论文信息 - An Architecture for Computing Zech's Logarithms in GF(2m)

An Architecture for Computing Zech's Logarithms in GF(2m)

In this paper, a new method for calculation of Zech's logarithm in GF(2/sup m/) is presented. For a given element, the logarithm is calculated by bit operations performed on its binary representation. No look-up tables are used. The proposed method makes feasible the implementation of an universal-type device for finite field arithmetic.

Carlos Eduardo Pedreira | Francisco M. Assis

[1] Klaus Huber. Solving equations in finite fields and some results concerning the structure of GF(pm) , 1992, IEEE Trans. Inf. Theory.

[2] Christof Paar,et al. A New Architecture for a Parallel Finite Field Multiplier with Low Complexity Based on Composite Fields , 1996, IEEE Trans. Computers.

[3] Jehoshua Bruck,et al. Depth efficient neural networks for division and related problems , 1993, IEEE Trans. Inf. Theory.

[4] F. MacWilliams,et al. The Theory of Error-Correcting Codes , 1977 .

[5] R. Blahut. Theory and practice of error control codes , 1983 .

[6] T. Elgamal. A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[7] Kyoki Imamura. A method for computing addition tables in GF(pn) (Corresp.) , 1980, IEEE Trans. Inf. Theory.

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

[9] Elwyn R. Berlekamp,et al. Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[10] Jehoshua Bruck,et al. Neural computation of arithmetic functions , 1990 .

[11] Thomas Kailath,et al. Depth-Size Tradeoffs for Neural Computation , 1991, IEEE Trans. Computers.

[12] Christof Paar,et al. Some remarks on efficient inversion in finite fields , 1995, Proceedings of 1995 IEEE International Symposium on Information Theory.

[13] Klaus Huber. Some comments on Zech's logarithms , 1990, IEEE Trans. Inf. Theory.