Fast Bitwise Implementation of the Algebraic Normal Form Transform

Abstract

The representation of Boolean functions by their algebraic normalforms (ANFs) is very important for cryptography, coding theory andother scientific areas. The ANFs are used in computing the algebraic degreeof S-boxes, some other cryptographic criteria and parameters of errorcorrectingcodes. Their applications require these criteria and parameters tobe computed by fast algorithms. Hence the corresponding ANFs should alsobe obtained by fast algorithms. Here we continue our previous work on fastcomputing of the ANFs of Boolean functions. We present and investigatethe full version of bitwise implementation of the ANF transform. The experimental results show that this implementation ismore than 25 times faster in comparison to the well-known byte-wise ANFtransform.ACM Computing Classification System (1998): F.2.1, F.2.2.