Title:

Transformation of Elliptic Curve Discrete Logarithm Problem to QUBO Using Direct Method in Quantum Annealing Applications, Journal of Telecommunications and Information Technology, 2024, nr 1

Group publication title:

2024, nr 1, JTIT-artykuły

Creator:

Wroński, Michał ; Burek, Elżbieta ; Dzierzkowski, Łukasz ; Żołnierczyk, Olgierd

Subject and Keywords:

cryptanalysis ; D-Wave ; elliptic curve discrete logarithm problem ; quantum annealing

Abstrakt:

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.

Publisher:

National Institute of Telecommunications

Date:

2024

Resource Type:

artykuł

Resource Identifier:

ISSN 1509-4553, on-line: ISSN 1899-8852

DOI:

10.26636/jtit.2024.1.1463

ISSN:

1509-4553

eISSN:

1899-8852

Source:

Journal of Telecommunications and Information Technology

Language:

ang

License:

CC BY 4.0

rights owner:

Instytut Łączności - Państwowy Instytut Badawczy