Division 1 property is a generalized integral property proposed by Todo at Eurocrypt 2015, which ... more Division 1 property is a generalized integral property proposed by Todo at Eurocrypt 2015, which has been used in the analysis of various symmetric-key algorithms. At Asiacrypt 2017, Sun et al. proposed automatic tools based on Boolean Satisfiability Problem (SAT) to detect the division property of ARX ciphers. In this paper, we first exploit Karnaugh map to simplify the logical SAT expressions given by Sun et al., thereby reducing the number of variables and expressions used in modeling the division property propagation of Copy, AND and XOR, as well as other complicated operations based on these three basic operations. en, we show how to model the division property propagation against the modular multiplication operation. Note that the modular multiplication operation has not been handled in previous work but used in some block ciphers like IDEA. CCS CONCEPTS • Security and privacy → Cryptography → Cryptanalysis and other aacks
Division 1 property is a generalized integral property proposed by Todo at Eurocrypt 2015, which ... more Division 1 property is a generalized integral property proposed by Todo at Eurocrypt 2015, which has been used in the analysis of various symmetric-key algorithms. At Asiacrypt 2017, Sun et al. proposed automatic tools based on Boolean Satisfiability Problem (SAT) to detect the division property of ARX ciphers. In this paper, we first exploit Karnaugh map to simplify the logical SAT expressions given by Sun et al., thereby reducing the number of variables and expressions used in modeling the division property propagation of Copy, AND and XOR, as well as other complicated operations based on these three basic operations. en, we show how to model the division property propagation against the modular multiplication operation. Note that the modular multiplication operation has not been handled in previous work but used in some block ciphers like IDEA. CCS CONCEPTS • Security and privacy → Cryptography → Cryptanalysis and other aacks
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