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Improved Three-Way Split Formulas for Binary Polynomial and Toeplitz Matrix Vector Products

Murat Cenk 1 Christophe Negre 2, 3 Anwar Hasan 1
1 ECE - Department of Electrical and Computer Engineering [Waterloo]
2 UPVD - Université de Perpignan Via Domitia
3 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : In this paper, we consider three-way split formulas for binary polynomial multiplication and Toeplitz matrix vector product (TMVP). We first recall the best known three-way split formulas for polynomial multiplication: the formulas with six recursive multiplications given by Sunar in a 2006 IEEE Transactions on Computers paper and the formula with five recursive multiplications proposed by Bernstein at CRYPTO 2009. Second, we propose a new set of three-way split formulas for polynomial multiplication that are an optimization of Sunar's formulas. Then, we present formulas with five recursive multiplications based on field extension. In addition, we extend the latter formulas to TMVP. We evaluate the space and delay complexities when computations are performed in parallel and provide a comparison with best known methods.
Keywords : subquadratic space complexity multiplier Polynomials Vectors Delay Complexity theory Interpolation Cryptography Logic gates finite field Binary polynomial Toeplitz matrix
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https://hal.archives-ouvertes.fr/hal-00839945
Contributor : Christophe Negre Connect in order to contact the contributor
Submitted on : Monday, July 1, 2013 - 11:24:43 AM
Last modification on : Tuesday, March 15, 2022 - 12:55:40 PM

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  • HAL Id : hal-00839945, version 1

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CNRS | UNIV-PERP | DALI | LIRMM | MIPS | UNIV-MONTPELLIER | AXESECULIRMM

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Murat Cenk, Christophe Negre, Anwar Hasan. Improved Three-Way Split Formulas for Binary Polynomial and Toeplitz Matrix Vector Products. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2013, 62 (7), pp.1345-1361. ⟨hal-00839945⟩

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