中文摘要：

设计了基于整数近似GCD问题新的全同态加密方案。跟随Gentry设计模式,构造somewhat同态加密方案,并归约其安全性到整数近似GCD;引入稀疏子集和难度假设来压缩解密电路,使其具有自举性;最后转换somewhat同态加密方案到全同态加密方案。与文献[1]方案相比,提出的somewhat同态加密方案更接近于文献[2]中公钥加密方案。

英文摘要：

This paper desiged a fully homomorphic encryption（ FHE） scheme based on approximate integer GCD problem.Following Gentry＇s scheme,firstly,it construced a somewhat homomorphic encryption（SHE） scheme,and reduced its security to approximate integer GCD. Then it squashed decryption circuit to achieve bootstrapping by applying SSSP assumption. Finally,it transfered SHE into FHE. The SHE is closer to the public key scheme in literature[2]than [1].