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O(log(n)) parallel time finite field inversion

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VLSI Algorithms and Architectures (AWOC 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 319))

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Abstract

Let p be prime and assume that GF(p n) is given via an irreducible nth degree GF(p) polynomial. We exhibit a boolean circuit of size n O(1) and depth O(log(n)) such that for any x ε GF(p n) the circuit produces x −1. The circuit is based upon an interesting connection between finite field computations and the eigenvalues of certain matrices. The issue of circuit uniformity is also considered.

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References

  1. P. Beame,S. Cook,H. Hoover,“Log Depth Circuits for Division and Related Problems”, SIAM J. Comput.,vol.15,no.4,pp.994–1003,1986

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Berkowitz, “On Computing the Determinant in Small Parallel Time using a Small Number of Processors”,Inf.Proc.Lett.,vol.18, pp.147–150,1984

    Article  MATH  MathSciNet  Google Scholar 

  3. E. Berlekamp,Algebraic Coding Theory,McGraw-Hill,1968

    Google Scholar 

  4. S. Cook, “A Taxonomy of Problems with Fast Parallel Algorithms”, Inf. and Control, vol.64,pp.2–22,1985

    Article  MATH  Google Scholar 

  5. L. Csanky, “Fast Parallel Matrix Inversion Algoritms”, SIAM J. Comput.,vol.5,pp.618–623, 1976

    Article  MATH  MathSciNet  Google Scholar 

  6. G.Davida,B.Litow, “Fast Parallel Inversion in Finite Fields”,19th CISS at Johns Hopkins,pp.305–308,1985

    Google Scholar 

  7. G. Davida,B.Litow, “Fast Parallel Comparison and Division in Modular Representation 1987,in preparation

    Google Scholar 

  8. G. Davida, “Inverse of Elements of a galois Field”, Electronics Lett.,vol.8,21,Oct.1972

    Google Scholar 

  9. N.Koblitz,p-Adic Analysis and Zeta Functions,GTM 58,Springer Verlag,1977

    Google Scholar 

  10. B.Litow, “Complexity of Polynomial Root Approximation”,manuscript,1987

    Google Scholar 

  11. K. Mulmuley, “A Fast Parallel Algorithm to Compute the Rank of a matrix Over an Arbitrary Field”,Proc. 18th ACM STOC,pp.338–339,1986

    Google Scholar 

  12. W. Ruzzo, “On Uniform Circuit Complexity”, JCSS,vol. 22,pp.365–383,1981

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Electrical Engineering and Computer Science Department, University of Wisconsin-Milwaukee, USA

    Bruce E. Litow & George I. Davida

Authors
  1. Bruce E. Litow
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  2. George I. Davida
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John H. Reif

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© 1988 Springer-Verlag Berlin Heidelberg

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Litow, B.E., Davida, G.I. (1988). O(log(n)) parallel time finite field inversion. In: Reif, J.H. (eds) VLSI Algorithms and Architectures. AWOC 1988. Lecture Notes in Computer Science, vol 319. Springer, New York, NY. https://doi.org/10.1007/BFb0040375

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  • DOI: https://doi.org/10.1007/BFb0040375

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96818-6

  • Online ISBN: 978-0-387-34770-7

  • eBook Packages: Springer Book Archive

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