Fast Bitwise Implementation of the Algebraic Normal Form Transform
Serdica Journal of Computing, Tome 11 (2017) no. 1, pp. 045-057.

Voir la notice de l'article dans Bulgarian Digital Mathematics Library

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.
Mots-clés : Boolean Function, Algebraic Normal Form Transform, Möbius (Moebius) Transform, Zhegalkin Transform, Positive Polarity Reed-Muller Transform, Bitwise Implementation 
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Bakoev, Valentin. Fast Bitwise Implementation of the Algebraic Normal Form Transform. Serdica Journal of Computing, Tome 11 (2017) no. 1, pp. 045-057. https://geodesic-test.mathdoc.fr/item/SJC_2017_11_1_a3/