Abstract
Is it possible that a block cipher apparently immune to classical differential cryptanalysis can be attacked considering a different operation on the message space? Recently Calderini and Sala showed how to effectively compute alternative operations on a vector space which can serve as message space for a block cipher such that the resulting structure is still a vector space. The latter were used to mount a linearisation attack against a toy cipher. Here we investigate how alternative operations interact with the layers of a substitution–permutation network and show how they influence the differential probabilities, when the difference taken into consideration is different from the usual bit-wise addition modulo two. Furthermore, we design a block cipher which appears to be secure with respect to classical differential cryptanalysis, but weaker with respect to our attack which makes use of alternative operations.
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Notes
Note that the distributivity of \(\circ \) over \(+\) does not hold.
Note that only the resistance to differential cryptanalysis is considered and we do not claim any other resistance criteria for the security of this small cipher.
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Acknowledgements
Roberto Civino thankfully acknowledges support by the Department of Mathematics of the University of Trento and by COST Action IC1306. Roberto Civino and Massimiliano Sala are grateful to MIUR-Italy for financial support via PRIN 2015TW9LSR “Group theory and applications”.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.
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Civino, R., Blondeau, C. & Sala, M. Differential attacks: using alternative operations. Des. Codes Cryptogr. 87, 225–247 (2019). https://doi.org/10.1007/s10623-018-0516-z
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DOI: https://doi.org/10.1007/s10623-018-0516-z