Research On Inner Product Encryption Based On R-LWE

With the rapid development of quantum computer,the security of many cryptographic mechanisms based on traditional difficult problems is threatened.For the reason that,the study of public key cryptosystem which is able to resist quantum attack has attracted the attention of many scholars.Lattice cryptosystem is recognized as a cryptographic technique that can effectively resist quantum attacks.The emphasis of this paper is to study the inner product encryption based on learning with errors over ring(R-LWE)on lattice.As a general extension of traditional public key cryptography,inner product encryption can realize ”partial access” of data and provide a method for data processing to satisfy both data confidentiality and effective access control.And the rich expressions of the function encryption make it widely used in cloud environment.Inner product encryption can not only meet the above advantages,but also realize the hiding of access control strategy.Therefore,it can provide a progressive privacy protection ability for data access control.Inner product encryption has become one of the hot research issues in public key cryptosystem.We have obtained the following two research results:1.By the literature [Asiacrypt 2011],Agrawal et.al constructed the first inner product encryption scheme based on learning with errors(LWE).R-LWE is as a variant of the LWE problem,one sample from the R-LWE distribution is equivalent to n samples from the LWE distribution.Inspired by this,our paper proposes a new inner product encryption algorithm whose security can reduce to the difficult problem of R-LWE.The size of common parameters can reduce a factor of O_ncompared with the inner product encryption algorithm based on LWE problem proposed by Agrawal et al.2.On the basis of the first scheme,our paper uses the g₁ matrix G_n,2,m to embed predicate and attribute vectors into private key and plaintext,and proposes a compact inner product encryption scheme based on R-LWE.Common parameters of this scheme require only two random vectors and one polynomial.Compared with the first scheme,both the size of common parameters and ciphertexts can reduce a factor of O(log_q),where q is a polynomial related to the safety parameter.