Design of Systolic Multiplier/Squarer over Finite Field $GF(2^m )$
Gi Yeong Yu, Jeong Jun Kim · Jeongbo gwahaghoe nonmunji. si'seu'tem mich i'lon · 2001
In this paper, a new LSB-first multiplier with a linear full-size systolic array structure for computing the modular multiplication A(x).B(x) mod p(x) over finite field GF(2m) is presented. A bit-wise recurrence equation which is driven from LSB-first modular multiplication algorithm usingfirst the LSB of multiplic and B(x) is obtained.By space-time transformation, a new systolic multiplier is designed from the recurrence equation with regular data flows, and then is analyzed. The area-time performance of the proposed systolic multiplier is improved by 10% and 18%, respectively compared to two well-known multipliers. Moreover, a new systolic multiplier/squarer for computing multiplication and square simultaneously is proposed by using the same design method. For the modular exponentiation over the finite field, the use of the proposed systolic multiplier/squarer shows 26% better area-time performance than the use of only multiplier.