基于中国剩余定理的门限RSA签名方案的改进

针对基于中国剩余定理的门限RSA签名方案无法签署某些消息，以及部分签名合成阶段运算量大的问题，论文提出一种基于虚拟群成员的改进方法，使得改进后的方案能够签署所有消息，同时能够极大地减少部分签名合成阶段的运算量，当门限值为10时，可以将部分签名合成阶段的运算量减少为原来的1/6。对改进方案进行了详细的安全性和实用性分析。结果表明，改进方案在适应性选择消息攻击下是不可伪造的，且其运算效率较其他门限RSA签名方案更高。

Improvement of Threshold RSA Signature Scheme Based on Chinese Remainder Theorem

To slove the problems that Chinese Remainder Theorem (CRT) based threshold RSA signature scheme can not be used to sign some messages and the amount of computation in partial signatures combining phase is large, an improving method is proposed, in which a virtual group member is introduced, making the scheme can be used to sign all messages and significantly reducing the amount of computation in partial signatures combining phase, e.g. when the threshold value is 10, the amount of computation in partial signatures combining phase can be reduced to 1/6 of the original. The security and practicability of the improved scheme are analyzed. Results show that it is non-forgeable against an adaptive chosen message attack and more efficient than other threshold RSA signatures.