Inside Euclid’s Algorithm

  • Willard L. Eastman
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 20)


The polynomial version of Euclid’s algorithm is expanded to remove the inherent polynomial division. The expanded algorithm exhibits a two loop structure. The choice of which loop to execute at a given iteration depends on whether the iteration completes, or does not complete, a polynomial division. It is shown that one of the loops can be deleted, producing a clean version of the algorithm suitable for implementation in VLSI. The new version of Euclid’s algorithm is computationally equivalent to the standard long division version, but is more efficient in terms of hardware. Processing cells are presented for a two-dimensional systolic array architecture capable, with pipelining, of computing polynomial gcd’s in constant time. The new version of Euclid’s algorithm bears a strong resemblance to the Berlekamp-Massey algorithm.

Key words

Euclid’s algorithm polynomial division greatest common divisor VLSI implementation 


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Copyright information

© Springer-Verlag New York, Inc. 1990

Authors and Affiliations

  • Willard L. Eastman
    • 1
  1. 1.The MITRE CorporationBedfordUSA

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