Identity Based Linkable Ring Signature with Logarithmic Size

Abstract

Anonymity is an inevitable and sensitive matter of concern, especially in the age where people are willing to use digital devices and Internet to deal with almost all things in their work and daily life. To support anonymity, modern cryptography is one of the most suitable choices in the algorithm level. Particularly, in the scenarios, such as e-voting, crypto-currency, and smart grid etc., a cryptographic primitive, called linkable ring signature, has shown its ability to handle anonymity problems. However, signature schemes will introduce additional costs to those e-commerce systems, so that they should be as efficient as possible. On the other side, a signature scheme that requires the public key infrastructure (PKI) brings much unnecessary inconvenience to its users, since typically, users of the aforementioned systems are not familiar with cryptographic skills and the system establishers are trusted by them in some sense. As a result, an identity-based (ID-based) signature scheme with small size fulfills the visible requirements of e-commerce systems. In this paper, we proposed an ID-based linkable ring signature scheme with logarithmic size from pairing and elliptic curve discrete logarithm problem (ECDLP), and gave all the security proofs in detail. Besides that, the scheme needs no trusted setup, except that the key generation center knows the secret key of each user and it is a property of ID-based cryptography in nature.