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SAT-based impossible differential cryptanalysis of GRANULE cipher
Xiaonian WU, Jing KUANG, Runlian ZHANG, Lingchen LI
Journal of Computer Applications    2024, 44 (3): 797-804.   DOI: 10.11772/j.issn.1001-9081.2023040435
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The Boolean SATisfiability problem (SAT)-based automated search methods can directly describe logical operations such as AND, OR, NOT, XOR, and establish more efficient search models. In order to efficiently evaluate the ability of GRANULE cipher to resist impossible differential attacks, firstly, the SAT model described by the S-box differential property was optimized based on the S-box differential distribution table property. Then, the SAT model of bit-oriented impossible differential distinguisher was established for GRANULE cipher, and multiple 10-round impossible differential distinguishers of GRANULE cipher were obtained by solving the SAT model. Furthermore, an improved SAT automated verification method was given, by which the impossible differential distinguishers were verified. Finally, 16-round impossible differential attack was performed on GRANULE-64/80 cipher, where the impossible differential distinguisher was further extended forward 3-round and backward 3-round respectively. As a result, 80-bit master key was recovered with the time complexity of 251.8 16-round encryptions and the data complexity of 241.8 chosen-plaintexts. Compared with the suboptimal results for impossible differential cryptanalysis of the GRANULE cipher, the number of distinguisher rounds and key recovery attack rounds obtained are improved by 3 rounds, and the time complexity and data complexity are further reduced.

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