Cryptology ePrint Archive: Report 2006/224
Generalizations of the Karatsuba Algorithm for Efficient Implementations
André Weimerskirch and Christof Paar
Abstract: In this work we generalize the classical Karatsuba Algorithm (KA) for
polynomial multiplication to (i) polynomials of arbitrary degree and (ii) recursive use. We determine exact complexity expressions for the KA and focus on how to use it with the least number of operations. We develop a rule for the optimum order of steps if the KA is used recursively. We show how the usage of dummy coefficients may improve performance. Finally we provide detailed information on how to use the KA with least cost, and also provide tables that describe the best possible usage of the KA for polynomials up to a degree of 127. Our results are especially useful for efficient implementations of cryptographic and coding schemes over fixed-size fields like $GF(p^m)$.
Category / Keywords: implementation / Karatsuba, polynomial multiplication
Date: received 2 Jul 2006
Contact author: aweimerskirch at escrypt com
Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation
Version: 20060703:071946 (All versions of this report)
Short URL: ia.cr/2006/224
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