Computing Modular Exponentiation for Fixed-Exponent

Exponentiation is computing ge, where g is an element of a group G and e is a positive integer. In modular exponentiation the underlying group is Zn or Z*n. This paper describe the methods to compute exponentiation where a fixed-exponent e is raised to several bases g of a group G. We describe modular exponentiation based on Bernstein's algorithm for multiplication by constant. We also present a modified approach to modular exponentiation based on k-ary String Replacement (SR(k)) representation.