针对基于身份的多接收者签密方案不能抵抗量子攻击以及存在的密钥托管问题,基于多变量公钥密码体制,提出一个多接收者模型下的无证书签密方案.新方案不仅避免了基于身份密码体制的密钥托管问题,而且继承了多变量公钥密码体制的优势,实现了“抗量子攻击”的高安全性.与现有方案相比,新方案无需双线性对操作,具有更少的计算量,更高的计算效率,适用于智能卡等计算能力较小的终端设备.最后,在随机预言模型下,给出了该文方案基于MQ困难问题假设和IP困难问题假设的安全性证明.分析表明,该文方案具有不可否认性、前向安全性、后向安全性、保护接收者隐私等安全属性.%Aiming at the vulnerability under quantum attacks and the inherent key escrow problem of the existing ID-based multi-receiver signcryption schemes, we propose an efficient certificateless multi-receiver signcryption scheme (CLMSC), which is based on the multivariate public key cryptography (MPKC). The new scheme can not only avoid the inherent key escrow problem in the identity-based cryptographic system,but also have the advantage of MPKC, that is, it can withstand the quantum attack. The proposed scheme does not require any pairing operations in signcrypting a message for any number of receivers. Therefore, compared with the existing signcryption schemes, the proposed scheme is more efficient, and thus it is suitable for terminals which have lower computation capacity like smart card. Finally, we prove its semantic security under the hardness of Multivariate Quadratic (MQ) problem and its unforgeability under the Isomorphism of Polynomials (IP) assumption in the random oracle model respectively. The proposed scheme also has the security properties of non-repudiation, forward security, backward security and the recipient privacy protection.
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