On the additive index of the Diffie-Hellman mapping and the discrete logarithm
Number Theory
2026-01-21 v1
Abstract
Several complexity measures such as degree, sparsity and multiplicative index for cryptographic functions including the Diffie-Hellman mapping and the discrete logarithm in a finite field have been studied in the literature. In 2022, Reis and Wang introduced another complexity measure, the additive index, of a self-mapping of a finite field. In this paper, under certain conditions, we determine lower bounds on the additive index of the univariate Diffie-Hellman mapping and a self-mapping of which can be identified with the discrete logarithm in a finite field.
Cite
@article{arxiv.2601.13034,
title = {On the additive index of the Diffie-Hellman mapping and the discrete logarithm},
author = {Pierre-Yves Bienvenu and Arne Winterhof},
journal= {arXiv preprint arXiv:2601.13034},
year = {2026}
}