The Nonhomomorphicity of Boolean Functions

Abstract. We introduce the notion of nonhomomorphicity as an alternative criterion that forecasts nonlinear characteristics of a Boolean function. Although both nonhomomorphicity and nonlinearity re ect a \di erence" between a Boolean function and all the a ne functions, they are measured from di erent perspectives. We are interested in nonhomomorphicity due to several reasons that include (1) unlike other criteria, we have not only established tight lower and upper bounds on the nonhomomorphicity of a function, but also precisely identi ed the mean of nonhomomorphicity over all the Boolean functions on the same vector space, (2) the nonhomomorphicity of a function can be estimated e ciently, and in fact, we demonstrate a fast statistical method that works both on large and small dimensional vector spaces. Key Words Boolean Functions, Cryptography, Nonhomomorphicity, Nonlinear Characteristics. 1 Motivation of this Research It is known that a function f on Vn is a ne if and only if...

• Type: Conference
• Year: 1998
• Where: SACRYPT
• Authors: Xian-Mo Zhang, Yuliang Zheng
• Keywords: Boolean Functions, Cryptology, Ne Function, Nonlinear Characteristics, SACRYPT 1998