On the Higher Order Nonlinearities of Boolean Functions and S-Boxes, and Their Generalizations
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Information Sciences: an International Journal
On the lower bounds of the second order nonlinearities of some Boolean functions
Information Sciences: an International Journal
Best affine and quadratic approximations of particular classes of Boolean functions
IEEE Transactions on Information Theory
A note on fast algebraic attacks and higher order nonlinearities
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
On equivalence classes of boolean functions
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
A Lower Bound of the Second-order Nonlinearities of Boolean Bent Functions
Fundamenta Informaticae
On Second-order Nonlinearities of Some D 0 Type Bent Functions
Fundamenta Informaticae - Cryptology in Progress: 10th Central European Conference on Cryptology, Będlewo Poland, 2010
On the second-order nonlinearities of some bent functions
Information Sciences: an International Journal
| Hi-index | 754.90 |
The nonlinearity profile of a Boolean function (i.e., the sequence of its minimum Hamming distances nlr(f) to all functions of degrees at most r, for r ges 1) is a cryptographic criterion whose role against attacks on stream and block ciphers has been illustrated by many papers. It plays also a role in coding theory, since it is related to the covering radii of Reed-Muller codes. We introduce a method for lower-bounding its values and we deduce bounds on the second-order nonlinearity for several classes of cryptographic Boolean functions, including the Welch and the multiplicative inverse functions (used in the S-boxes of the Advanced Encryption Standard (AES)). In the case of this last infinite class of functions, we are able to bound the whole profile, and we do it in an efficient way when the number of variables is not too small. This allows showing the good behavior of this function with respect to this criterion as well.