Enhancing the MILP/MIQCP-Based Automatic Search for Differential-Linear Distinguishers of IoT-Friendly Block Ciphers Simon and Simeck

<inline-formula> <tex-math notation="LaTeX">\textsf {Simon} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula> are two famous lightweight block cipher families,...

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Bibliographic Details
Published in:IEEE internet of things journal Vol. 12; no. 5; pp. 5655 - 5671
Main Authors: Chen, Siwei, Xiang, Zejun, Zeng, Xiangyong, Qin, Guangxue
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.03.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Automatic tool
Automation
Ciphers
Clustering
Computational modeling
Correlation
differential-linear (DL) cryptanalysis
Genetic expression
Integer programming
Internet of Things
lightweight cryptography
Linear approximation
Linear programming
Merging
Mixed integer
mixed-integer linear programming/mixed-integer quadratic constraint programming (MILP/MIQCP)
Search problems
Security
Simeck
Simon
Wireless communication
ISSN:2327-4662, 2327-4662
Online Access:Get full text
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Summary:<inline-formula> <tex-math notation="LaTeX">\textsf {Simon} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula> are two famous lightweight block cipher families, both of which have good implementation performance benefiting from their extremely simple round functions. So, they are suitable and friendly in use for the Internet of Things devices that require high security but low-latency and low-energy. In this article, we aim to improve the mixed-integer linear programming/mixed-integer quadratic constraint programming (MILP/MIQCP)-based method, to find better differential-linear (DL) distinguishers for the above ciphers, which can be exploited to mount distinguishing or key-recovery attacks. In particular, first, we give the completely precise mixed-integer linear programming (MILP) model to describe the linear part, and utilize the general expressions of <inline-formula> <tex-math notation="LaTeX">\textsf {Gurobi} </tex-math></inline-formula> optimizer to model middle part in a quite easy way. Second, to explore DL trails in a reasonable time, we propose two heuristic strategies to speed up the searching process. Lastly, we introduce the transforming technique, which exploits the clustering effect on DL trails, to improve the estimated correlation of the DL approximation. By applying our enhanced method, we improve the DL distinguisher correlation from <inline-formula> <tex-math notation="LaTeX">2^{-59.75} </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">2^{-59.62} </tex-math></inline-formula> for 32-round <inline-formula> <tex-math notation="LaTeX">\textsf {Simon128} </tex-math></inline-formula>, and extend the number of longest rounds of valid DL distinguishers for <inline-formula> <tex-math notation="LaTeX">\textsf {Simon32/48/64/96} </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">11/16/16/25 </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">14/17/21/26 </tex-math></inline-formula>. For <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula>, we do not outperform the currently best work, but refresh Zhou et al.'s results (the first work to automate finding DL distinguishers for <inline-formula> <tex-math notation="LaTeX">\textsf {Simon/Simeck} </tex-math></inline-formula> using MILP/MIQCP). Our work not only provides a new insight on the automatic DL cryptanalysis, but also further confirms that <inline-formula> <tex-math notation="LaTeX">\textsf {Simon} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\textsf {Simeck} </tex-math></inline-formula> are sufficiently strong to resist the DL attacks.
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ISSN:2327-4662
2327-4662
DOI:10.1109/JIOT.2024.3486965