中文摘要：

详细分析了环LWE上NTRU基本加密方案的噪声特性与同态性,引出了＂零次同态加密＂的概念,并且说明了环LWE上NTRU基本加密方案是一个零次同态加密。提出了2个同态加密方案,展示了如何基于NTRU零次同态加密,设计NTRU型BGN同态加密方案与全同态加密方案。在该NTRU型全同态加密方案中,其密钥在密文计算中始终保持不变,因此,无需密钥交换就获得了一个全同态加密方案。此外,该NTRU型全同态加密的密文是一个向量,相比密文是矩阵的GSW全同态加密方案,具有存储与传输上的优势。

英文摘要：

In order to construct a fully homomorphic encryption scheme based on NTRU cryptosystem from ring learning with errors, noise growth and homomorphic property in the NTRU cryptosystem were analyzed. The concept of zero homomorphic encryption was introdced and that the NTRU cryptosystem was zero homomorphic en- cryption was shown. A BGN homomorphic encryption scheme and a fully homomorphic encryption scheme were proposed based on the NTRU cryptosystem. In the proposed NTRU-type fully homomorphic encryption scheme, the secret key doesn＇t change in homomorphic multiplications. Thus a fully homomorphic encryption scheme can be obtained without key switching that was used in the previous fully homomorphic encryption schemes. Moreover, the cipbertext is a vector in the proposed NTRU-type fully homomorphic encryption scheme which has the advantage of storage and transmission compared to GSW fully homomorphic encryption scheme where the ciphertext is a matrix.