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Loss Of Precision In Implementations Of The Toom-Cook Algorithm, Marcus Elia

Graduate College Dissertations and Theses

Historically, polynomial multiplication has required a quadratic number of operations. Several algorithms in the past century have improved upon this. In this work, we focus on the Toom-Cook algorithm. Devised by Toom in 1963, it is a family of algorithms parameterized by an integer, n. The algorithm multiplies two polynomials by recursively dividing them into smaller polynomials, multiplying many small polynomials, and interpolating to obtain the product. While it is no longer the asymptotically fastest method of multiplying, there is a range of intermediate degrees (typically less than 1000) where it performs the best.

Some applications, like quantum-resistant cryptosystems, require …