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Title:
Affine-evasive Sets Modulo a Prime
Authors: Divesh Aggarwal
Abstract:In this work, we describe a simple and efficient construction of a large subset S of F_p, where p is a prime, such that the set A(S) for any non-identity affine map A over F_p has small intersection with S. Such sets, called affine-evasive sets, were defined and constructed in~\cite{ADL14} as the central step in the construction of non-malleable codes against affine tampering over F_p, for a prime p. This was then used to obtain efficient non-malleable codes against split-state tampering. Our result resolves one of the two main open questions in~\cite{ADL14}. It improves the rate of non-malleable codes against affine tampering over F_p from log log p to a constant, and consequently the rate for non-malleable codes against split-state tampering for n-bit messages is improved from n^6 log^7 n to n^6.
ePrint: https://eprint.iacr.org/2014/328
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