Vectorial Boolean functions are usually called Substitution Boxes (S-Boxes) and are used as basic component of block ciphers in Cryptography. The ciphers that are Substitution-permutation networks use bijective S-Boxes i.e., Boolean permutations. S-Boxes with low differential uniformity and high nonlinearity are considered as cryptographically strong. In this paper we study some properties of S...

In this paper we prove that there are only differential 4-uniform functions which are on distance 1 from an APN function. Also we prove that there are no APN functions of distance 1 from another APN functions up to dimension 5. We determine some properties of the set of values of an arbitrary vectorial Boolean function from F2 to F2 in connection to the set of values of its derivatives. These r...

Propagation criterion of degree l and order k (PC(l) of order k) and resiliency of vectorial Boolean functions are important for cryptographic purpose (see [1, 2, 3, 6, 7,8,10,11,16]. Kurosawa , Stoh [8] and Carlet [1] gave a construction of Boolean functions satisfying PC(l) of order k from binary linear or nonlinear codes. In this paper, algebraic-geometric codes over GF (2) are used to modif...

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...

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...

Modular addition modulo a power of two, is one of the most applicable operators in symmetric cryptography; therefore, investigating cryptographic properties of this operator has a significant role in design and analysis of symmetric ciphers. Algebraic properties of modular addition modulo a power of two have been studied for two operands by Braeken in fse’05. Also, the authors of this paper, ha...

CCZand EA-equivalence, which are originally defined for vectorial Boolean functions, are extended to mappings between finite abelian groups G and H. We obtain an extension theorem for CCZequivalent but not EA-equivalent mappings. Recent results in [1] are improved and generalized.