Software Implementation of the NIST Elliptic Curves Over Prime Fields

This paper presents an extensive study of the software implementation on workstations of the NIST-recommended elliptic curves over prime fields. We present the results of our implementation in C and assembler on a Pentium II 400MHz workstation. We also provide a comparison with the NIST-recommended curves over binary fields.

[1]  D. Chudnovsky,et al.  Sequences of numbers generated by addition in formal groups and new primality and factorization tests , 1986 .

[2]  Yukio Tsuruoka,et al.  Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method , 1992, CRYPTO.

[3]  Kouichi Itoh,et al.  Fast Implementation of Public-Key Cryptography ona DSP TMS320C6201 , 1999, CHES.

[4]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[5]  Taher ElGamal,et al.  A public key cyryptosystem and signature scheme based on discrete logarithms , 1985 .

[6]  Atsuko Miyaji,et al.  Efficient elliptic curve exponentiation , 1997, ICICS.

[7]  Donald E. Knuth,et al.  The art of computer programming. Vol.2: Seminumerical algorithms , 1981 .

[8]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[9]  Ernest F. Brickell,et al.  Fast Exponentiation with Precomputation (Extended Abstract) , 1992, EUROCRYPT.

[10]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[11]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[12]  Jerome A. Solinas,et al.  Efficient Arithmetic on Koblitz Curves , 2000, Des. Codes Cryptogr..

[13]  J. Solinas.  CORR 99-39 Generalized Mersenne Numbers , 1999 .

[14]  Donald E. Knuth.  The Art of Computer Programming 2 / Seminumerical Algorithms , 1971 .

[15]  Bart Preneel,et al.  On the Performance of Signature Schemes Based on Elliptic Curves , 1998, ANTS.

[16]  J. Olivos,et al.  Speeding up the computations on an elliptic curve using addition-subtraction chains , 1990, RAIRO Theor. Informatics Appl..

[17]  Mitsuru Matsui,et al.  A Practical Implementation of Elliptic Curve Cryptosystems over GF(p) on a 16-bit Microcomputer , 1998, Public Key Cryptography.

[18]  Atsuko Miyaji,et al.  Efficient Elliptic Curve Exponentiation Using Mixed Coordinates , 1998, ASIACRYPT.

[19]  Joos Vandewalle,et al.  Comparison of Three Modular Reduction Functions , 1993, CRYPTO.

[20]  Ian F. Blake,et al.  Elliptic curves in cryptography , 1999 .

[21]  Alfred Menezes,et al.  The Elliptic Curve Digital Signature Algorithm (ECDSA) , 2001, International Journal of Information Security.

[22]  Alfred Menezes,et al.  Software Implementation of Elliptic Curve Cryptography over Binary Fields , 2000, CHES.

[23]  Chae Hoon Lim,et al.  More Flexible Exponentiation with Precomputation , 1994, CRYPTO.