Inefficiency of common-multiplicand multiplication and exponentiation algorithms by performing binary complements

摘要

In order to speed up long integer modular multiplication and modular exponentiation computations that play the most important role of implementing public-key cryptographic systems, recently a result has been reported by developing a binary complement based approach on operands with larger Hamming weight in their binary representations. It is claimed that this new proposal achieves extremely good performance improvement due to the possible extensive Hamming weight reduction. Furthermore, in the conclusion of this recent result, it is claimed that the larger the bit length of the operands is, the better the performance will be in their algorithms. However, in this paper it will be shown precisely that the considered binary complement based approach on operands can only lead to an extremely negligible Hamming weight reduction. Detailed and exact analysis result is contrary to their claim, i.e., performance improvement of the binary complement based algorithms decreases considerably for larger bit length of the operands.