Download e-book for iPad: Coding Theory, Cryptography and Related Areas: Proceedings by Ángela I. Barbero, Øyvind Ytrehus (auth.), Johannes

By Ángela I. Barbero, Øyvind Ytrehus (auth.), Johannes Buchmann, Tom Høholdt, Henning Stichtenoth, Horacio Tapia-Recillas (eds.)

ISBN-10: 3540662480

ISBN-13: 9783540662488

ISBN-10: 3642571891

ISBN-13: 9783642571893

This e-book includes 23 contributions provided on the "International convention on Coding thought, Cryptography and similar components (ICCC)", held in Guanajuato, Mexico, in April 1998.
It contains a sequence of study papers on quite a few points of coding conception (geometric-algebraic, deciphering, exponential sums, etc.) and cryptography (discrete logarithm challenge, public key cryptosystems, primitives, etc.), in addition to in different study parts, resembling codes over finite earrings and a few features of functionality fields and algebraic geometry over finite fields.
The publication includes new effects at the topic, by no means released in the other shape. it will likely be priceless to scholars, researchers, pros, and tutors attracted to this quarter of research.

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Extra info for Coding Theory, Cryptography and Related Areas: Proceedings of an International Conference on Coding Theory, Cryptography and Related Areas, held in Guanajuato, Mexico, in April 1998

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2i - 1 . It is worthwhile examining different variants of producing the (d i ), because ideally the (d i ) should behave like a random sequence. 25vn until an element of G occurs twice. The original sequence of Pollard uses a partition of G = 8 1 U 82 U 83 with equally sized 8 i and is defined by di +1:= { adi, d i E 8 1 dr, di E 8 2 bdi , di E 83 where an arbitrary product of the form akbl may be chosen as a start value. The sequence of exponents of a produced by this definition are computed by Discrete Logarithms: Recent Progress 47 = ei + 1 and eHl = 2ei, starting from some eo = k + xl.

We call these standard functions. (Zuccherato calls them quadratic irrationalities, but this seems a bit hard on the other functions in K(C) \ K(x)). The needed facts on CFE's are summarized in the following proposition (which, but for item 2, holds in fact for an arbitrary function in K(C) \ K[x]). Proposition 1 Let f be a standard function, and consider the CFE of f. For all i 2: 0 : 1. deg ai > 0 for i > O. 2. The reducts, the functions gi, are standard functions. 3. degql = 0, and for i 2: 2, degqi = L:j:'~ degaj' Hence degqi+1 deg ai and {deg qd is a strictly increasing sequence.

Berry Departamento de Matematicas Puras y Aplicadas Universidad Simon Bolivar Caracas Venezuela. ve Abstract. Known results on hyperelliptic continued fractions, and in particular the Baby-Step Giant-Step algorithm, are obtained using algebro-geometric techniques. The methods used are valid in all characteristics and the proofs are simpler than those based on analogies with real quadratic number fields. 1 Introduction This article contains virtually no new results. Its purpose is to show how the known properties of hyperelliptic continued fraction expansions, in particular the Baby-Step Giant-Step algorithm, can be derived very easily by algebro-geometric methods.

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Coding Theory, Cryptography and Related Areas: Proceedings of an International Conference on Coding Theory, Cryptography and Related Areas, held in Guanajuato, Mexico, in April 1998 by Ángela I. Barbero, Øyvind Ytrehus (auth.), Johannes Buchmann, Tom Høholdt, Henning Stichtenoth, Horacio Tapia-Recillas (eds.)


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