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Latin American Symposium on Theoretical Informatics

LATIN 1998: LATIN'98: Theoretical Informatics pp 305–315Cite as

The CREW PRAM complexity of modular inversion

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1380))

Abstract

One of the long-standing open questions in the theory of parallel computation is the parallel complexity of the integer gcd and related problems, such as modular inversion. We present a lower bound Ω(log n) for the CREW PRAM complexity for inversion modulo certain n-bit integers, including all such primes. For infinitely many moduli, our lower bound matches asymptotically the known upper bound. We obtain a similar lower bound for computing a specified bit in a large power of an integer. Our main tools are certain estimates for exponential sums in finite fields.

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Author information

Authors and Affiliations

  1. FB Mathematik-Informatik, Universität-GH Paderborn, 33095, Paderborn, Germany

    Joachim van zur Gathen

  2. School of Mathematics, Physics, Computing and Electronics, Macquarie University, 2109, Sydney, NSW, Australia

    Igor Shparlinski

Authors
  1. Joachim van zur Gathen
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  2. Igor Shparlinski
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Editor information

Cláudio L. Lucchesi Arnaldo V. Moura

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© 1998 Springer-Verlag Berlin Heidelberg

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van zur Gathen, J., Shparlinski, I. (1998). The CREW PRAM complexity of modular inversion. In: Lucchesi, C.L., Moura, A.V. (eds) LATIN'98: Theoretical Informatics. LATIN 1998. Lecture Notes in Computer Science, vol 1380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054331

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  • DOI: https://doi.org/10.1007/BFb0054331

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64275-6

  • Online ISBN: 978-3-540-69715-2

  • eBook Packages: Springer Book Archive

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