Theory And Applications Of Ring Signatures Over Elliptic Curves

The notion of digital signatures is one of the most important components of cryptography. It is the base of theory for the message integrity, freshness, and source authenticity. For different applications, various functions of digital signatures broaden and further the applications of digital signatures. This paper mainly contributes to short signatures, one-time signatures and ring signatures over elliptical curves. The main works are as follows: We review the practical applications of short signatures, one-time signatures,ring signatures and proxy signatures, with a good analysis of the schemes proposed and their security models.A novel one-time signature scheme is proposed with a short signature size of about 160 bits while much better computation efficiency than the BLS short signature. Based on the infeasibility of large integer fraction, the scheme is proven existentially unforgeable against chosing message attacks. As a short one-time signature, the security of the scheme does not rely on random oracles. Also, the scheme can be converted to achieve multiple signatures with the same signing key.New ring signature scheme and proxy ring signature scheme are presented. Both schemes are constructed from bilinear pairings. Finally, the security of the schemes is analyzed based on rational computational assumptions.