Fast Bitwise Implementation of the Algebraic Normal Form Transform

Valentin Bakoev

Abstract


The representation of Boolean functions by their algebraic normal
forms (ANFs) is very important for cryptography, coding theory and
other scientific areas. The ANFs are used in computing the algebraic degree
of S-boxes, some other cryptographic criteria and parameters of errorcorrecting
codes. Their applications require these criteria and parameters to
be computed by fast algorithms. Hence the corresponding ANFs should also
be obtained by fast algorithms. Here we continue our previous work on fast
computing of the ANFs of Boolean functions. We present and investigate
the full version of bitwise implementation of the ANF transform.
The experimental results show that this implementation is
more than 25 times faster in comparison to the well-known byte-wise ANF
transform.

ACM Computing Classification System (1998): F.2.1, F.2.2.


Keywords


Boolean function; algebraic normal form transform; Möbius (Moebius) transform; Zhegalkin transform; positive polarity Reed–Muller transform; bitwise implementation

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ISSN 1314-7897 - Online
ISSN 1312-6555 - Print