Implementation of Elliptic Curve Cryptosystems using the SRC Reconfigurable Computer Final Project Specification Sang Han 1. Introduction The most popular public-key cryptography for encryption and digital signature has been RSA. In order to measure against the increasingly sophisticated attacks, the length of RSA key has increased over the recent years. Increasing the length of RSA key requires more computing power and presents burden on commercial applications that demand fast and secure transactions. Recently Elliptic Curve Cryptography (ECC) has become a very attractive and viable option because it requires shorter key length and provides great resistance against attacks. This project will specially focus on the scalar multiplication on ECC. The algorithm that is to be investigated is Montgomery’s method and its extended version proposed by Lopez and Dahab. Furthermore, the paper will investigate on efficient algorithms on field multiplication and field inversion operations, the main operations in the ECC scalar multiplication. This project will also focus on implementation of ECC scalar multiplication on reconfigurable computer. Hardware implementation of ECC is advantageous over that of software because ECC requires complex mathematical operations that can be efficiently implemented on hardware level. 2. Design Entry Method SRC will be used for the implementation. VHDL and C are employed for the development, and the verification of developed modules is done through comparing the outputs with expected outputs that can be obtained either from simulation using a ECC software available in public domain or from test vectors previously generated in the security lab in GMU. 3. Schedule Date Goals 3/8 Final Spec Submission 3/23 SRC tool familiarity Understanding of ECC and Montgomery’s method First Progress Report 4/6 Implementation of modules in SRC Understanding of ONB-Type II multiplication algorithm Second Progress Report4/20 Continue working the implementation Understanding of Itoh’s inversion algorithm Third Progress Report 4/30 Rough project draft submission 5/7 Project Presentation 4. Reference • Ian Blake, Gadiel Seroussi, and Nigel Smart, Elliptic Curves in Cryptography, Cambridge University Press, 1999. • Andreas Enge, Elliptic Curves and Their Applications to Cryptography, Kluwer Academic Publishers, 1999. • William Stallings, Cryptography and network Security: Principles and Practice, 3rd ed., Prentice Hall, Upper Saddle River, 1999. • Nghi Nguyen, Kris Gaj, David Caliga, Tarek El-Ghazawi, Implementation of Elliptic Curve Cryptosystems on a Reconfigurable Computer, IEEE International Conference on Field-Programmable Technology, 2003 • SRC Inc, Web Page, http://www.srccomp.com/ • Itoh, T., Tsujii, S.: A Fast Algorithm for Computing Multiplicative Inverses in GF(2m) Using Normal Bases. Information and Computation. Vol.. 78 (1988), 171-177 • Kwon, S.: A Low Complexity and a Low Latency Bit Parallel Systolic Multiplier for GF(2m) Using Optimal Normal Basis of Type II, ISCAS 2003 • Kwon, S., and Ryu, H., Efficient Bit Serial Multiplication Using Optimal Normal Bases of Type II in GF(2m), ISC 2002, LNCS 2433, pp. 300-308, 2002 • López, J., and Dahab, R.: Fast Multiplication on Elliptic Curves over GF(2m) without precomputation. CHES’99, LNCS 1717,
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