基于双服务器模型的可公开验证多元多项式外包计算方案

结合云安全外包计算中的隐私保护问题，针对任意多元多项式函数的外包计算，利用同态加密算法和多线性映射，构造了基于双服务器模型的可公开验证外包计算方案。该方案能够保证多项式函数输入与输出的隐私性和安全性，用户或者任意第三方都可以对云服务器计算的结果进行验证，实现了可公开验证性和可用性。云返回给用户的结果处于密文状态，只有拥有解密密钥的用户才能够输出最终的结果，一定程度上保证了计算结果的安全性。分析结果表明，该方案在标准模型下能够达到输入的选择明文攻击（CPA）安全，用户的计算代价远远小于服务器以及直接计算多项式函数的计算代价。

Publicly verifiable outsourced computation scheme for multivariate polynomial based on two-server model

Combining with the privacy-preserving problem of secure outsourced computation in the cloud and aiming at arbitrary outsourcing multivariate polynomials, a publicly verifiable outsourced computation scheme based on two-server model was constructed by homomorphic encryption and multilinear mapping. The scheme can guarantee the privacy and security of inputs and outputs of polynomial functions, and reach the goal that users or any third party can verify the correctness of the results, thus achieving open verification and availability. The results returned by the cloud are in the state of encryption, only users who have decryption key can output the final results, which can ensure the security of computation. Besides, the scheme can achieve Chosen Plaintext Attack (CPA) security of inputs in the standard model, and the user's computational cost is much less than that of the server and direct computation.