High Speed and Low-Complexity Hardware Architectures for Elliptic Curve-Based Crypto-Processors

The elliptic curve cryptography (ECC) has been identified as an efficient scheme for public-key cryptography. This thesis studies efficient implementation of ECC crypto-processors on hardware platforms in a bottom-up approach. We first study efficient and low-complexity architectures for finite field multiplications over Gaussian normal basis (GNB). We propose three new low-complexity digit-level architectures for finite field multiplication. Architectures are modified in order to make them more suitable for hardware implementations specially focusing on reducing the area usage. Then, for the first time, we propose a hybrid digit-level multiplier architecture which performs two multiplications together (double-multiplication) with the same number of clock cycles required as the one for one multiplication. We propose a new hardware architecture for point multiplication on newly introduced binary Edwards and generalized Hessian curves. We investigate higher level parallelization and lower level scheduling for point multiplication on these curves. Also, we propose a highly parallel architecture for point multiplication on Koblitz curves by modifying the addition formulation. Several FPGA implementations exploiting these modifications are presented in this thesis. We employed the proposed hybrid multiplier architecture to reduce the latency of point multiplication in ECC crypto-processors as well as the double-exponentiation. This scheme is the first known method to increase the speed of point multiplication whenever parallelization fails due to the data dependencies amongst lower level arithmetic computations. Our comparison results show that our proposed multiplier architectures outperform the counterparts available in the literature. Furthermore, fast computation of point multiplication on different binary elliptic curves is achieved.

Name thesis:degree_name

Ph D

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Grantor dc:publisher

The University of Western Ontario

Year dc:date.issued

2011

Author dc:creator

• Azarderakhsh, Reza

Advisor dc:contributor.advisor

• Reyhani-Masoleh, Arash

• Elliptic curve cryptography
• Gaussian normal basis
• digit-level finite field multiplication
• hybrid multiplier
• point multiplication

Language dc:language.iso

en_ca

Handle dc:identifier.uri

https://hdl.handle.net/20.500.14721/36053

OAI identifier oai:identifier

oai:uwo.scholaris.ca:20.500.14721/36053