The Implementation Of Elliptic Curve Cryptography On DSP Chips

In the eighties of last century, Miller and Koblitz originate Elliptic Curve Cryptography (ECC). Being a new public key cryptography, ECC has many superiorities such as high intensity, high speed and low resource, etc. So it attracted attention of mathematicians and cryptographers all over the world. In the last 20 years, theory and implementation about ECC have made great progress. A lot of countries and organizations have made standards of ECC, including IEEE P1363 P1363a, ANSI X9.62 X9.63, ISO/IEC14888 etc. But in china, the standard doesn't exist. In practice, some research groups and companies have actualized ECC. For example, Certicom of Canada is the most famous corporation in cryptogram technology in the world. It has authorized more than 300 companies to use the ECC cryptogram technology. In China, cryptographers have done some works but the productivity of ECC is far behind the other countries.At the present time, some companies use software to implement some kinds of cryptogram, such as using assemble language to implement cryptogram on DSP chips, and using the DSP as main chip to make encryption card. Although it couldn't compare with specially designed chips in security and speed, but for its easiness in upgrading, low cost and good capability, we can still consider it as a excellent solving method.Combining the characters of ECC and TMS320C54x chips of TI corporation, this paper proposed the ECC adapted to this kind of chips, and discussed its establishment and implement. In this paper, we mainly discussed ECC on finite field with its characteristic being big prime number. The main works of the author is as follows:1. Introducing the mathematical basis of ECC.2. Proposing a method of establishing one kind of random ECC and some kinds of existing implemented methods.3. Proposing a kind of safe ECC suitable for TMS320C54x chips.4. Proposing the calculating formula and efficiency comparison of point addition and point doubling when using different projective coordinates.5. Improving NAF algorithm and window NAF algorithm.6. Proposing the point multiplying method of only using x coordinate on finite field with its characteristic being big prime number.7. Implementing the Elliptic Curve Digital Signature Algorithm, and comparing the performance with RSA of the same intensity and the same environment.This paper is divided into 6 chapters. In the first chapter we introduced the background of the research of ECC and TMS320C54x chips. In the second chapter we introduce the math basis of ECC. In the third chapter we introduce the basic concept of Elliptic Curve and ECDSA. In the fourth chapter we described the method of creating parameters of random ECC and gived a kind of Elliptic Curve adapt to TMS320C54x chips. In the fifth chapter we studied the fast implement of ECC on DSP chips. We mainly discussed the fast algorithm of point addition, point doubling and point multiplying. We also improved NAF algorithm, window NAF algorithm and introduced Frobenius algorithm. In the last chapter we described the implement of ECDSA, and compared the performance with RSA algorithm of the same intensity and the same environment. The author added notations on all algorithms mentioned in this paper.