Propagation characteristics of Boolean functions
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Discrete Applied Mathematics - Coding, cryptography and computer security
Homogeneous Bent Functions, Invariants, and Designs
Designs, Codes and Cryptography
Evolving Boolean Functions Satisfying Multiple Criteria
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Construction of nonlinear boolean functions with important cryptographic properties
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Correlation-immunity of nonlinear combining functions for cryptographic applications (Corresp.)
IEEE Transactions on Information Theory
A spectral characterization of correlation-immune combining functions
IEEE Transactions on Information Theory
Note: On the weight and nonlinearity of homogeneous rotation symmetric Boolean functions of degree 2
Discrete Applied Mathematics
Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
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
Results on rotation-symmetric S-boxes
Information Sciences: an International Journal
A differential fault attack on the grain family of stream ciphers
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
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
Designs, Codes and Cryptography
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Rotation symmetric (RotS) Boolean functions have been used as components of different cryptosystems. This class of Boolean functions are invariant under circular translation of indices. Using Burnside's lemma it can be seen that the number of n-variable rotation symmetric Boolean functions is 2^g^"^n, where g"n=(1/n)@?"t"|"n@f(t)2^n^/^t, and @f(.) is the Euler phi-function. In this paper, we find the number of short and long cycles of elements in F"2^n having fixed weight, under the RotS action. As a consequence we obtain the number of homogeneous RotS functions having algebraic degree w. Our results make the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by executing computer programs. We study RotS bent functions up to 10 variables and observe (experimentally) that there is no homogeneous rotation symmetric bent function having degree 2. Further, we studied the RotS functions on 5,6,7 variables by computer search for correlation immunity and propagation characteristics and found some functions with very good cryptographic properties which were not known earlier.