Research On Identity-Based Matrix Fully Homomorphic Encryption Algorithm From Lattice

In the age of big data,with data become strategic resource for enterprises,more and more people pay attention to data security issues.Fully homomorphic encryption is a cryptographic scheme,which is good at both encryption and computing.However,many existing fully homomorphic encryption have low efficiency for single bit encrypt,poor anti-noise capacity and shallower depth of homomorphic calculation.A lattic-based fully homomorphic encryption algorithm of matrix is proposed in this paper,which resolve the cryptosystem security in post Moore era and the performance problems caused by accessing public key institutions.At first,proposed an improved identity-based matrix encryption algorithm.Algorithm is based on determine learning with error problem in lattice,which can resist the attack of quantum algorithm,and use FRD-coding sampling identity features to construct public key that solve the performance bottleneck due to obtaining the public key through a trusted third party.Secondly,construct a single homomorphic encryption algorithm by realizing homomorphic addition,homomorphic multiplication and homomorphic Hadamard product in matrix.The key switch algorithm is used to solve the problem of the size expansion in ciphertext and secret key,the modulus switch algorithm is used to reduce the noise in the ciphertext.In this way achieving a leveled fully homomorphic encryption algorithm.It is proved by attack game that the algorithm satisfied INDs ID-CPA.In efficiency,algorithm's time complexity is under polynomial time.In noise control,the improved identity-based matrix encryption algorithm's up bound of noise is about 6 times higher than other algorithm when m equal 2,with the increase of m,the reduction speed is slower.Compare key switch algorithm with algorithm in other paper,the noise introduced by homomorphic multiplication and homomorphic Hadamard product is only 0.68% and 2.06%.There are 20 pictures,tables 10 and 70 references.