FPGA Implementations of Elliptic Curve Cryptography and Tate Pairing over Binary Field

Elliptic curve cryptography (ECC) is an alternative to traditional techniques for public key cryptography. It offers smaller key size without sacrificing security level. Tate pairing is a bilinear map used in identity based cryptography schemes. In a typical elliptic curve cryptosystem, elliptic curve point multiplication is the most computationally expensive component. Similarly, Tate pairing is also quite computationally expensive. Therefore, it is more attractive to implement the ECC and Tate pairing using hardware than using software. The bases of both ECC and Tate pairing are Galois field arithmetic units. In this thesis, I propose the FPGA implementations of the elliptic curve point multiplication in GF (2283) as well as Tate pairing computation on supersingular elliptic curve in GF (2283). I have designed and synthesized the elliptic curve point multiplication and Tate pairing module using Xilinx's FPGA, as well as synthesized all the Galois arithmetic units used in the designs. Experimental results demonstrate that the FPGA implementation can speedup the elliptic curve point multiplication by 31.6 times compared to software based implementation. The results also demonstrate that the FPGA implementation can speedup the Tate pairing computation by 152 times compared to software based implementation.

Grantor dc:publisher

University of North Texas

Year dc:date

2007

Author dc:creator

• Huang, Jian

Contributors dc:contributor

• Li, Hao
• Sweany, Philip H.
• Kavi, Krishna M.

• FPGA
• hardware
• elliptic curve cryptography
• bilinear map
• Tate pairing
• Computer security.
• Data encryption (Computer science)
• Field programmable gate arrays.
• Curves, Elliptic.
• Cryptography -- Mathematics.

Statement dc:rights

• Public
• Copyright
• Huang, Jian
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 191207316
https://digital.library.unt.edu/ark:/67531/metadc3963/
ark: ark:/67531/metadc3963

OAI identifier oai:identifier

info:ark/67531/metadc3963