Boolean Function Algebraic Normal Form Transform Möbius (Moebius) Transform Zhegalkin Transform Positive Polarity Reed-Muller Transform Bitwise Implementation
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Journal of Computing, Vol. 11, No 1, (2017), 045p-057p
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
ACM Computing Classification System (1998): F.2.1, F.2.2.