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.

Keywords

• Multiplicative inverse over GF($2^{m}$);
• Hardware design;
• Underlying field arithmetic operation;
• Elliptic curve cryptography

• 타원곡선암호;
• GF($2^{m}$)상에서 승법에 대한 역원연산;
• 하드웨어 설계;
• 기저체 연산;

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References

1. Working Draft IEEE P1363, Part 6
2. http://www.kordic.re.kr/
3. http://www.etimesi.com/
4. Neal Koblitz, 'A Course in Number Theory and Cryptography.' Springer-Verlag pub., 1994
5. Michael Rosing, 'Implementing Elliptic Curve Cryptography.' Manning pub., 1999
6. Certicom ECC Whitepaper, 1999
7. Sarwono Sutikno, Ronny Effendi, Andy Surya 'Design and implementation of arithmetic processor $F_{2^155}$ for elliptic curve cryptosystems,' IEEE APCCAS, 1998, Pages: 647-650 https://doi.org/10.1109/APCCAS.1998.743903
8. Robert J., McEliece, 'Finite Fields for Computer Scientists and Engineers.' Kluwer Academic pub., 1989
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