Paper 2003/075

Almost Security of Cryptographic Boolean Functions

Kaoru Kurosawa

Abstract

$PC(l)$ of order $k$ is one of the most general cryptographic criteria of secure Boolean functions. In this paper, we introduce its $\epsilon$-almost version. The new definition requires {\it only} that $f(X)+f(X+\Delta)$ is {\it almost} uniformly distiributed (while the original definition of $PC(l)$ of order $k$ requires that it is {\it strictly} uniformly distiributed). We next show its construciton. Better parameters are then obtained than normal $PC(l)$ of order $k$ functions.