• Journal of the Korea Institute of Information Security & Cryptology
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• v.30 no.3
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• pp.325-336
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• 2020

Nonlinear Invariant Attack is an attack that should be considered when constructing lightweight block ciphers with relatively simple key schedule. A shortcut to prove a block cipher's resistance against nonlinear invariant attack is checking the smallest dimension of linear layer-invariant linear subspace which contains all known differences between round keys is equal to the block size. In this paper, we presents the following results. We identify the structure and number of optimal bit-permutations which require only one known difference between round keys for a designer to show that the corresponding block cipher is resistant against nonlinear invariant attack. Moreover, we show that PRESENT-like block ciphers need at least two known differences between round keys by checking all PRESENT-like bit-permutations. Additionally, we verify that the variants of PRESENT-like bit-permutations requiring the only two known differences between round keys do not conflict with the resistance against differential attack by comparing the best differential trails. Finally, through the distribution of the invariant factors of all bit-permutations that maintain BOGI logic with GIFT S-box, GIFT-variant block ciphers require at least 8 known differences between round keys for the resistance.