An Algorithm for Modular Exponentiation

Abstract A practical technique for improving the performance of modular exponentiations (ME) is described. The complexity of the ME algorithm is O ( n log n ) modular multiplications (MMs), where n is the length of the exponent, requiring an O(n2) precomputed look-up table size with very small constant of proportionality. The algorithm uses a double-based number system which we introduce in this paper.