Abstract
The motivation of studying high-speed and space-efficient algorithms for modular exponentiation (ME) comes from the applications in cryptography. In this paper, a new parallel Montgomery binary exponentiation algorithm was proposed. This algorithm is based on the Montgomery modular reduction technique, binary method, common-multiplicand-multiplication (CMM) algorithm, and the least-signed-digit recoding (LSD) technique. By using the CMM algorithm of computing the common part from two modular multiplications, the same common part in two modular multiplications can be computed once rather twice, we can thus improve the efficiency of the binary exponentiation algorithm by decreasing the number of modular multiplications. Furthermore, by using the proposed parallel CMM-LSD Montgomery binary exponentiation algorithm, the total number of single-precision multiplications can be reduced by about 66.7% and 30% as compared with the original Montgomery algorithm and the Ha-Moon's improved Montgomery algorithm, respectively.
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