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Authors: Yin Li 1 and Christophe Negre 2

Affiliations: 1 Institute of Information Security, Shanghai jiaotong University, China ; 2 Team DALI/ELIAUS, University of Perpignan, France

Keyword(s): Finite Field, Multiplication, Montgomery, Binomial residue representation.

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

Abstract: In this paper, we propose an extension of the algorithm proposed by Bajard, Imbert and Negre in (Bajar et al., 2006), refered as BIN algorithm. We use binomial residue representation of field elements instead of the Lagrange representation of (Bajar et al., 2006). Specifically, every elements in Fpk is represented by a set of residue modulo fixed binomials. We propose two versions of our algorithm, one in general form with a sub-quadratic complexity equal to O(k1.5 ) operations in Fp . The second one is optimized with the use of FFT. In this case the cost is O(k log(k)) operations in Fp . For fields GF ( pk ) suitable for elliptic curve cryptography our algorithm roughly improves the time delay of (Bajar et al., 2006) by 45%.

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Paper citation in several formats:
Li, Y. and Negre, C. (2008). AN EFFICIENT MULTIPLICATION ALGORITHM USING BINOMIAL RESIDUE REPRESENTATION. In Proceedings of the International Conference on Security and Cryptography (ICETE 2008) - SECRYPT; ISBN 978-989-8111-59-3; ISSN 2184-3236, SciTePress, pages 319-324. DOI: 10.5220/0001924503190324

@conference{secrypt08,
author={Yin Li. and Christophe Negre.},
title={AN EFFICIENT MULTIPLICATION ALGORITHM USING BINOMIAL RESIDUE REPRESENTATION},
booktitle={Proceedings of the International Conference on Security and Cryptography (ICETE 2008) - SECRYPT},
year={2008},
pages={319-324},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001924503190324},
isbn={978-989-8111-59-3},
issn={2184-3236},
}

TY - CONF

JO - Proceedings of the International Conference on Security and Cryptography (ICETE 2008) - SECRYPT
TI - AN EFFICIENT MULTIPLICATION ALGORITHM USING BINOMIAL RESIDUE REPRESENTATION
SN - 978-989-8111-59-3
IS - 2184-3236
AU - Li, Y.
AU - Negre, C.
PY - 2008
SP - 319
EP - 324
DO - 10.5220/0001924503190324
PB - SciTePress