Note: On the degree of homogeneous bent functions
Discrete Applied Mathematics
Rotation symmetric Boolean functions-Count and cryptographic properties
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
Affine equivalence of cubic homogeneous rotation symmetric functions
Information Sciences: an International Journal
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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We improve parts of the results of [T. W. Cusick, P. Stanica, Fast evaluation, weights and nonlinearity of rotation-symmetric functions, Discrete Mathematics 258 (2002) 289-301; J. Pieprzyk, C. X. Qu, Fast hashing and rotation-symmetric functions, Journal of Universal Computer Science 5 (1) (1999) 20-31]. It is observed that the n-variable quadratic Boolean functions, f"n","s(x)@?@?"i"="1^nx"ix"i"+"s"-"1 for 2@?s@?@?n2@?, which are homogeneous rotation symmetric, may not be affinely equivalent for fixed n and different choices of s. We show that their weights and nonlinearity are exactly characterized by the cyclic subgroup of Z"n. If ngcd(n,s-1), the order of s-1, is even, the weight and nonlinearity are the same and given by 2^n^-^1-2^n^2^+^g^c^d^(^n^,^s^-^1^)^-^1. If the order is odd, it is balanced and nonlinearity is given by 2^n^-^1-2^n^+^g^c^d^(^n^,^s^-^1^)^2^-^1.