Design And Implementation Of Identity Based Encryption Scheme With Short Public Parameters Over Ideal Lattice

Identity-based encryption(IBE)is an interesting cryptographic primitive.It directly uses the string representing the user’s identity as the public key to realize the implicit verification of the user’s public key.It uses an interesting idea to reduce the cost of establishing and maintaining public key infrastructure.During the past several decades,most IBEs are based on the pairing problem.However,most pairing-related security assumptions suffer from known quantum algorithmic attacks.Therefore,the construction of lattice-based IBE became one of the hot directions in recent years.In the existing lattice-based IBEs,each bit of a user’s identity is always associated with a parameter matrix,and these matrices will form the public parameters of the system,which leads to a sharp increase in the size of the public parameters.Moreover,the schemes contain a large number of matrix operations.This leads to a large amount of computational overhead in practical applications.In order to overcome the above-mentioned problems,we combines the blocking technology,ideal lattice and gadget-based trapdoor to design an efficient IBE scheme with short public parameters over ideal lattice.In addition,we also designs a hierarchical IBE scheme with short public parameters over ideal lattice.The main work of this paper are as follows:(1)Based on RLWE problem,this paper designs an identity-based encryption scheme with short public parameters over ideal lattice.In the standard model,our scheme achieves the indistinguishability of ciphertexts against adaptively chosen identity and chosen plaintext attack.We use the blocking technology to reduce the size of the public parameters.Moreover,we use the ring-version trapdoor generation algorithm and pre-image sampling algorithm.The ring setting also reduces the calculation overhead of our scheme.(2)Hierarchical identity-based encryption(HIBE)is an extension of basic identity-based encryption.It uses a hierarchical structure to reduce the workload of the private-key generator in large networks.According to the above design ideas,this paper also proposes a hierarchical identity-based encryption scheme with short public parameters over ideal lattice.In the standard model,we prove that our HIBE scheme also achieves the indistinguishability of ciphertexts against adaptively chosen identity and chosen plaintext attack.(3)While designing the above schemes,we also studied the software implementation method of IBEs over ideal lattice.We explore the principle of the trapdoor generation algorithm and the pre-image sampling algorithm.At the same time,we use NFLlib to implement the fast ring polynomial operation.Finally,we complete the implementation of IBE over ideal lattice.