基于素数幂次阶分圆多项式环的多密钥全同态方案

传统的全同态加密方案允许对单个用户的密文进行任意计算,计算结果解密后能够得到与明文计算相一致的结果。多密钥全同态加密方案允许云服务器对多个用户的密文进行任意计算,更适用云计算的应用场景。基于公钥加密方案NTRU的多密钥全同态加密方案被称为NTRU型多密钥全同态加密方案,具有密钥和密文尺寸短、运算速度快和潜在的抗量子攻击等特性。但是,现有的NTRU型多密钥全同态加密方案存在可选的环结构少、使用的环结构容易受到子域攻击等问题。文章以NTRU型多密钥全同态加密方案LTV12为研究对象,将该方案中的2的幂次阶分圆多项式环替换为素数幂次阶分圆多项式环,密钥生成算法采用正则嵌入下的高斯分布,优化了LTV12方案,增加了可选环结构的数量,并使其免受子域攻击的危害,对其实用性和安全性具有推动意义。

Multi-key Fully Homomorphic Encryption Scheme over Prime Power Cyclotomic Rings

The traditional fully homomorphic encryption scheme allows arbitrary evaluations on the ciphertext from a single user.After decryption,a result consistent with the plaintext evaluations can be obtained.The multi-key fully homomorphic encryption schemes allow the cloud server to perform arbitrary evaluations on ciphertexts from multiple parties,which is more suitable for cloud computing application.The multi-key fully homomorphic encryption schemes based on NTRU have the characteristics of short keys,small ciphertext sizes,high operation speed and potential resistant from quantum attacks.However,the existing NTRU multi-key fully homomorphic encryption schemes have the problems that they have rare optional ring structures,and the ring structure is vulnerable to subfield attacks.In this paper,the power of 2 cyclotomic ring in the multi-key homomorphic scheme LTV12 was changed into the prime power cyclotomic ring.The key generation algorithm uses the Gaussian distribution over canonical embedding.Therefore,the number of optional ring structures increased and the scheme is not vulnerable to subfield attacks anymore,which has a driving significance for the practicability and security of the scheme,which has a driving significance for the practicability and security of the scheme.