The celebrated S-lemma establishes a powerful equivalent condition for the nonnegativity of a quadratic function over a single quadratic inequality. However, this lemma fails without the technical condition, known as the Slater condition. In this paper, we first show that the Slater condition is indeed necessary for the S-lemma and then establishes a regularized form of the S-lemma in the absen...

In this article we give a characterization of monoids for which torsion freeness, ((principal) weak, strong) flatness, equalizer flatness or Condition (E) of finitely generated and (mono) cyclic acts and Condition (P) of finitely generated and cyclic acts implies regularity. A characterization of monoids for which all (finitely generated, (mono) cyclic acts are regular will be given too. We als...

Differentially 4-uniform permutations on F22k with high nonlinearity are often chosen as Substitution boxes in both block and stream ciphers. Recently, Qu et al. introduced a class of functions, which are called preferred functions, to construct a lot of infinite families of such permutations [14]. In this paper, we propose a particular type of Boolean functions to characterize the preferred fu...

In this paper we propose two cryptographic algorithm AES and RSA Using Chaos. Chaos has attracted much attention in the field of cryptography. It describes a system which is sensitive to initial condition. It generates apparently random behavior but at the same time is completely deterministic Chaos function is used to increase the complexity and Security of the System.AES and RSA are the two c...

Differentially 4-uniform permutations on F22k with high nonlinearity are often chosen as Substitution boxes in both block and stream ciphers. Recently, Qu et al. introduced a class of functions, which are called preferred functions, to construct a lot of infinite families of such permutations [14]. In this paper, we propose a particular type of Boolean functions to characterize the preferred fu...