Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
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
BDD-Based Cryptanalysis of Keystream Generators
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Transitive q-Ary Functions over Finite Fields or Finite Sets: Counts, Properties and Applications
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Extended BDD-based cryptanalysis of keystream generators
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
IEEE Transactions on Information Theory
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
Reversible circuit synthesis of symmetric functions using a simple regular structure
RC'13 Proceedings of the 5th international conference on Reversible Computation
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A multivalued function is a function from a set $E_{q}^{n}$ to a set E m , where E k is a set which contains k elements. These functions are used in cryptography: cipher design, hash function design and in theoretical computer science. In this paper, we study the representation of these functions with Multivalued Decision Diagrams (MDD). This representation can be used both to measure complexity and to implement efficiently the functions in hardware. We are especially interested in symmetric functions. We show that symmetric functions MDDs have much lower size than classical functions MDDs. One major result is to determine exactly their MDD's maximum size. Notably, we highlight the links between De Bruijn sequences and the most complex symmetric functions and new functions are exhibited in the case q驴=驴2 and any m. Enumeration of these functions are supplied, they are shown to be sufficiently numerous to allow many applications.