Titlebook: Topics in Geometry, Coding Theory and Cryptography; Arnaldo Garcia,Henning Stichtenoth Book 2007 Springer Science+Business Media B.V. 2007

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议程

Arnaldo Garcia,Henning StichtenothServes as an introduction and invitation to several main directions of research in the area of Function Fields over Finite Fields and their various applications to Information Theory.Reasonably access

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EXPLICIT TOWERS OF FUNCTION FIELDS OVER FINITE FIELDS,r finite fields. More specifically, we treat here the case of explicit towers; i.e., towers where the function fields are given by explicit equations. The asymptotic behaviour of the genus and of the number of rational places in towers are important features for applications to coding theory and to cryptography (cf. Chapter 2).

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FUNCTION FIELDS OVER FINITE FIELDS AND THEIR APPLICATIONS TO CRYPTOGRAPHY,ography. This has led researchers in a natural way to consider methods based on some specified function fields in order to construct cryptographic schemes, such as schemes for unconditionally secure authentication, traitor tracing, secret sharing, broadcast encryption and secure multicast, just to mention a few.

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ARTIN-SCHREIER EXTENSIONS AND THEIR APPLICATIONS, is the degree of the field extension .. If n is relatively prime to ., and there is a primitive . . root of unity in ., then . is a ., i.e. . = .(.) with . . ∈ .. If . = ., then . is an ., i.e. . = .(.) with . . – . ∈ .. Finally, if . = . . for . > 1, then the extension . can be described in terms of .. For these facts, see [34, Section VI.7].

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Algebra and Applicationshttp://image.papertrans.cn/u/image/926183.jpg

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https://doi.org/10.1007/1-4020-5334-4algebra; coding theory; cryptography; finite field; information; information theory; number theory