Tytuł:

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

Tytuł publikacji grupowej:

2024, nr 1, JTIT-artykuły

Autor:

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

Temat i słowa kluczowe:

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.

Wydawca:

National Institute of Telecommunications

Data wydania:

2024

Typ zasobu:

artykuł

Identyfikator zasobu:

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

DOI:

10.26636/jtit.2024.1.1463

ISSN:

1509-4553

eISSN:

1899-8852

Źródło:

Journal of Telecommunications and Information Technology

Język:

ang

Licencja:

CC BY 4.0

Właściciel praw:

Instytut Łączności - Państwowy Instytut Badawczy