Abstract
Various probabilities of accidental linearities occurring in a random, reversible substitution lookup table (S-box) with m address and m contents bits are calculated. These probabilities decrease very dramatically with increasing m. It is conjectured that good S-boxes may be built by choosing a random, reversible table of sufficient size.
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References
Federal Information Processing Standard Publication no 46. Department of Commerce. National Bureau of Standards, Gaithersburg, Md, USA.
Shannon, C.E. “A Mathematical theory of Secrecy System” Bell System Technical Journal 1948.
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© 1983 Springer-Verlag Berlin Heidelberg
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Gordon, J.A., Retkin, H. (1983). Are Big S-Boxes Best?. In: Beth, T. (eds) Cryptography. EUROCRYPT 1982. Lecture Notes in Computer Science, vol 149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39466-4_18
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DOI: https://doi.org/10.1007/3-540-39466-4_18
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