Welcome to the resource topic for 2022/399
Title:
The Inverse of \chi and Its Applications to Rasta-like Ciphers
Authors: Fukang Liu, Santanu Sarkar, Willi Meier, Takanori Isobe
Abstract:At ASIACRYPT 2021, Liu et al. pointed out a weakness of the Rasta-like ciphers neglected by the designers. The main strategy is to construct exploitable equations of the n-bit \chi operation denoted by \chi_n. However, these equations are all obtained by first studying \chi_n for small n. In this note, we demonstrate that if the explicit formula of the inverse of \chi_n denoted by \chi_n^{-1} is known, all these exploitable equations would have been quite obvious and the weakness of the Rasta-like ciphers could have been avoided at the design phase. However, the explicit formula of \chi_n^{-1} seems to be not well-known and the most relevant work was published by Biryukov et al. at ASIACRYPT 2014. In this work, we give a very simple formula of \chi_n^{-1} that can be written down in only one line and we prove its correctness in a rigorous way. Based on its formula, the formula of exploitable equations for Rasta-like ciphers can be easily derived and therefore more exploitable equations are found.
ePrint: https://eprint.iacr.org/2022/399
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