# 타원곡선을 암호시스템에 사용되는 최적단위 연산항을 기반으로 한 기저체 연산기의 하드웨어 구현

• Jo, Seong-Je (Dept. of Aviation Communication Information Engineering, Hankuk Aviation University) ;
• Kwon, Yong-Jin (School of Electro., Telecomm. and Computer Eng., Hankuk Aviation Uvi.)
• 조성제 (한국항공대학교 항공통신정보공학과) ;
• 권용진 (한국항공대학교 전자정보통신컴퓨터공학부)
• Published : 2002.02.01

#### Abstract

In recent years, the security of hardware and software systems is one of the most essential factor of our safe network community. As elliptic Curve Cryptosystems proposed by N. Koblitz and V. Miller independently in 1985, require fewer bits for the same security as the existing cryptosystems, for example RSA, there is a net reduction in cost size, and time. In this thesis, we propose an efficient hardware architecture of underlying field arithmetic processor for Elliptic Curve Cryptosystems, and a very useful method for implementing the architecture, especially multiplicative inverse operator over GF$GF (2^m)$ onto FPGA and futhermore VLSI, where the method is based on optimized unit operation components. We optimize the arithmetic processor for speed so that it has a resonable number of gates to implement. The proposed architecture could be applied to any finite field $F_{2m}$. According to the simulation result, though the number of gates are increased by a factor of 8.8, the multiplication speed We optimize the arithmetic processor for speed so that it has a resonable number of gates to implement. The proposed architecture could be applied to any finite field $F_{2m}$. According to the simulation result, though the number of gates are increased by a factor of 8.8, the multiplication speed and inversion speed has been improved 150 times, 480 times respectively compared with the thesis presented by Sarwono Sutikno et al. [7]. The designed underlying arithmetic processor can be also applied for implementing other crypto-processor and various finite field applications.

#### References

1. Working Draft IEEE P1363, Part 6
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9. Sutikno, S., Surya, A., Effendi, R., 'An implementation of ElGamal elliptic curves cryptosystems.' Circuits and Systems, 1998. IEEE APCCAS 1995. The 1998 IEEE Asia-Pacific Conference on, 1998, Pages: 483-486 https://doi.org/10.1109/APCCAS.1998.743829
10. 조성제, 권용진, '타원곡선 암호시스템을 위한 기저체 연산기의 FPGA 구현', 대한전자공학회 추계종합학술 발표대회 논문집 II, 2000. 11, Pages: 148-151