Research On Secret-Shanring And Digital Signature Based On Elliptic Curve Public Key Cryptosystem

After more than 10 years of research, the elliptic curve public key cryptosystem starts from the academic fundamental research stage to move towards the practical application stage gradually.It becomes one of the most promising kinds of the present public key cryptosystems.Through the analysis of elliptic curve cryptosystem's newest research results, the article has been divided seven chapters to summarize a series of research work which this domain has completed. The 1st chapter has drawn out the elliptic curve public key cryptosystem through the discussion of cryptology development course, analysis of threat and the security requieements, and it introduced the full text main content and author's main research results.The 2nd chapter mainly introduced the background knowledge and basic mathematics rationale which the elliptic curve cryptosystem is connected in the present paper. The 3rd chapter mainly introduced the definition of elliptic curve, as well as definition the elliptic curve operational rules on different fields. The 4th chapter discussed the elliptic curve discrete logarithmic problem which is base on the limited group issue,and induced the criterion of selecting secure elliptic curves.The 5th chapter and the 6th chapter introduced some classical cryptosystems and some pratical system, and through analyzing deficiencies of existing crypto schemes , two crypto schemes which were based on elliptic curves cryptosystem were proposed, including a new multi-secret sharing scheme and a new fair blind signature scheme. The 7th chapter has summarized the entire paper, and has c forecasted the future of the elliptic curve cryptosystem.In the paper, the research results mainly include:(1)Has made the corresponding induction to the current Elliptic Curve Cryptosystem;(2) Through analysis of the shortcomings and loopholes in the existing cryptographic protocol, new cryptographic protocols were proposed, including a multi-secret sharing scheme and a fair blind signature scheme, and provided a detailed analysis of their security and the efficiencies;(3) Some typical cryptosystem, such as encryption, decryption, signature and verification,were realized with Matlab,which is a kind of mathematic software.