A new systolic squarer and its application to compute exponentiations in GF(2/sup m/)

This paper presents a new systolic squarer and a new systolic exponentiator for GF(2/sup m/) with the standard basis representation. While computing squares in GF(2/sup m/), the proposed systolic squarer has smaller latency and less hardware requirement than a dedicated systolic multiplier. The proposed systolic exponentiator consists of [m/2] squarers, one multiplier, and [(m-1)/2] power-sum circuits (for AB/sup 2/+C). As compared to existing related exponentiators, it involves less hardware complexity and smaller latency. Both of the proposed architectures involve the features of regularity, modularity, and unidirectional data flow. As a consequence, they are well suited to VLSI implementation with fault-tolerant design.

[1]  H. T. Kung,et al.  Fault-Tolerance and Two-Level Pipelining in VLSI Systolic Arrays , 1983 .

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

[3]  Trieu-Kien Truong,et al.  Systolic Multipliers for Finite Fields GF(2m) , 1984, IEEE Transactions on Computers.

[4]  A. Ghafoor,et al.  Systolic architecture for finite field exponentiation , 1989 .

[5]  Shyue-Win Wei.  A Systolic Power-Sum Circuit for GF(2^m) , 1994, IEEE Trans. Computers.

[6]  H. T. Kung.  Why systolic architectures? , 1982, Computer.

[7]  Keshab K. Parhi,et al.  Low latency standard basis GF(2/sup m/) multiplier and squarer architectures , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[8]  W. W. Peterson,et al.  Error-Correcting Codes. , 1962 .

[9]  Chin-Liang Wang.  Bit-Level Systolic Array for Fast Exponentiation in GF(2^m) , 1994, IEEE Trans. Computers.

[10]  C.-L. Wang,et al.  A new systolic architecture for fast exponentiation in GF(2m) , 1995 .

[11]  Shyue-Win Wei.  VLSI architectures for computing exponentiations, multiplicative inverses, and divisions in GF(2/sup m/) , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

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

[13]  S. Kung,et al.  VLSI Array processors , 1985, IEEE ASSP Magazine.