Algorithms in invariant theory
Algorithms in invariant theory
On the bent boolean functions that are symmetric
European Journal of Combinatorics
Two new classes of bent functions
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Discrete Mathematics
On the Symmetric Property of Homogeneous Boolean Functions
ACISP '99 Proceedings of the 4th Australasian Conference on Information Security and Privacy
Homogeneous Bent Functions, Invariants, and Designs
Designs, Codes and Cryptography
Rotation symmetric Boolean functions-Count and cryptographic properties
Discrete Applied Mathematics
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A new surprising connection between invariant theory and the theory of bent functions is established. This enables us to construct Boolean function having a prescribed symmetry given by a group action. Besides the quadratic bent functions the only other known homogeneous bent functions are the six variable degree three functions constructed in [14]. We show that these bent functions arise as invariants under an action of the symmetric group on four letters. Extending to more variables we apply the machinery of invariant theory to construct previously unknown homogeneous bent functions of degree three in 8 and 10 variables. This approach gives a great computational advantage over the unstructured search problem. We finally consider the question of linear equivalence of the constructed bent functions.