Titlebook: Applications of Finite Fields; Ian F. Blake,XuHong Gao,Tomik Yaghoobian,Alfred J. Book 1993 Springer-Verlag US 1993 algorithms.coding theo

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Book 1993Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of studen

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Affiliated Values Bidding Modelcrete logarithm problem in . is believed to be intractable, elliptic curve cryptosystems have the potential to provide security equivalent to that of existing public key schemes, but with shorter key lengths. Having short key lengths is a factor that can be crucial in some applications, for example the design of smart card systems.

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Introduction to Finite Fields and Bases,n is on the existence of certain types of bases, their duals and their enumeration. There has been considerable activity in this area in the past decade and while many of the questions are resolved, a few of the important ones remain open. The presentation here tries to complement that of Lidl and N

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Factoring Polynomials over Finite Fields, . and . . ≠ 0. To be more precise, . (.) is called a . to distinguish the more general situation where more indeterminates are involved. Most of this chapter will deal with univariate polynomials but the multivariate case will be briefly mentioned at the end.

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Optimal Normal Bases,in either hardware or software, is required. Work in this area has resulted in several hardware and software designs or implementations [7, 8, 22, 23, 24, 27], including single-chip exponentiators for the fields ., and an encryption processor for . public key cryptography. These products are based o

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Elliptic Curve Cryptosystems,logarithms of elements in G is infeasible. We may take . to be a cyclic subgroup of .(..), the group of ..-rational points of an elliptic curve defined over ..; this was first suggested by N. Koblitz [10] and V. Miller [17]. Since the addition in this group is relatively simple, and moreover the dis