography to provide a secured and integrated solution. This work aims to develop hardware and software designs for the algorithm on FPGAs and standard processors.

The hardware and software implementation of PSEC-KEM is over the field GF(p), where p is a prime of 256 bits. Random curves, optimal extension fields, and curves with efficient endomorphisms are implemented.

Source Code and Documentation

  • Characteristic p Fields for Random Curves in Hardware and Software

  • Characteristic p Fields for Koblitz Curves in Hardware and Software

  • Software for OEF Fields

  • Design and Performance Document for Characteristic p Fields

  • Design over OEF (Section 4)

  • Performance Results over OEF (Section 2.2)

    References

  • NTT Information Sharing Platform Laboratories, NTT Corporation. Standars for Efficient Cryptography, SEC 2: Recommended Elliptic Curve Domain Parameters (Version 2.0), Working Draft (January 27, 2010).

  • NTT Information Sharing Platform Laboratories, NTT Corporation. PSEC-KEM Specification (Version 2.0), June 2007.

  • NTT Information Sharing Platform Laboratories, NTT Corporation. Standards for Efficient Cryptogra- phy, SEC X.1: Supplemental Document for Odd Characteristic Extension Fields, Working Draft (Version 0.7), May 2009.

  • NTT Information Sharing Platform Laboratories, NTT Corporation. Standars for Efficient Cryptography, SEC X.2: Recommended Elliptic Curve Domain Parameters, Working Draft (Version 0.6). August 2008. c NTT Corporation, IIT Kharagpur, 2011

  • Certicom Research. Standards for Efficient Cryptography, SEC 1: Elliptic Curve Cryptography (Version 1.0), September 2000

  • SHA Opencores, http://opencores.org/project,sha core

  • Jerome A. Solinas, “Effecient Arithmetic on Koblitz Curves”, Design, Codes and Cryptography, 2009, pages 195-249

  • Billy Bob Brumley and Kimmo U. J ̈rvinen, “Conversion Algorithms and Implementations for Koblitz Curve Cryptography”, IEEE Transactions on Computers, 2010, pages 81-92.

  • The GNU Multiple Precision Arithmetic Library, http://gmplib.org/.

  • D. Hankerson, A. Menezes, S. Vanstone, “Guide to Elliptic Curve Cryptography”

  • R. P. Gallant, R. J. Lambert, S. A. Vanstone, “Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms”, Crypto 2001

  • T. Guneysu and Christof Paar, “Ultra High Performance ECC over NIST Primes on Commercial FPGAs”, CHES 2008





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