For vectorial Boolean functions, the behavior of iteration has consequence in the diffusion property of the system. We present a study on the diffusion property of iterated vectorial Boolean functions. The measure that will be of main interest here is the notion of the degree of completeness, which has been suggested by the NESSIE project. We provide the first (to the best of our knowledge) two...

We prove that, for bent vectorial functions, CCZ-equivalence coincides with EA-equivalence. However, we show that CCZ-equivalence can be used for constructing bent functions which are new up to CCZequivalence. Using this approach we construct classes of nonquadratic bent Boolean and bent vectorial functions.

In this paper, we investigate some statistical properties of multiplication mod 2 for cryptographic use. For this purpose, we introduce a family of T-functions similar to modular multiplication, which we call M-functions. We obtain the probability distribution of M-functions as vectorial Boolean functions. At first, we determine the joint probability distribution of arbitrary number of the outp...

In this paper, we show the rst method to construct vecto-rial bent functions which satisfy both the largest degree and the largest number of output bits simultaneously. We next apply this method to construct balanced vectorial Boolean functions which have larger non-linearities than previously known constructions.

We investigate the security of n-bit to m-bit vectorial Boolean functions in stream ciphers. Such stream ciphers have higher throughput than those using single-bit output Boolean functions. However, as shown by Zhang and Chan at Crypto 2000, linear approximations based on composing the vector output with any Boolean functions have higher bias than those based on the usual correlation attack. In...

At Crypto 2008, Shamir introduced a new algebraic attack called the cube attack, which allows us to solve black-box polynomials if we are able to tweak the inputs by varying an initialization vector. In a stream cipher setting where the filter function is known, we can extend it to the cube attack with annihilators: By applying the cube attack to Boolean functions for which we can find low-degr...

Let n be an even positive integer, and m<n one of its divisors. In this paper, inspired by the work Tang et al. (2017) [23] on constructing large classes bent functions from known ones, we consider construction vectorial plateaued (n,m)-functions form H(x)=G(x)+g(x), where G is a (n,m)-function, g Boolean function. We find efficient generic method to construct such kind (plateaued) establishing...