论文信息 - On Computing Multiplicative Inverses in GF(2^m)

On Computing Multiplicative Inverses in GF(2^m)

The design of a modular standard basis inversion for Galois fields GF(2/sup m/) based on Euclid's algorithm for computing the greatest common divisor of two polynomials is presented. The asymptotic complexity is linear with m both in computation time and area requirement, thus resulting in an AT-complexity of O(m/sup 2/). This is a significant improvement over the best previous proposal which achieves AT-complexity of only O(m/sup 3/). >

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

[2] Trieu-Kien Truong,et al. VLSI Architectures for Computing Multiplications and Inverses in GF(2m) , 1983, IEEE Transactions on Computers.

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

[4] H. T. Kung,et al. Systolic VLSI Arrays for Polynomial GCD Computation , 1984, IEEE Transactions on Computers.

[5] Toshi T. Doi,et al. The Compact Disc Digital Audio System: Modulation and Error Correction , 1980 .

[6] Yuzo Takamatsu,et al. Exponetiation in Finite Fields Using Dual Basis Multiplier , 1990, AAECC.

[7] Chin-Liang Wang,et al. Systolic array implementation of multipliers for finite fields GF(2/sup m/) , 1991 .

[8] T. Itoh,et al. A Fast Algorithm for Computing Multiplicative Inverses in GF(2^m) Using Normal Bases , 1988, Inf. Comput..

[9] Gui Liang Feng. A VLSI Architecture for Fast Inversion in GF(2^m) , 1989, IEEE Trans. Computers.

[10] Whitfield Diffie,et al. New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[11] Kiyomichi Araki,et al. Fast Inverters over Finite Field Based on Euclid's Algorithm , 1989 .

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