Implementation of a pipelined Scalar Multiplier using Extended Euclid Algorithm for Elliptic Curve Cryptography(ECC)

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Vol. 11, No. 5, pp. 17-30, Oct. 2001
10.13089/JKIISC.2001.11.5.17, Full Text:
Keywords: ECC scalar multiplier, Public Key Cryptography, euclid algorithm, finite field arithmetic
Abstract

In this paper, we implemented a scalar multiplier needed at an elliptic curve cryptosystem over standard basis in $GF(2^{163})$. The scalar multiplier consists of a radix-16 finite field serial multiplier and a finite field inverter with some control logics. The main contribution is to develop a new fast finite field inverter, which made it possible to avoid time consuming iterations of finite field multiplication. We used an algorithmic transformation technique to obtain a data-independent computational structure of the Extended Euclid GCD algorithm. The finite field multiplier and inverter shown in this paper have regular structure so that they can be easily extended to larger word size. Moreover they can achieve 100% throughput using the pipelining. Our new scalar multiplier is synthesized using Hyundai Electronics 0.6$\mu\textrm{m}$ CMOS library, and maximum operating frequency is estimated about 140MHz. The resulting data processing performance is 64Kbps, that is it takes 2.53ms to process a 163-bit data frame. We assure that this performance is enough to be used for digital signature, encryption & decryption and key exchange in real time embedded-processor environments.

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Cite this article
[IEEE Style]
김종만, 김영필, 정용진, "Implementation of a pipelined Scalar Multiplier using Extended Euclid Algorithm for Elliptic Curve Cryptography(ECC)," Journal of The Korea Institute of Information Security and Cryptology, vol. 11, no. 5, pp. 17-30, 2001. DOI: 10.13089/JKIISC.2001.11.5.17.

[ACM Style]
김종만, 김영필, and 정용진. 2001. Implementation of a pipelined Scalar Multiplier using Extended Euclid Algorithm for Elliptic Curve Cryptography(ECC). Journal of The Korea Institute of Information Security and Cryptology, 11, 5, (2001), 17-30. DOI: 10.13089/JKIISC.2001.11.5.17.