标准模型下基于强RSA假设的身份签名方案

ID Based Signature Scheme from Strong RSA Assumption in the Standard Model

基于身份的密码学一直是密码界的热点研究方向,因为它节约了证书管理的庞大开销.目前,基于身份的密码方案大量涌现,但是其中绝大部分方案都是基于双线性配对实现的,其安全性依赖于配对困难问题.无需配对的基于身份的密码方案仍然是密码学中值得关注的一个课题.目前,有少量无需配对的身份签名方案被提出,但是其中一些方案未给出安全性证明,另一些则是随机预言模型下的可证安全方案,还没有在标准模型下可证安全的非配对的身份签名方案被提出.基于Hohenberger和Waters签名提出了一个身份签名方案,该方案在标准模型下被证明是弱安全的,并且其安全性可以归约到强RSA问题.同时,在引入卡梅隆Hash函数后,该方案可被转换成标准安全的身份签名方案.

ID based cryptography is always the interested field in the cryptography research, since it has the advantage of eliminating user＇s certificates, and the cost of certificate management is saved. Although many ID based cryptographic primitives have been proposed, most of them are constructed from bilinear pairing, and based on the hardness assumptions in bilinear pairing. Since pairing usually involves heavy computational costs, how to construct ID based cryptographic primitives without pairing is still a valuable issue in the cryptography. A few ID based signature schemes have been presented, however, some of them have not provided the security proof, and others can only be proved secure in the random oracle. There is still no true ID based signature schemes in the standard model. In this paper, an ID based signature scheme from Hohenberger and Waters signature is proposed, which can be proved weakly secure under the strong RSA assumption. Furthermore, with the help of Chameleon Hash function, the proposed scheme can be transformed into a provably secure scheme in the standard model. In the proposed scheme, the signature involves 2 elements in N N , and the signing algorithm only needs 2 modular exponentiations.