Work

Transformation of Elliptic Curve Discrete Logarithm Problem to QUBO Using Direct Method in Quantum Annealing Applications

Year: 2024

Type: article

Abstract: This paper investigates how to reduce the elliptic curve discrete logarithm problem over prime fields to the quadratic unconstrained binary optimization (QUBO) problem in order to obtain as few logical qubits as possible. In the best case scenario, if n is the bitlength of a characteristic of prime field Fp, approximately 3n³ logical qubits are required for such a reduction in the Edwards curve case. We present a practical attack on an elliptic curve discrete logarithm problem over the 3-bit prime field F7 for an elliptic curve with the subgroup of order 8. We solved this problem using the D-Wave Advantage QPU. To the best of the authors' knowledge, no one has made, so far, a practical attack on the elliptic curve discrete logarithm over a prime field using the direct quantum method.

Source: Journal of Telecommunications and Information Technology

DOI: 10.26636/jtit.2024.1.1463

Authors: Michał Wroński, Elżbieta Burek, Łukasz Dzierzkowski, Olgierd Żołnierczyk

Institutions: NASK National Research Institute, Military University of Technology in Warsaw, University of Military Science and Technology

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Wojskowa Akademia Techniczna

Award: G1603785027