Abstract
The unrestricted circuit complexity C(.) over the basis of all logic 2-input/1-output gates is considered. It is proved that certain explicitly defined families of permutations {f n} are feebly-one-way of order 2, i.e., the functions f n satisfy the property that, for increasing n, C(f −1n ) approaches 2 · C(f n) while C(f n) tends to infinity. Both these functions and their corresponding complexities are derived by a method that exploits certain graphs called (n−1,s)-stars.
In this paper we consider only families of permutations so that their inverses are always defined.
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© 1993 Springer-Verlag Berlin Heidelberg
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Hiltgen, A.P.L. (1993). Constructions of feebly-one-way families of permutations. In: Seberry, J., Zheng, Y. (eds) Advances in Cryptology — AUSCRYPT '92. AUSCRYPT 1992. Lecture Notes in Computer Science, vol 718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57220-1_80
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DOI: https://doi.org/10.1007/3-540-57220-1_80
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