You are looking at a specific version 20210517:062724 of this paper. See the latest version.

Paper 2021/620

Algebraic attacks on block ciphers using quantum annealing

Elżbieta Burek and Michał Misztal and Michał Wroński

Abstract

This paper presents method for transformation of algebraic equations of symmetric cipher into the QUBO problem. After transformation of given equations $f_1, f_2, \dots, f_n$ to equations over integers $f'_1, f'_2, \dots, f'_n$, one has to linearize each, obtaining $f'_{lin_i}=lin(f'_i)$, where $lin$ denotes linearization operation. Finally, one can obtain problem in the QUBO form as $\left( f'_{lin_1} \right)^2+\dots+\left( f'_{lin_n} \right)^2+Pen$, where $Pen$ denotes penalties obtained during linearization of equations and $n$ is the number of equations. In this paper, we show examples of the transformation of some block ciphers to the QUBO problem. What is more, we present the results of the transformation of the full AES-128 cipher to the QUBO problem, where the number of variables of equivalent QUBO problem is equal to $237,915$, which means, at least theoretically, that problem may be solved using the D-Wave Advantage quantum annealing computer. Unfortunately, it is hard to estimate the time this process would require.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
CryptanalysisAESsymmetric ciphersalgebraic attacksquantum annealing
Contact author(s)
elzbieta burek @ wat edu pl,michal misztal @ wat edu pl,michal wronski @ wat edu pl
History
2021-05-17: received
Short URL
https://ia.cr/2021/620
License
Creative Commons Attribution
CC BY
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.