对一个环Zn上圆锥曲线数字签名的分析与改进

Analysis and Improvement of a Digital Signature Based on Conic Curve over Zn

摘要:

杨慧等人基于环Z_n上的圆锥曲线构造了一个ElGamal型数字签名方案，文章分析指出，该方案的私钥可以从公钥和签名中恢复出来，因而该签名方案是不安全的。对杨慧等人的签名方案进行了改进，通过分析可知改进方案能够抵抗密钥恢复攻击。基于改进数字签名方案构造了一个多重数字签名方案，该多重数字签名方案无需进行多次交换数据以获得同一个参数，减少了通信量。

Abstract: Under the analyses of an ElGamal digital signature scheme based on conic curve over Z_n proposed by Yang Hui et al., this paper reveals that the secret key can be gained by the public key and the signature, so Yang et al.’s scheme is not security. An improved digital signature scheme is given, and it can resist the secret key gaining attack. Moreover, a multi-signature digital scheme is supplied based on the improved digital signature scheme. The multi- signature digital scheme has the advantage not to exchange many times among singers to get the same parameter, and therefore reduces the communication traffic.