t-multiple discrete logarithm problem and solving difficulty

TL;DR

This paper introduces the t-multiple discrete logarithm problem, analyzes its difficulty, and discusses quantum resistance conditions, highlighting its significance in cryptography and quantum computing contexts.

Contribution

It defines the t-multiple discrete logarithm problem, examines factors affecting its difficulty, and provides conditions for resistance against quantum algorithms.

Findings

The problem is non-degenerate with a unique solution.

Index-calculus algorithm is unsuitable for this problem.

Two conditions for quantum resistance are proposed.

Abstract

Considering the difficult problem under classical computing model can be solved by the quantum algorithm in polynomial time, t-multiple discrete logarithm problems presented. The problem is non-degeneracy and unique solution. We talk about what the parameter effects the problem solving difficulty. Then we pointed out that the index-calculus algorithm is not suitable for the problem, and two sufficient conditions of resistance to the quantum algorithm for the hidden subgroup problem are given.