Fast Exponentiation Using Data Compression

We present the first exponentiation algorithm that uses the entropy of the source of the exponent to improve on existing exponentiation algorithms when the entropy is smaller than $(1+w(S)/l(S))^{-1}$, where $w(S)$ is the Hamming weight of the exponent, and $l(S)$ is its length. For entropy 1 it is comparable to the best-known general purpose exponentiation algorithms.