Identity-Based Signature from Quadratic Residues and Its Extension to ID-Based Multi-Signature

ID-based signature has drawn the attention of the community since Shamir proposed the concept in 1985. In an ID-based signature scheme, a user can choose any string, which directly links to the user, as her/his public key. Therefore, the management issue of the traditional "certificate authority approach" can be resolved. Due to the usefulness and powerfulness of bilinear maps, most of the existing ID-based signature schemes are constructed from pairing groups. However, pairing is one of the most costly operation in modern cryptography. Thus, lots of cryptographer have paid attention to pairing-free ID-based signature. In this manuscript, we proposed an ID-based signature scheme from quadratic residues. The security of the proposed scheme has been proven based on the hardness of the square root problem. We have also extended our ID-based signature scheme into an multi-signature setting, where multiple signer can simultaneously sign on a same message.