TY - JOUR
AU - Rasoolzadeh, Shahram
PY - 2023/09/19
Y2 - 2023/12/04
TI - Classification of All t-Resilient Boolean Functions with t + 4 Variables
JF - IACR Transactions on Symmetric Cryptology
JA - ToSC
VL - 2023
IS - 3
SE - Articles
DO - 10.46586/tosc.v2023.i3.213-226
UR - https://tosc.iacr.org/index.php/ToSC/article/view/11189
SP - 213-226
AB - <p>We apply Siegenthaler’s construction, along with several techniques, to classify all (<em>n</em>−4)-resilient Boolean functions with n variables, for all values of <em>n</em> ≥ 4, up to the extended variable-permutation equivalence. We show that, up to this equivalence, there are only 761 functions for any <em>n</em> larger than or equal to 10, and for smaller values of <em>n</em>, i.e., for n increasing from 4 to 9, there are 58, 256, 578, 720, 754, and 760 functions, respectively. Furthermore, we classify all 1-resilient 6-variable Boolean functions and show that there are 1 035 596 784 such functions up to the extended variable-permutation equivalence.</p>
ER -