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Transformation of the discrete logarithm problem over F2n to the QUBO problem using normal bases

Wroński Michał, Leśniak Mateusz

International Journal of Electronics and Telecommunications

2025

Vol. 71, No. 1

47-53

Quantum computations are very important branch of modern cryptology. According to the number of working physical qubits available in general-purpose quantum computers and in quantum annealers, there is no coincidence, that nowadays quantum annealers allow to solve larger problems. In this paper we focus on solving discrete logarithm problem (DLP) over binary fields using quantum annealing. It is worth to note, that however solving DLP over prime fields using quantum annealing has been considered before, no author, until now, has considered DLP over binary fields using quantum annealing. Therefore, in this paper, we aim to bridge this gap. We present a polynomial transformation of the discrete logarithm problem over binary fields to the Quadratic Unconstrained Binary Optimization (QUBO) problem, using approximately 3n2 logical variables for the binary field F2n . In our estimations, we assume the existence of an optimal normal base in the given fields. Such a QUBO instance can then be solved using quantum annealing.

The Possible Impact of Quantum Annealing on Cybersecurity

Leśniak Mateusz, Wroński Michał, Burek Elżbieta

Safety & Defense

2024

42--56

Quantum annealing is an approach to quantum computing that serves as an alternative to general-purpose quantum computing. However, the cryptographic community does not currently view quantum annealing as a significant threat to cryptographic algorithms. Recent findings indicate that quantum annealing could be used for the efficient cryptanalysis of stream ciphers. Furthermore, although additional analysis is necessary, cryptanalysis with quantum annealing appears to require a relatively small amount of resources, suggesting its practical applicability. This contrasts with Grover's algorithm, which necessitates quantum circuits of substantial depth and billions of quantum gates. This paper will explore the potential cybersecurity risks if the implications of quantum annealing are not taken seriously.