Algorithm Design And Application For Parallel Fully Homomorphic Encryption Based On AGCD

Fully homomorphic encryption is a kind of encryption method with homomorphism, allowing one to compute arbitrary functions over encrypted data without the decryption key. The decrypted result is equivalent to the corresponding computation over the plaintext. The fully homomorphic encryption scheme based on AGCD intractable problem on the integer needs re-encryption when to perform homomorphism operations over encrypted data. This will cause the low speed of the scheme and seriously affect its performance because of a lot of big integer multiplication. For this reason, the parallel fully homomorphic encryption algorithm based on integer AGCD was designed in this thesis, optimizing the performance of these fully homomorphic encryption schemes which were constructed based on AGCD intractable problem on the integer. And the scheme was applied to the private information retrieval.Fully homomorphic encryption has the nice algebra homomorphic properties, which makes it can be well applied to the field of face recognition, private information retrieval, anonymous voting and digital watermarking.However, the fully homomorphic encryption schemes are improved, but the computational efficiency and the availability are very low when the number of homomorphic operations is more and even infinite.In addition, it cannot be widely used in the real life. The performance of the the fully homomorphic encryption scheme based on AGCD intractable problem on the integer was improved in this thesis, increasing the practicability of the scheme in the above areas.In order to improve the performance of the fully homomorphic encryption scheme which was constructed based on AGCD intractable problem on the integer, this thesis do the following work:(1) The serial algorithm of the the fully homomorphic encryption scheme based on AGCD was implemented and the Fast Fourier Transform(FFT) was used to optimize the large integer arithmeticof the fully homomorphic encryption scheme based on AGCD intractable problem on the integer,and an improved fully homomorphic encryption scheme based on FFT was proposed in this thesis.(2) We designed a parallel fully homomorphic encryption algorithm based on the above-mentioned scheme, and experimented it on the MapRaduce.(3) In order to protect the data privacy of both sides of communication, the fully homomorphic encryption was applied to private information retrieval.The FFT was used to design a private information retrieval scheme based on FHE. The private information retrieval scheme was designed based on MapReduce model.