Browse > Article
http://dx.doi.org/10.6109/JKIICE.2009.13.10.2154

A GF($2^{163}$) Scalar Multiplier for Elliptic Curve Cryptography for Smartcard Security  

Jeong, Sang-Hyeok (금오공과대학교 전자공학부)
Shin, Kyung-Wook (금오공과대학교 전자공학부)
Abstract
This paper describes a scalar multiplier for Elliptic curve cryptography for smart card security. The scaler multiplier has 163-bits key size which supports the specifications of smart card standard. To reduce the computational complexity of scala multiplication on finite field, the non-adjacent format (NAF) conversion algorithm which is based on complementary recoding is adopted. The scalar multiplier core synthesized with a 0.35-${\mu}m$ CMOS cell library has 32,768 gates and can operate up to 150-MHz@3.3-V. It can be used in hardware design of Elliptic curve cryptography processor for smartcard security.
Keywords
Elliptic curve cryptography (ECC); Complementary recoding;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 C.C Chang, Y.T. Kuo, and C.H. Lin, "Fast algorithm for common-multiplicand multipli- cation and exponentiation by performing complements", Proc. of the 17th Int. Conf. on Advanced Information Networking and Application (AINA '03), pp. 807-811, 2003
2 S.K. Jain, L. Song and K.K. Parhi, "Efficient Semi-Systolic Architectures for Finite Field Arithmetic", IEEE Trans. VLSI Syst., vol. 6, no. 1, pp. 101-113, Mar. 1998   DOI   ScienceOn
3 최용재, 김호원, 김무섭, 박영수, "IC 카드를 위한 polynomial 기반의 타원곡선 암호시스템 연산기 설계", 대한전자공학회 하게종합학술대회 논문집, 제24권 제1호, pp.305-308, 2001
4 lH. Guo and C.L. Wang, "Systolic Array Implementation of Euclid's Algorithm for Inversion and Division in GF($2^{m}$)", IEEE Trans. Computers., vol. 47, no. 10, pp. 1161-1167, Oct. 1998   DOI
5 문상국, "소프트웨어/하드웨어 최적화된 타원곡선 유한체 연산 알고리즘의 개발과 이를 이용한 고성능 정보보호 SoC설계", 한국해양정보통신학회 논문지, 제13권 제2호, pp.293-298, 2009
6 A. Menezes, Elliptic curve pubic key cryptosystem, Kluwer Academic Publishers, 1993
7 Certicom research, The Elliptic Curve Cryptosystem, Certicom, April 1997
8 A.D. Booth, "A signed binary multiplication technique", Journal of Applied Mathematics 4, pp. 236-240,1951
9 C.D. Walter, "Systolic modular multipli- cation", IEEE Trans. on Computers, vol. 42, no. 3, pp. 376-378, Mar., 1993   DOI   ScienceOn
10 P. Balasubramaniam and E. Karthikeyan, "Elliptic curve scalar multiplication algorithm using complementary recoding", Elsevier, 2007
11 김창훈, 권순학, 홍준표, 유기영, "타원곡석 암호프로세서의 재구성형 하드웨어 구현을 위한 CF($2^{m}$) 상의 새로운 연산기", 정보과학회 논문지, 제31권 제8호, pp.453-464, 2004
12 G. Orlando, C. Paar, "A Super-Serial Galois Fields Multiplier for FPGAs and its Application to Public-Key Algoritlnns", Pro. of 7th Annual IEEE Symp. on Field-Pro- grammable Custom Computing Machines, pp. 232-239, 1999
13 R. Schroeppel, H. Orman, S. O'Malley and O. Spatscheck, "Fast key exchange with elliptic curve systems", Advances in Cryp- tology CRYPTO 95, pp. 43-56, 1995
14 K. Okeya, "Signed binary representations revisited", Proceedings of CRYPTO '04, pp. 123-139, 2004