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The CREW PRAM complexity of modular inversion

  • Joachim van zur Gathen
  • Igor Shparlinski
Conference paper
Part of the Lecture Notes in Computer Science book series (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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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Joachim van zur Gathen
    • 1
  • Igor Shparlinski
    • 2
  1. 1.FB Mathematik-InformatikUniversität-GH PaderbornPaderbornGermany
  2. 2.School of Mathematics, Physics, Computing and ElectronicsMacquarie UniversitySydneyAustralia

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