Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
Designs, Codes and Cryptography
Exact combinational logic synthesis and non-standard circuit design
Proceedings of the 5th conference on Computing frontiers
Information Security and 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
Improved lower bound on the number of balanced symmetric functions over GF(p)
Information Sciences: an International Journal
A logic programming framework for combinational circuit synthesis
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Enumeration of balanced symmetric functions over GF(p)
Information Processing Letters
De Bruijn sequences and complexity of symmetric functions
Cryptography and Communications
On the algebraic immunity of symmetric boolean functions
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Efficient computation of algebraic immunity for algebraic and fast algebraic attacks
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
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
Hi-index | 754.84 |
We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. Besides the reduction of the amount of memory required for representing a symmetric function, this property has some consequences from a cryptographic point of view. For instance, it leads to a new general bound on the order of resiliency of symmetric functions, which improves Siegenthaler's bound. The propagation characteristics of these functions are also addressed and the algebraic normal forms of all their derivatives are given. We finally detail the characteristics of the symmetric functions of degree at most 7, for any number of variables. Most notably, we determine all balanced symmetric functions of degree less than or equal to 7.