BIT-PARALLEL COPROCESSOR
FOR STANDARD ECC- GF(2m) ON FPGA
Maurício Araújo Dias1, Márcio R.A. Gouveia2
José Raimundo de Oliveira3, Ignacio Bravo Muñoz4
1Department of Mathematics and Computation
School of Science and Technology
São Paulo State University (UNESP)
Roberto Simonsen street, 305
Presidente Prudente, SP, 19060-900, BRAZIL
2Department of Mathematics
Institute of Biosciences, Letters and Science
São Paulo State University (UNESP)
Cristvão Colombo street, 2265, Jardim Nazareth
São José do Rio Preto, SP, 15054-000, BRAZIL
3Department of Computer Engineering and Industrial Automation
School of Electrical and Computer Engineering
State University of Campinas (UNICAMP)
Av. Albert Einstein, 400, Cid. Universitária Zeferino
Vaz Distrito Barão Geraldo, Campinas, SP, 13083-852, BRAZIL
4Electronics Department
University Alcala
DO-217. Polytechnic School
Ctra. Madrid - Barcelona km. 33.6
Alcalá de Henares, Madrid, 28871, SPAIN
Abstract. This paper presents the design of a high-speed coprocessor for Elliptic Curve Cryptography over binary Galois Field (ECC- GF(2m)). The purpose of our coprocessor is to accelerate the scalar multiplication performed over elliptic curve points represented by affine coordinates in polynomial basis. Our method consists of using elliptic curve parameters over GF(2163) in accordance with international security requirements to implement a bit-parallel coprocessor on field-programmable gate-array (FPGA). Our coprocessor performs modular inversion by using a process based on the Stein's algorithm. Results are presented and compared to results of other related works. We conclude that our coprocessor is suitable for comparing with any other ECC-hardware proposal, since its speed is comparable to projective coordinate designs.
AMS Subject Classification: 14H52, 94A60, 97P60
Key Words and Phrases: elliptic curves; GF(2m), cryptography, bit-parallel, coprocessor, FPGA


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DOI: 10.12732/ijam.v26i2.10

Volume: 26
Issue: 2
Year: 2013