High-Performance Hardware of the Sliding-Window Method for Parallel Computation of Modular Exponentiations

Abstract

Modular exponentiation is a basic operation in various applications, such as cryptography. Generally, the performance of this operation has a tremendous impact on the efficiency of the whole application. Therefore, many researchers have devoted special interest to providing smart methods and efficient implementations for modular exponentiation. One of these methods is the sliding-window method, which preprocesses the exponent into zero and non-zero partitions. Zero partitions allow for a reduction of the number of modular multiplications required in the exponentiation using the sliding-window method. The partitioning strategy used allows variable-length non-zero partitions, which increases the average number of zero partitions and so decreases that of non-zero partitions. It performs the partitioning process in parallel with the pre-computation step of the exponent so no overhead is introduced. The implementation is efficient when compared against related existing hardware implementations.