Idempotents in the neighbourhood of Patterson-Wiedemann functions having Walsh spectra zeros
Designs, Codes and Cryptography
Note: On the weight and nonlinearity of homogeneous rotation symmetric Boolean functions of degree 2
Discrete Applied Mathematics
On the existence of (10, 2, 7, 488) resilient functions
IEEE Transactions on Information Theory
Constructions of almost optimal resilient Boolean functions on large even number of variables
IEEE Transactions on Information Theory
9-variable Boolean functions with nonlinearity 242 in the generalized rotation symmetric class
Information and Computation
Note: On homogeneous rotation symmetric bent functions
Discrete Applied Mathematics
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
A recursive formula for weights of Boolean rotation symmetric functions
Discrete Applied Mathematics
Weights of Boolean cubic monomial rotation symmetric functions
Cryptography and Communications
Affine equivalence of cubic homogeneous rotation symmetric functions
Information Sciences: an International Journal
Equivalence classes for cubic rotation symmetric functions
Cryptography and Communications
On the immunity of rotation symmetric Boolean functions against fast algebraic attacks
Discrete Applied Mathematics
Affine equivalence of quartic homogeneous rotation symmetric Boolean functions
Information Sciences: an International Journal
| Hi-index | 754.96 |
For the first time Boolean functions on 9 variables having nonlinearity 241 are discovered, that remained as an open question in literature for almost three decades. Such functions are found by heuristic search in the space of rotation symmetric Boolean functions (RSBFs). This shows that there exist Boolean functions on n (odd) variables having nonlinearity >2n-1-2n-1/2 if and only if n>7. Using similar search technique, balanced Boolean functions on 9, 10, and 11 variables are attained having autocorrelation spectra with maximum absolute value <2lceiln/2rceil. On odd number of variables, earlier such functions were known for 15, 21 variables; there was no evidence of such functions at all on even number of variables. In certain cases, our functions can be affinely transformed to obtain first-order resiliency or first-order propagation characteristics. Moreover, 10 variable functions having first-order resiliency and nonlinearity 492 are presented that had been posed as an open question at Crypto 2000. The functions reported in this paper are discovered using a suitably modified steepest descent based iterative heuristic search in the RSBF class along with proper affine transformations. It seems elusive to get a construction technique to match such functions