多重数字签名方案及其安全性证明

基于因数分解和二次剩余困难性假设,构造了一个新的按序多重数字签名方案和广播多重数字签名方案.新方案的特点是:多重签名不是由签名成员所生成的多个单签名的累加,而是每个签名成员生成部分签名,以合作的方式生成多重签名;部分签名的长度固定,不随签名人数的改变而变化;部分签名算法和验证算法的复杂度与签名人数的多少无关;新的按序多重签名方案的签名成员不能擅自改变签名顺序.新方案抗现存的对多重签名方案的几种攻击.基于因数分解和二次剩余困难性假设,在随机预言模型下证明了方案的安全性.

Digital Multi-Signature Scheme and Its Security Proof

A new sequential digital multi-signature scheme and a new broadcasting digital multi-signature scheme are proposed based on the difficulty assumption of factoring and quadratic residues.The advantages of the proposed schemes are as follows:the multi-signature is a co-signature which is generated by multiple signers in collaborative and simultaneous manner,in which,per signer generates partly signature,rather than accumulating per signer's single signature.The length of the partly signatures does not grow with the number of the signers.The computation complicacy of the partly signature algorithm and the verification algorithm is independent of the signer's number.The signing sequence of the proposed sequential digital multi-signature scheme is fixed and unable to be changed freely by the signers.Proposed schemes have lower computation complicacy and more efficient,and are secure against existent attacks for multi-signature schemes.Their securities are proved under the difficulty assumption of factoring and quadratic residues in the random oracle model.