Titlebook: Arithmetic of Finite Fields; 5th International Wo ?etin Kaya Ko?,Sihem Mesnager,Erkay Sava? Conference proceedings 2015 Springer Internatio

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?etin Kaya Ko?,Sihem Mesnager,Erkay Sava?Includes supplementary material:

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Lecture Notes in Computer Sciencehttp://image.papertrans.cn/b/image/161619.jpg

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https://doi.org/10.1007/978-3-319-16277-5Algebraic Curves; Bent Function; Boolean Function; Code-based Cryptography; Cryptography; Elliptic Curve;

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978-3-319-16276-8Springer International Publishing Switzerland 2015

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Computing Discrete Logarithms in , and , Using Magmainite field . with very modest computational resources. Our . implementation was the first to illustrate the effectiveness of Joux’s algorithm for computing discrete logarithms in small-characteristic finite fields that are not Kummer or twisted-Kummer extensions.

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Quadratic Residue Codes over , codes of length . over . quadratic residue codes over . are defined by their generating idempotents and their extension codes are discussed. Examples of codes and idempotents for small values of . and . are given. As a by-product almost MDS codes over . and . are constructed.

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