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- W3121017621 abstract "We focus on a set of r-valued n-variable functions that are defined by a partition P on the set of rn input vectors. Specifically, each block of P specifies input vectors, all of which map to the same function value. For example, a symmetric function is defined by a partition where input vectors in the same block are permutations of each other. Given the partition P and the set S of functions associated with P, we analyze the set S' of functions that are a maximal distance from S. Such functions hold promise for use in crypto-systems.In this paper, we characterize functions in S'. From this, we compute the distance to their corresponding partition functions. We show that, when r and n increase without bound, this distance approaches the maximum possible, rn. Bent functions achieve only half the maximum possible distance when n is large. We show that functions a maximal distance from partition functions tend to have a uniform distribution across the r possible function values. Such functions tend to be immune to statistics-based attacks. Finally, we show that, if the set S' of functions is maximally distant from a set S of partition functions, then the converse is true; that is, S is maximally distant from S'." @default.
- W3121017621 created "2021-01-18" @default.
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- W3121017621 date "2020-11-01" @default.
- W3121017621 modified "2023-09-25" @default.
- W3121017621 title "Properties of Multiple-Valued Partition Functions" @default.
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- W3121017621 doi "https://doi.org/10.1109/ismvl49045.2020.00-25" @default.
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