Paper 2021/527
Solving discrete logarithm problem over prime fields using quantum annealing and $\frac{n^3}{2}$ logical qubits
Michał Wroński
Abstract
Shor's quantum algorithm for integer factorization and discrete logarithm is one of the fundamental approaches in modern cryptology. The application of Shor's algorithm requires a general-purpose quantum computer. On the other hand, there are known methods of transformation of factorization problem to the QUBO problem and then solving it using quantum annealing computing with approximately $\frac{n^2}{4}$ logical qubits, for example, using D-Wave computer. It is believed that this approach also may be helpful, primarily until large general-purpose quantum computers will exist. Until now algorithm of similar efficiency for computing discrete logarithm over prime fields was unknown. In this paper, we present a method of reducing discrete logarithm problem to the QUBO problem, which requires approximately $\frac{n^3}{2}$ logical qubits. We also show how to apply quantum annealing to compute discrete logarithm modulo composite numbers, where a quantum annealing factorization algorithm may be used to reduce discrete logarithm modulo composite to several discrete logarithm problems modulo prime number.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- discrete logarithm problemD-Wavequantum annealingcryptanalysis
- Contact author(s)
- michal wronski @ wat edu pl
- History
- 2021-12-30: revised
- 2021-04-23: received
- See all versions
- Short URL
- https://ia.cr/2021/527
- License
-
CC BY