Fast Bitwise Implementation of the Algebraic Normal Form Transform

Bakoev, Valentin. "Fast Bitwise Implementation of the Algebraic Normal Form Transform." Serdica Journal of Computing 11.1 (2017): 045-057. <http://eudml.org/doc/289521>.

@article{Bakoev2017,
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.},
author = {Bakoev, Valentin},
journal = {Serdica Journal of Computing},
keywords = {Boolean Function; Algebraic Normal Form Transform; Möbius (Moebius) Transform; Zhegalkin Transform; Positive Polarity Reed-Muller Transform; Bitwise Implementation},
language = {eng},
number = {1},
pages = {045-057},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Fast Bitwise Implementation of the Algebraic Normal Form Transform},
url = {http://eudml.org/doc/289521},
volume = {11},
year = {2017},
}

TY - JOUR
AU - Bakoev, Valentin
TI - Fast Bitwise Implementation of the Algebraic Normal Form Transform
JO - Serdica Journal of Computing
PY - 2017
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 11
IS - 1
SP - 045
EP - 057
AB - 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.
LA - eng
KW - Boolean Function; Algebraic Normal Form Transform; Möbius (Moebius) Transform; Zhegalkin Transform; Positive Polarity Reed-Muller Transform; Bitwise Implementation
UR - http://eudml.org/doc/289521
ER -