Proxy signature is an active cryptographic research area, and a wide range of literatures can be found nowadays suggesting improvement and generalization of existing protocols in various directions. However, from the efficiency view, many proposed proxy signature schemes in these literatures are not satisfying and cannot fit to the mobile communication. Therefore, there is a desire to design efficient proxy signature schemes. Based on Boneh et al＇s pairing-based short signature, this paper presents two proxy signature schemes. One is proxy-protected signature scheme, and the other is proxy aggregate signature scheme. Since both of them can achieve high efficiency, it is believed that they are specially suitable for mobile communication environment.
Identity-based （ID-based） cryptography has drawn great concerns in recent years, and most of ID-based schemes are constructed from bilinear parings. Therefore, ID-based scheme without pairing is of great interest in the field of cryptography. Up to now, there still remains a challenge to construct ID-based signature scheme from quadratic residues. Thus, we aim to meet this challenge by proposing a concrete scheme. In this paper, we first introduce the technique of how to calculate a 2^lth root of a quadratic residue, and then give a concrete ID-based signature scheme using such technique. We also prove that our scheme is chosen message and ID secure in the random oracle model, assuming the hardness of factoring.
