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Modeling finite fields with mathematica

Applications to the computation of exponential sums and to the solution of equations over finite fields

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  • First Online:
Design and Implementation of Symbolic Computation Systems (DISCO 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 722))

Abstract

This paper proposes an implementation model for finite fields GF[mq], m prime, based on a hybrid architecture that integrates symbolic programming developed in Mathematica with an imperative C language module. Its aim is to enable the user to write algorithms to perform calculations in GF's by using Mathematica's programming language and built-in math functions. First, the system's architecture is presented and it is shown that the proposed model has linear time complexity (O(q)) for all algebraic operations. Finally, we show the developed modules for the computation of exponential sums and the solution of equations over finite fields.

This research was supported by the Puerto Rico Research Center for Science and Engineering and by the Center for Academic Research of the University of the Sacred Heart.

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References

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Authors and Affiliations

  1. Computer Science Program, University of the Sacred Heart, PO Box 12383, 00914-0383, San Juan, Puerto Rico

    Antonio Vantaggiato

Authors
  1. Antonio Vantaggiato
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Alfonso Miola

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© 1993 Springer-Verlag Berlin Heidelberg

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Vantaggiato, A. (1993). Modeling finite fields with mathematica. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1993. Lecture Notes in Computer Science, vol 722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013191

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  • DOI: https://doi.org/10.1007/BFb0013191

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57235-0

  • Online ISBN: 978-3-540-47985-7

  • eBook Packages: Springer Book Archive

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