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http://dx.doi.org/10.6109/jkiice.2017.21.6.1083

A small-area implementation of public-key cryptographic processor for 224-bit elliptic curves over prime field  

Park, Byung-Gwan (School of Electronic Engineering, Kumoh National Institute of Technology)
Shin, Kyung-Wook (School of Electronic Engineering, Kumoh National Institute of Technology)
Publication Information
Journal of the Korea Institute of Information and Communication Engineering / v.21, no.6, 2017 , pp. 1083-1091 More about this Journal
Abstract
This paper describes a design of cryptographic processor supporting 224-bit elliptic curves over prime field defined by NIST. Scalar point multiplication that is a core arithmetic function in elliptic curve cryptography(ECC) was implemented by adopting the modified Montgomery ladder algorithm. In order to eliminate division operations that have high computational complexity, projective coordinate was used to implement point addition and point doubling operations, which uses addition, subtraction, multiplication and squaring operations over GF(p). The final result of the scalar point multiplication is converted to affine coordinate and the inverse operation is implemented using Fermat's little theorem. The ECC processor was verified by FPGA implementation using Virtex5 device. The ECC processor synthesized using a 0.18 um CMOS cell library occupies 2.7-Kbit RAM and 27,739 gate equivalents (GEs), and the estimated maximum clock frequency is 71 MHz. One scalar point multiplication takes 1,326,985 clock cycles resulting in the computation time of 18.7 msec at the maximum clock frequency.
Keywords
ECC; projective coordinate; Jacobian's coordinate; Fermat's little theorem; ECDH key exchange protocol;
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