let $d$ be an integral domain and $star$ a semistar operation stable and of finite type on it. we define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong s-domains. as an application, we give new characterizations of $star$-quasi-pr"{u}fer domains and um$t$ domains in terms of dimension ine...

Let $D$ be an integral domain and $star$ a semistar operation stable and of finite type on it. We define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong S-domains. As an application, we give new characterizations of $star$-quasi-Pr"{u}fer domains and UM$t$ domains in terms of dimension inequal...

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...

Block ciphers are widely used in modern cryptography. Substitution boxes (S–boxes) are main elements of these types of ciphers. In this paper we propose a new method to create S–boxes, which is based on application of Cellular Automata (CA). We present the results of testing CA-based S–boxes. These results confirm that CA are able to realize efficiently the Boolean function corresponding to cla...

Most modern block and stream ciphers can be expressed as certain arrangement of Vector Boolean Functions. Thus, in the context of block and stream ciphers’ design (mainly in S-boxes and combining functions respectively), it is essential to define criteria which measure the cryptographic strength of Boolean Functions and Vector Boolean Functions. Ideally, some of the following requirements must ...

Since Seidenberg’s (1953-54) papers [35, 36] and Jaffard’s (1960) pamphlet [28] on the dimension theory of commutative rings, the literature abounds in works exploring the prime ideal structure of polynomial rings, including four pioneering articles by Arnold and Gilmer on dimension sequences [3, 4, 5, 6]. Of particular interest is Bastida-Gilmer’s (1973) precursory article [8] which establishe...

the strong ground motions recorded during the 2002 avaj earthquake have been used to estimates wave attenuation, qβ, and spectral decay parameter, κ, for the avaj region. qβ for shear wave is estimatedas a function of frequency in the range of 0.6- 18 hz. the results show that qβ increases with frequency in theform of qβ=62.7 f 0.9. our estimates are within the estimated range for different par...