The Karatsuba integer middle product

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Abstract

We study the problem of computing middle products of multiple-precision integers. In particular we adapt the Karatsuba polynomial middle product algorithm to the integer case, showing how to efficiently mitigate the failure of bilinearity of the integer middle product noted by Hanrot, Quercia and Zimmermann.

Keywords

Middle product
Integer arithmetic
Efficient algorithm

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1

Tel.: +61 2 9385 7088; fax: +61 2 9385 7123.

2

Current address: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia.