Almost security of cryptographic Boolean functions

Authors:
K. Kurosawa;R. Matsumoto
Affiliations:
Dept. of Comput. & Inf. Sci., Ibaraki Univ. Nakanarusawa, Japan;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

The propagation criterion, PC(ℓ) of order k, is one of the most general cryptographic criteria of secure Boolean functions f. In this paper, we formalize its ε-almost version. The new definition requires that f(X)+f(X+Δ) is almost uniformly distributed while in the original definition, it must be strictly uniformly distributed. Better parameters are then obtained than the strict PC(ℓ) of order k functions. To construct ε-almost PC(ℓ) of order k functions, we introduce a notion of domain distance.