Title: Microblaze-based parallel implementations of elliptic curve scalar multiplication over F_p on FPGA

Authors: Ahmed Mohamed Bellemou; Nadjia Benblidia; Mohamed Anane; Mohamed Issad

Addresses: LRDSI Laboratory, Department of Electronics, Blida 1 University, SOUMÂA road BP 270, Blida (09000), Algeria; Ecole Supérieure d'Informatique, BP. 68M, Oued Smar, El Harrach, 16270 Algiers, Algeria; Department of System and Multimedia Architecture, CDTA, BP. 17 Cite 20 Aout 1956 Baba Hassen, 16081, Algiers, Algeria ' LRDSI Laboratory, Department of Electronics, Blida 1 University, SOUMÂA road BP 270, Blida (09000), Algeria; Ecole Supérieure d'Informatique, BP. 68M, Oued Smar, El Harrach, 16270 Algiers, Algeria; Department of System and Multimedia Architecture, CDTA, BP. 17 Cite 20 Aout 1956 Baba Hassen, 16081, Algiers, Algeria ' LRDSI Laboratory, Department of Electronics, Blida 1 University, SOUMÂA road BP 270, Blida (09000), Algeria; Ecole Supérieure d'Informatique, BP. 68M, Oued Smar, El Harrach, 16270 Algiers, Algeria; Department of System and Multimedia Architecture, CDTA, BP. 17 Cite 20 Aout 1956 Baba Hassen, 16081, Algiers, Algeria ' LRDSI Laboratory, Department of Electronics, Blida 1 University, SOUMÂA road BP 270, Blida (09000), Algeria; Ecole Supérieure d'Informatique, BP. 68M, Oued Smar, El Harrach, 16270 Algiers, Algeria; Department of System and Multimedia Architecture, CDTA, BP. 17 Cite 20 Aout 1956 Baba Hassen, 16081, Algiers, Algeria

Abstract: This paper presents flexible software/hardware parallel architectures for embedded elliptic curve cryptosystem (ECC) on FPGA as multi-processor system on programmable circuit (MPSoPC) design. The implementations perform elliptic curve scalar multiplication (ECSM) over arbitrary prime fields (F_p) using montgomery power ladder (MPL) algorithm and Chudnovsky projective system. Our aim is to achieve the best trade-off between flexibility, area and speed. In fact, the integration of multi Microblaze processors allows not only the flexibility of the overall system but also the exploitation of the parallelism in ECSM computation with several degrees. At the low abstraction level, the critical finite field operation which is Montgomery modular multiplication (MMM) is implemented in hardware Accelerator MMM (AccMMM) core based on the modified high radix-r (r = 2³²) MMM algorithm. The proposed architectures have been implemented in Xilinx Virtex-5 FPGA. The execution times for performing 256-bit and 521-bit ECSM are 19.98 ms and 81.42 ms, respectively.

Keywords: embedded elliptic curve cryptosystem; parallel scalar multiplication; montgomery power ladder; MPL; projective coordinates system; montgomery modular multiplication; MPSoC; FPGA.

DOI: 10.1504/IJITST.2020.104580

International Journal of Internet Technology and Secured Transactions, 2020 Vol.10 No.1/2, pp.171 - 195

Received: 14 Feb 2018
Accepted: 07 Jun 2018
Published online: 21 Jan 2020 *

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