The aim of this paper is to show a new algorithm for key exchange and reliable data transmission through the mobile grid computing environment. The system uses very strong one way functions based on the combination of a family of algebraic curves and a Low-Density Parity-Check code (LDPC). The security of the whole scheme is guaranteed by the intractability of the discrete logarithm problem on ...

Ideas from algebraic geometry became useful in coding theory after Goppa’s construction [8]. He had the beautiful idea of associating to a curve X defined over Fq, the finite field with q elements, a code C. This code, called Algebraic-Geometric (AG) code, is constructed from two divisors D and G on X , where one of them, say D, is the sum of n distinct Fq-rational points of X . It turns out th...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

Dynamic optimization problems can be numerically solved by direct, indirect and HamiltonJacobi-Bellman methods. In this paper, the differential-algebraic approach is incorporated into a hybrid method, extending the concepts of structural and differential indexes, consistent initialization analysis, index reduction and dynamic degrees of freedom to the optimal control problem. The resultant diff...

Methods are needed to help using formal speciications in a practical way. We herein present a method for the development of mixed systems, i.e. systems with both a static and a dynamic part. Our method helps the speciier providing means to structure the system in terms of communicating subcomponents and to give the sequential components using a semi-automatic concurrent automata generation with...

Based on a generic construction, two classes of ternary three-weight linear codes are obtained from a family of power functions, including some APN power functions. The weight distributions of these linear codes are determined through studying the properties of some exponential sum related to the proposed power functions. Index Terms linear code, weight distribution, exponential sum, quadratic ...