Design And Analysis Of Inner Product Encryption

With the rapid development of emerging applications such as “cloud” services, the need for fine-grained and more complex access control policies frequently arises. The traditional public key cryptosystem, with coarse-grained access control and poor expandability, is difficult to meet the needs of emerging applications. To this end, several kinds of functional public key encryption schemes have been studied. As a generalized concept, function encryption(FE) covers a series of encryption system such as identity-based encryption(IBE), attribute-based encryption(ABE) and inner product encryption(IPE). IPE can be seen as a generalization of identity-based encryption(IBE). Ciphertexts and private keys are respectively associated with vectors xr and vr. According to the difference of decrypt conditions, IPE can be classified to zero IPE(ZIPE) and non-zero IPE(NIPE). According to the difference of security requirement, IPE can be classified to attribute-hiding IPE(AHIPE) and public-attribute IPE(PAIPE). AHIPE can be directly used in the field of public key searchable encryption. PAIPE implies an identity-based broadcast encryption(IBBE) system. Hierarchical inner product encryption(HIPE) can provide the capacity of delegate for inner product encryption, which can effectively reduce the workload of private key generator of the system. The applications of(H)IPE can be broaden and generalized to cover other cryptographic primitives such as(H)IBE, generalized keyword search and hidden vector encryption(HVE), which can be seen as a very powerful tool for constructing a series of public key encryption schemes. This thesis mainly study on the size of ciphertexts and security of(H)IPE, the main results are listed as following:All inner product encryption schemes are based on the symmetric bilinear pairing up to now, whereas current research suggests that asymmetric bilinear pairing is better than symmetric bilinear pairing in terms of the size of elements, computing performance and flexibility. We present a new IPE scheme in the setting of asymmetric bilinear pairing. The new scheme has advantage in two aspects: Making the new scheme more efficient by taking the advantage of the efficiency in asymmetric pairing; reducing the communication bandwidth by cutting down the ciphertexts. The proposed IPE scheme achieves fully security under reasonable assumption in the standard model.With reference to the method of sparse matrix that presented by Okamoto and Takashima, we present a new IPE scheme by using of the dual pairing vector space(DPVS) in the setting of asymmetric pairing. The new scheme achieves constant size ciphertexts and fully security. The security is proven under a standard assumption in the standard model.Hierarchical inner product encryption can provide the capacity of delegate for inner product encryption, and it can effectively reduce the workload of private key generator. However, the existing HIPE scheme cannot achieve high efficiency as the ciphertexts is linear to the number of levels. We propose a short ciphertexts IPE scheme by making use of the new technique for dual system encryption. By making use of the IPE scheme as building blocks, we then present a new HIPE scheme that achieves constant-size ciphertexts and full security in the standard model. Security is based on three static assumptions whose size does not depend on the number of queries. The new realization of dual system encryption does not use tags, which makes the compression of ciphertexts is possible.