An efficient common-multiplicand-multiplication method to the Montgomery algorithm for speeding up exponentiation

Fast batch modular exponentiation with common-multiplicand multiplication

“…Common-multiplicand multiplication (CMM for short) is a widely used method for enhancing the performance of exponentiations [25,46,47,49,50]. The CMM method reduces the time for performing multiplications, and enhances the performance of exponentiation.…”

“…In this thesis, we are particullary interested in the methods based on Montgomery multiplication since it efficiently evalutes modular multiplication. Ha and Moon [25] extended Montgomery multiplication to handle two multiplications with a common-multiplicand efficiently, and Wu [46] generalized Ha and Moon's work for an arbitrary number of multiplications.…”

“…One approach to improve the efficiency of the multiplication is to take advantage of a special form of multiple multiplications {A i ⇥ C | i = 1, 2, ..., t} that share an identical multiplicand C [25,46,47,49,50]. Yen and Laih [50] proposed an algorithm for common-multiplicand multiplications (CMM for short)…”

“…Ha and Moon [25] introduced an efficient algorithm for Montgomery multiplication where two multiplications share a common multiplicand. Wu [46] extended Ha and Moon's algorithm to handle more than two multiplications.…”

A New Modified CMM Modular Exponentiation Algorithm

“…In [16] CMM method in [15] is used in multiplication phase. Wu in [17] proposed divide the signed-digit exponent into three equal lengths and use of CMM technique in order to compute common part of multiplications, once rather than several times.…”