Adaptive Modular Exponentiation Methods v.s. Python's Power Function

TL;DR

This paper introduces adaptive modular exponentiation algorithms implemented in Python, which outperform standard methods by reducing computation time for large exponents, through adaptive parameter selection and benchmarking.

Contribution

The paper presents novel adaptive m-ary and sliding-window modular exponentiation methods in Python, optimized for large exponents, with empirical benchmarking showing performance improvements.

Findings

Reduce 1-5% computation time for exponents over 3072 bits

Adaptive methods outperform industry-standard implementations

Effective parameter tuning based on exponent length

Abstract

In this paper we use Python to implement two efficient modular exponentiation methods: the adaptive m-ary method and the adaptive sliding-window method of window size k, where both m's are adaptively chosen based on the length of exponent. We also conduct the benchmark for both methods. Evaluation results show that compared to the industry-standard efficient implementations of modular power function in CPython and Pypy, our algorithms can reduce 1-5% computing time for exponents with more than 3072 bits.