FINITE FIELD MULTIPLICATION IN LAGRANGE REPRESENTATION USING FAST FOURRIER TRANSFORM

Christophe Negre

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Paper

FINITE FIELD MULTIPLICATION IN LAGRANGE REPRESENTATION USING FAST FOURRIER TRANSFORM

Topics: Public Key Crypto Applications

In Proceedings of the International Conference on Security and Cryptography - Volume 0ICETE, 320-324, 2006 , Setúbal, Portugal

Author: Christophe Negre

Affiliation: Équipe DALI, LP2A, Université de Perpignan, France

Keyword(s): Finite field arithmetic, FFT, multiplication.

Related Ontology Subjects/Areas/Topics: Cryptographic Techniques and Key Management ; Information and Systems Security ; Public Key Crypto Applications

Abstract: The multiplication in Fpn can be performed using a polynomial version of Montgomery multiplication (Montgomery, 1985). In (Bajard et al., 2003) Bajard et al. improved this method by using a Lagrange representation: the elements of Fpn are represented by their values at a fixed set of points. The costly operations in this new algorithm are the two changes of Lagrange representation which require 2r2 operations in Fp with n ≤ r ≤ 2⌈log2 (n)⌉ . In this paper we present a new method to perform the change of Lagrange representation. This method uses Fast Fourier Transform and has a cost equal to 3rlog2 (r) operations in Fp with r = 2⌈log2 (n)⌉ .

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Paper citation in several formats:

Negre, C. (2006). FINITE FIELD MULTIPLICATION IN LAGRANGE REPRESENTATION USING FAST FOURRIER TRANSFORM. In Proceedings of the International Conference on Security and Cryptography (ICETE 2006) - SECRYPT; ISBN 978-972-8865-63-4; ISSN 2184-3236, SciTePress, pages 320-324. DOI: 10.5220/0002096503200324

@conference{secrypt06,
author={Christophe Negre.},
title={FINITE FIELD MULTIPLICATION IN LAGRANGE REPRESENTATION USING FAST FOURRIER TRANSFORM},
booktitle={Proceedings of the International Conference on Security and Cryptography (ICETE 2006) - SECRYPT},
year={2006},
pages={320-324},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002096503200324},
isbn={978-972-8865-63-4},
issn={2184-3236},
}

TY - CONF

JO - Proceedings of the International Conference on Security and Cryptography (ICETE 2006) - SECRYPT
TI - FINITE FIELD MULTIPLICATION IN LAGRANGE REPRESENTATION USING FAST FOURRIER TRANSFORM
SN - 978-972-8865-63-4
IS - 2184-3236
AU - Negre, C.
PY - 2006
SP - 320
EP - 324
DO - 10.5220/0002096503200324
PB - SciTePress