A modified architecture for Optimal Normal Basis multiplication based on pre-computation

In this paper, a newly modified optimal normal basis multiplier based on the Massey-Omura method is proposed. Improvements in both area and critical path delay have been achieved over the next best architecture in the literature, through the use of pre-computation. These improvements allow for the design of small, fast multipliers for the implementation of Elliptic Curve Cryptography.

[1]  Mohammed Benaissa,et al.  GF(2^m) Multiplication and Division Over the Dual Basis , 1996, IEEE Trans. Computers.

[2]  A. Reyhani-Masoleh,et al.  Low complexity sequential normal basis multipliers over GF(2/sup m/) , 2003, Proceedings 2003 16th IEEE Symposium on Computer Arithmetic.

[3]  S. Vanstone,et al.  OPTIMAL NORMAL BASES IN GF(p”)* , 2002 .

[4]  M. Anwar Hasan,et al.  Efficient Multiplication Beyond Optimal Normal Bases , 2003, IEEE Trans. Computers.

[5]  M. Anwar Hasan,et al.  Low complexity word-level sequential normal basis multipliers , 2005, IEEE Transactions on Computers.

[6]  Gordon B. Agnew,et al.  An implementation for a fast public-key cryptosystem , 2004, Journal of Cryptology.

[7]  Harald Niederreiter,et al.  Introduction to finite fields and their applications: Preface , 1994 .

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

[9]  Ronald C. Mullin,et al.  Optimal normal bases in GF(pn) , 1989, Discret. Appl. Math..

[10]  M. Anwar Hasan,et al.  A New Construction of Massey-Omura Parallel Multiplier over GF(2m) , 2002, IEEE Trans. Computers.

[11]  L. Adleman,et al.  The use of public key cryptography in communication system design , 1978, IEEE Communications Society Magazine.

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

[13]  Hua Li,et al.  Low-Complexity Versatile Finite Field Multiplier in Normal Basis , 2002, EURASIP J. Adv. Signal Process..

[14]  Trieu-Kien Truong,et al.  A Comparison of VLSI Architecture of Finite Field Multipliers Using Dual, Normal, or Standard Bases , 1988, IEEE Trans. Computers.

[15]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

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

[17]  Taher El Gamal A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, IEEE Trans. Inf. Theory.