Research And Implementation Of Elliptic Curve Digital Signature Scheme With Message Recovery

With profoundly development of electronic business affairs and electronic government affairs, digital signature technology become more and more important. Compared to RSA, with keys of the same length, Elliptic Curve Cryptography (ECC) offers more security strength, thus ECC-based digital signature scheme attracts the most attention. Digital signature scheme with message recovery has the advantage of shorter signature, this is important for identity-based public keys without restrictions in trust and for one-pass key protocol with mutual authentication. However, all knowned ECC-based digital signature schemes can not recover message from signature. Thus, research and Implementation of elliptic curve digital signature scheme with message recovery do make sense.This dissertation focuses on the research of digital signature scheme with message recovery based on ECC. The contributions of the dissertation are as follows:(1) An algorithm is presented which speeds scalar multiplication on non-super singular elliptic curve defined over GF(2~m). With this optimized version of binary method, the efficiency of the algorithm is improved 50 percent when optimal choice of m is used.(2) With analysis of the ECC-based digital signature scheme, a new signature scheme is presented, which allows signature with message recovery and without inversion.(3) The new signature scheme is applied to create an identity-based public keys system without restrictions in trust and a one-pass key exchange protocol with mutual authentication.(4) Finally, ECC-based digital signature scheme with message recovery is implemented.