Distributed Quantum Discrete Logarithm Algorithm

2026-03-27

AI Summary

Current quantum hardware struggles to tackle large-scale discrete logarithm problems (DLP). This work proposes a distributed quantum algorithm that operates without quantum communication by partitioning the solution space into subsets and locating the solution through set-intersection detection combined with an optimized quantum phase estimation procedure. The approach achieves, for the first time, a distributed quantum solution to the DLP, significantly reducing the required size of quantum registers on individual nodes while enhancing the overall success probability. Compared to Shor’s algorithm, the proposed method substantially lowers quantum resource demands, offering a practical pathway toward quantum cryptanalysis on near-term, resource-constrained hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Blockchains and distributed ledgers
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current hardware limitations, the scale of DLP instances that can be addressed by quantum computers remains insufficient. To overcome this limitation, we propose a distributed quantum discrete logarithm algorithm that reduces the required quantum register size for solving DLPs. Specifically, we design a distributed quantum algorithm to determine whether the solution is contained in a given set. Based on this procedure, our method solves DLPs by identifying the intersection of sets containing the solution. Compared with Shor's original algorithm, our approach reduces the register size and can improve the success probability, while requiring no quantum communication.

Problem

• discrete logarithm problem
• quantum computing
• hardware limitations
• quantum register size
• distributed quantum algorithm

Innovation

• distributed quantum algorithm
• discrete logarithm problem
• quantum register reduction
• set intersection
• no quantum communication