Scalable and systolic architecture for computing double exponentiation over GF(2m)

Double-exponentiation is a crucial arithmetic operation for many cryptographic protocols. Several efficient double-exponentiation algorithms based on systolic architecture have been proposed. However, systolic architectures require large circuit space, thus increasing the cost of the protocol. This would be a drawback when designing circuits in systems requiring low cost and low power consumption. However, some cost savings can be attained by compromising speed, as in portable devices and many embedded systems. This study proposes a scalable and systolic AB(2) and a scalable and systolic A x B, which are the core circuit modules of double-exponentiation. A scalable and systolic double-exponentiation can thus be obtained based on the proposed scalable AB(2) and A x B architecture. Embedded system engineers may specify a target double-exponentiation with appropriate scaling systolic circuits. The proposed circuit has lower circuit space/cost and low time/propagation than other circuits.