Research And Application Of Two Kinds Of Homomorphic Encryption Schemes

With the development of society and the advancement of technology,the mobile devices such as cellphone,portable computers have been increasingly used,the amount of data has also dramatically increased.The traditional cryptographic algorithms cannot meet people's demand for massive data transmission.Therefore,a homomorphic encryption algorithm is proposed,which directly operates the ciphertext without decrypting,and the correct plaintext can be obtained by decrypting the ciphertext after the operation.This algorithm not only improves the operation speed of the ciphertext,but also saves the operation time.However,the existing encryption-based homomorphic algorithms on integer are only designed for two participants,namely "one encryption and one decryption",and the length of the plaintext transmitted is limited to only one bit.So the computational efficiency is low and the plaintext space is small.It cannot be applied to big data environments,such as wireless sensor networks.Meanwhile,some problems still existed in this operation process,such as the length of the public/private keys is too long to be applied in the actual environment.To overcome above problems,this thesie proposes the scheme of integer based on homomorphic encryption and improves the identity based on homomorphic encryption scheme in lattice.The contributions of this thesis are as follows:(1)For the problems such as plaintext space is small,the participants are single,and the computational efficiency is low integer-based homomorphic encryption algorithms.Based on the existing schemes which designed for single message,two participants "one party encryption,one party decryption"(one-to-one),an improved scheme of homomorphic encryption with multiple participants "multi-party encryption,one-party decryption"(multi-to-one)is proposed In this scheme,decryption party receives ciphertexts from encryption and performs homomorphism operation.The proposed scheme simplifies the key generation process on the basis of guaranteeing the security,and gives the range of the number of encrypted parties that can be decrypted accurately in the process of homomorphic operation.Meanwhile,the plaintext space is extended from a single message to multiple messages,and an application scenario corresponding to the scheme is constructed.Simulation results show that the proposed scheme is more feasible in integer range,and meet the requirements of the users to the system response.(2)In the homomorphic encryption technology,the time complexity caused by the excessive length of the public key is too large to be applied in practice,to solve above problem,a multi-identity homomorphic encryption scheme is proposed.In this scheme,a conversion algorithm of identities is constructed on lattice by using indistinguishable obfuscation and sampling function,which can convert the ciphertexts of different identities into ciphertexts of the same identity and then perform homomorphic operations.Therefore,a homomorphic encryption scheme of single identity converted into multiple identities is proposed,the advantage of it can support the homomorphic operation between ciphertexts with different identities by choosing the user's identity as the public key,which greatly reduces the length of the public key.The scheme is selectively secured under the hardness of learning with errors in the standard model.Comparing with previous schemes,the results show that the proposed scheme not only improves the information transmission efficiency,but also reduces the length of the public key in the homomorphic operation process.(3)Considering the homomorphic encryption technology which have advantages of directly operating ciphertext can solve the problems of massive data transmission and low computational efficiency in the wireless sensor network.For above mentioned problems,the homomorphic data encryption and aggregation scheme based on wireless sensor network can be constructed,which have advantages of directly operating ciphertext.The existing homomorphic algorithm was adopted as a basic scheme to encrypt the privacy data,and the sensors' identities were included in digital signatures so as to provide the scheme with functions of data tracing and modification.This scheme adopts a cluster-type wireless sensor network and allocates interference factors to each sensor node in clusters,which not only resists internal attacks,but also improves the efficiency and the computational complexity of the scheme.