Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Enumerating boolean functions of cryptographic significance
Journal of Cryptology
Average and Worst Case Number of Nodes in Decision Diagrams of Symmetric Multiple-Valued Functions
IEEE Transactions on Computers
Least Upper Bounds for the Size of OBDDs Using Symmetry Properties
IEEE Transactions on Computers
Generalization of Siegenthaler Inequality and Schnorr-Vaudenay Multipermutations
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Results on rotation symmetric polynomials over GF(p)
Information Sciences: an International Journal
IEEE Transactions on Information Theory
Balanced Symmetric Functions Over
IEEE Transactions on Information Theory
De Bruijn sequences and complexity of symmetric functions
Cryptography and Communications
Enhanced count of balanced symmetric functions and balanced alternating functions
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
On the algebraic normal form and walsh spectrum of symmetric functions over finite rings
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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To implement efficiently and securely good non-linear functions with a very large number of input variables is a challenge. Partially symmetric functions such as transitive functions are investigated to solve this issue. Known results on Boolean symmetric functions are extended both to transitive functions and to q-ary functions (on any set of qelements including finite fields GF(q) for any q). In a special case when the number of variables is n= pkwith pprime, an extension of Lucas' theorem provides new counting results and gives useful properties on the set of transitive functions. Results on balanced transitive q-ary functions are given. Implementation solutions are suggested based on q-ary multiple-valued decision diagrams and examples show simple implementations for these kind of symmetric functions. Applications include ciphers design and hash functions design but also search for improved covering radius of codes.