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 …

Boolean functions used in cryptographic applications have to satisfy various cryptographic
criteria. Although the choice of the criteria depends on the cryptosystem in which they are …

The two main criteria evaluating, from cryptographic viewpoint, the complexity of Boolean
functions are the nonlinearity and the algebraic degree. Two other criteria can also be …

Nonlinear Boolean functions are necessary building blocks in cryptography; they often play
a key role in the design of many stream ciphers and block ciphers. In the design of stream …

This chapter deals with multi-output Boolean functions viewed from a cryptographic
viewpoint, that is, functions from the vector space Fn2, of all binary vectors of length n, to the …

The nonlinearity profile of a Boolean function (ie, the sequence of its minimum Hamming
distances nl r (f) to all functions of degrees at most r, for r ges 1) is a cryptographic criterion …

In this correspondence, we introduce a method to construct Boolean functions in any
number of variables, with optimal algebraic immunity. Remarkably, all functions of this type …

Three of the most important criteria for cryptographically strong Boolean functions are the
balancedness, the nonlinearity and the propagation criterion. This paper studies systematic …

It is known that Boolean functions used in stream and block ciphers should have good
cryptographic properties to resist algebraic attacks. Up until now, there have been several …

We study a representation of Boolean functions (and more generally of integer-
valued/complex-valued functions), not used until now in coding and cryptography, which …