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Implementing Fast Carryless Multiplication

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Conference object , Other literature type , Report 01 Jan 2017 France Publisher:Springer International Publishing
Authors: Joris van der Hoeven; Robin Larrieu; Grégoire Lecerf;

doi: 10.1007/978-3-319-72453-9_9

Implementing Fast Carryless Multiplication

Abstract

The efficient multiplication of polynomials over the finite field \(\mathbb {F}_2\) is a fundamental problem in computer science with several applications to geometric error correcting codes and algebraic crypto-systems. In this paper we report on a new algorithm that leads to a practical speed-up of about two over previously available implementations. Our current implementation assumes a modern AVX2 and CLMUL enabled processor.

Country
France
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Keywords

[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], [INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC], Frobenius FFT, ACM: G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS/G.1.0: General/G.1.0.0: Computer arithmetic, [INFO.INFO-AO]Computer Science [cs]/Computer Arithmetic, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], ACM: F.: Theory of Computation/F.2: ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY/F.2.1: Numerical Algorithms and Problems/F.2.1.0: Computation of transforms (e.g., Polynomial multiplication, Finite field, fast Fourier transform), 68W40, 68Q17, ACM: F.: Theory of Computation/F.2: ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY/F.2.1: Numerical Algorithms and Problems/F.2.1.1: Computations in finite fields, High performance, Implementation, MSC 68W30, [INFO.INFO-MS]Computer Science [cs]/Mathematical Software [cs.MS]

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    popularity
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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average