%0 Journal Article
%T APPLICATION OF NEW CLASSES OF MERSENNE PRIMES FOR FAST MODULAR REDUCTION FOR LARGE-INTEGER MULTIPLICATION
%A Suhas Sreehari
%A Huapeng Wu
%A Majid Ahmadi
%J International Journal of Cyber-Security and Digital Forensics
%D 2012
%I Society of Digital Information and Wireless Communications (SDIWC)
%X This paper attempts to speed-up the modular reduction as an independent step of modular multiplication, which is the central operation in public-key cryptosystems. Based on the properties of Mersenne and Quasi-Mersenne primes, we have described four distinct sets of moduli which are responsible for converting the single-precision multiplication prevalent in many of today's techniques into an addition operation and a few simple shift operations. We propose a novel revision to the Modified Barrett algorithm presented in [3]. With the backing of the special moduli sets, the proposed algorithm is shown to outperform (speed-wise) the Modified Barrett algorithm by 80% for operands of length 700 bits, the least speed-up being around 70% for smaller operands, in the range of around 100 bits.
%U http://sdiwc.net/digital-library/web-admin/upload-pdf/00000253.pdf