安全高效的无对运算无证书有序多重签名方案

针对目前多数有序多重签名方案存在安全性低或运算复杂的问题，提出了一种新的安全高效的无证书有序多重签名方案。为防止公钥替换攻击，将用户的身份标识与部分公钥进行哈希运算作为用户的部分私钥。签名用户需用指定的顺序验证签名阶段的部分签名，确保签名的有序性。在随机预言模型下，基于计算离散对数问题的困难性证明方案生成的签名是不可伪造、不可窜改。方案在签名和验证阶段主要涉及椭圆曲线点乘运算，不含双线性对操作，通过理论分析和仿真实验表明，与同类方案比较，所提方案最多提高了28%的效率。

Secure and efficient certificateless sequential multi-signature scheme with no pair operation

In order to address the problem of low security or complex computation in most existing sequential multi-signature schemes, this paper proposed a new secure and efficient certificateless sequential multi-signature scheme. To prevent public key replacement attacks, the scheme hashed the signer''s identity and part of public key as the partial private key of the signer. Signers verified the partial signatures generated in the signature stage with the specified signature order to ensure the order of signatures. Under the random oracle model, the scheme was proved to be unforgeable and immutable based on the difficulty of computing discrete logarithmic problems. In the signature and verification stage, the scheme mainly involved elliptic curve point multiplication without bilinear pair. Theoretical analysis and simulation experiments show that compared with similar schemes, the proposed scheme can improve the efficiency by up to 28%.