基于多变量密码体制的签密方案

Signcryption scheme based on multivariate cryptosystem

为了解决基于传统公钥密码的签密方案不能抵抗量子攻击的问题,提出了一种基于多变量公钥密码的签密方案。结合多层Matsumoto-Imai(MMI)方案中心映射的多层构造、CyclicRainbow签名方案,以及隐藏域方程(HFE)的中心映射构造,提出了一种改进的中心映射构造方法,并由此设计了相应的签密方案。分析表明,所设计的方案与MMI方案相比,在实现了加密和签名的同时,方案密钥量和密文量分别减少了5%和50%。在随机预言模型下,基于多变量方程组求解困难问题假设和多项式同构困难问题假设,证明了该方案在适应性选择密文攻击下具有不可区分性,在适应性选择消息攻击下具有不可伪造性。

Aiming at the problem that signcryption scheme of the conditional public key cryptosystems cannot resist the quantum attack, a new signcryption scheme based on muhivariate public key cryptosystems was proposed. Combining the central map of multilayer structure in Multi-layer Matsumoto-Imai （MMI） with the CyclicRainbow signature scheme, and using the constructure of the central map in Hidden Field Equation （HFE）, the signcryption scheme was designed by introducing an improved method of constructing central map. The analysis shows that, compared with the original MMI, the scheme＇s key size decreases by 5% and the ciphertext reduces by 50%, and it also makes encryption and signature both realizable at the same time. In the random oracle model, its indistinguishability under the hardness of Multivariate Quadratic （MQ） problem and its unforgeability under the Isomorphism of Polynomials （IP） assumption were proved respectively. And it shows that the proposed scheme has unforgeability under the adaptive chosen-ciphertext attack as well as indistinguishability under the adaptive chosen message attack.