Design of a Bit-Serial Divider in GF(2^m) for Elliptic Curve Cryptosystem 


Vol. 27,  No. 12, pp. 1288-1298, Dec.  2002


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  Abstract

To implement elliptic curve cryptosystem in GF(2^m) at high speed, a fast divider is required. Although bit-parallel architecture is well suited for high speed division operations, ellipticurve cryptosystem requires large m(at least 163) to support a sufficient security. In other words, since the bit-parallel architecture has an area complexity of O(㎡), it is not suited for this application. In this paper, we propose a new serial-in serial-out systolic array for computing division operations in GF(2") using the standard basis representation. Based on a moditied version of the binary extended greatest common divisor algorithm, we obtain a new data dependence graph and design an efficient bit-serial systolic divider. TIle proposed divider has O(m) time complexity and O(m) area complexity. If input data come in continuously, the proposed divider can produce division results at a rate of one per m clock cycles, after an initial delay of 5m-2 cycles. Analysis shows that the proposed divider provides a signiticant reduction in both chip area and computational delay time compared to previously proposed systolic dividers with the same I/O fomlat. Since the proposed divider can perform division operations at high speed with the reduced chip area, it is well suited for division circuit of elliptic curve crptosystem. Furthermore, since the proposed architecture does not restrict the choice of irreducible polynomial, and has a unidirectional data flow and regularity, it provides a high flexibility and scalability with respect to the field size m.

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  Cite this article

[IEEE Style]

C. H. Kim, C. P. Hong, N. S. Kim, S. Kwon, "Design of a Bit-Serial Divider in GF(2^m) for Elliptic Curve Cryptosystem," The Journal of Korean Institute of Communications and Information Sciences, vol. 27, no. 12, pp. 1288-1298, 2002. DOI: .

[ACM Style]

Chang Hoon Kim, Chun Pyo Hong, Nam Shik Kim, and Soonhack Kwon. 2002. Design of a Bit-Serial Divider in GF(2^m) for Elliptic Curve Cryptosystem. The Journal of Korean Institute of Communications and Information Sciences, 27, 12, (2002), 1288-1298. DOI: .

[KICS Style]

Chang Hoon Kim, Chun Pyo Hong, Nam Shik Kim, Soonhack Kwon, "Design of a Bit-Serial Divider in GF(2^m) for Elliptic Curve Cryptosystem," The Journal of Korean Institute of Communications and Information Sciences, vol. 27, no. 12, pp. 1288-1298, 12. 2002.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880