## A Sublinear-Time Parallel Algorithm for Integer Modular Exponentiation (1999)

Citations: | 8 - 0 self |

### BibTeX

@MISC{Sorenson99asublinear-time,

author = {Jonathan P. Sorenson},

title = {A Sublinear-Time Parallel Algorithm for Integer Modular Exponentiation},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

The modular exponentiation problem is, given integers x; a; m with m ? 0, compute x a mod m. Let n denote the sum of the lengths of x, a, and m in binary. We present a parallel algorithm for this problem that takes O(n= log log n) time on the common CRCW PRAM using O(n 2+ffl ) processors. This algorithm is based on Bernstein's Explicit Chinese Remainder Theorem combined with a fast method for parallel prefix summation. We also present a linear time algorithm for the EREW PRAM. 1 Introduction. In this paper we present a new parallel algorithm for the modular exponentiation problem. This problem is, given integers x; a and a positive integer m, compute x a mod m. Applications for this problem are quite numerous, and include primality testing, integer factoring, the discrete logarithm problem, and cryptographic protocols based on these problems such as RSA. It is not an overstatement to say that modular exponentiation is a fundamentally important problem, and fast algorithms for t...