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International Workshop on Computer Algebra and Parallelism

CAP 1990: Computer Algebra and Parallelism pp 51–61Cite as

Finite field arithmetic using the connection machine

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 584))

Abstract

A Connection Machine (model CM-2) with 32K processors has been used to carry out calculations in finite fields with as many as 221 elements and of various characteristics; a typical calculation is to determine the number of roots of a large family of polynomials. The programs use discrete logarithms, employing a table of “successor” logarithms to perform addition. The table is computed in advance, in parallel. The system can evaluate some 4 × 106 polynomial terms per second; performance is limited by the general communication time needed for table lookup. Orbits of the p-th power bijection (also calculated in parallel) are used to deal with common symmetries arising in the calculations. The techniques are illustrated by calculations to determine the number of rational points of a polynomial surface over several fields, quantities which are useful in analyzing certain cyclic codes.

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References

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Author information

Authors and Affiliations

  1. CIS-44-116 CST, Syracuse University, 13244-4100, Syracuse, NY

    Ernest Sibert & Harold F. Mattson

  2. Northeast Parallel Architectures Center, 3-201 Center for Science and Technology, Syracuse University, 13244-4100, Syracuse, NY

    Paul Jackson

Authors
  1. Ernest Sibert
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  2. Harold F. Mattson
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  3. Paul Jackson
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Editor information

Richard E. Zippel

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© 1992 Springer-Verlag Berlin Heidelberg

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Sibert, E., Mattson, H.F., Jackson, P. (1992). Finite field arithmetic using the connection machine. In: Zippel, R.E. (eds) Computer Algebra and Parallelism. CAP 1990. Lecture Notes in Computer Science, vol 584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55328-2_4

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  • DOI: https://doi.org/10.1007/3-540-55328-2_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55328-1

  • Online ISBN: 978-3-540-47026-7

  • eBook Packages: Springer Book Archive

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