Discrete Mathematics
Homogeneous Bent Functions, Invariants, and Designs
Designs, Codes and Cryptography
A constructive count of rotation symmetric functions
Information Processing Letters
Note: On the weight and nonlinearity of homogeneous rotation symmetric Boolean functions of degree 2
Discrete Applied Mathematics
Search for Boolean Functions With Excellent Profiles in the Rotation Symmetric Class
IEEE Transactions on Information Theory
A recursive formula for weights of Boolean rotation symmetric functions
Discrete Applied Mathematics
Affine equivalence for rotation symmetric Boolean functions with 2k variables
Designs, Codes and Cryptography
Weights of Boolean cubic monomial rotation symmetric functions
Cryptography and Communications
Equivalence classes for cubic rotation symmetric functions
Cryptography and Communications
Affine equivalence of quartic homogeneous rotation symmetric Boolean functions
Information Sciences: an International Journal
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Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions are affine equivalent. The simplest case of quadratic rotation symmetric functions which are generated by cyclic permutations of the variables in a single monomial was only settled in 2009. This paper studies the much more complicated cubic case for such functions. A new concept of patterns is introduced, by means of which the structure of the smallest group G"n, whose action on the set of all such cubic functions in n variables gives the affine equivalence classes for these functions under permutation of the variables, is determined. We conjecture that the equivalence classes are the same if all nonsingular affine transformations, not just permutations, are allowed. Our method gives much more information about the equivalence classes; for example, in this paper we give a complete description of the equivalence classes when n is a prime or a power of 3.