Research On Public Key Cryptography Based On Elliptic Curve

With the rapid development and wide application of information technology,security requirements of electronic information has increased quickly. RSA public keycryptography system is difficult to meet high security requirements. The elliptic curvecryptosystem has the highest security at present, Elliptic curve cryptography has themerits which are high security, low computational overhead, short key length andsmall bandwidth. It is considered the most common public key cryptography.In this paper, the following aspects were discussed: the theory research andapplications of elliptic curve cryptosystem：1. Introduce the basic concept of digital signature, function, the differencebetween digital signature and handwritten signature, and analyze digital signaturesecurity proof and attack methods. Base on these, a basic framework is formed.2. Introduce the basic concept of elliptic curves, properties and efficiency, andanalyze the existing digital signature scheme based on elliptic curve.3. By the analysis of existing digital signature schemes, two new signaturescheme based on elliptic curves are constructed. One is new digital signature schemebased on elliptic curve, and the other is self-certified public key signature schemebased on elliptic curve. By analyzing the existing proxy signature scheme four newproxy signature scheme are constructed:(1) anonymous proxy signature schemebased on DSA;(2) a new MUO proxy signature scheme with agent protection;(3)proxy signature scheme with message recovery based on ECC;(4) Anonymous ProxySignature Scheme based on Elliptic Curve.4. introduce an electronic voting scheme based on elliptic curve cryptosystem,and analyze it.