Research On Attribute Constraint And Access Policy Of Lattice Based Attribute Encryption

With the vigorous development of cloud computing technology and the rapid growth of the demand for controllable sharing of data assets,more and more users tend to store their encrypted data to the cloud,and supervise or share the data through the cloud server.In order to realize safe and efficient sharing of users’ data in the open cloud environment,attribute based encryption(ABE)technology,which support many to many communication mode and fine-grained access control,has also developed rapidly.Traditional ABE technology which is based on the elliptic curve has made great progress and is widely used in various industries,but it is facing the threat of quantum computing attack in the future.In the past ten years,scholars have proposed a series of lattice-based ABE schemes and its optimized proposal that can resist the attack of quantum computing.However,lattice-base ABE not only has the advantage of against quantum computing attack,but also has the problem of high ciphertext expansion rate of the lattice-based cryptography.Therefore,it is a cryptographic challenge to find an effective method to reduce the expansion rate of lattice-based encryption.In addition,the access policy of the existing lattice-based ABE schemes is less flexible,and only supports a single "and" gate or a single "threshold" operation,or supports the circuit type access policy composed of all the attributes of the system.Besides,the space of attributes is bounded and the user privacy protection involved in attributes is insufficient.Therefore,it is also a meaningful topic to explore the attribute organization structure and access policy with richer expressive ability and stronger privacy protection ability.Based on the above research motivation,the main research contents and constructions of this paper are as follows:(1)New construction of identity based dual receiver encryption scheme from lattice is proposed.In the previous identity based dual receiver encryption scheme scheme from lattices,the number of matrices in public parameters increases linearly with the bit-length of user’s identity,and these public parameters are required to participate in the computation in the process of key generation,encryption and decryption which will lead to a large storage overhead and a computation overhead.In order to solve this problem,we introduce an injective function and homomorphic notch gate computing technology to compress the user’s identity information.By doing this,the matrices of the same dimensions in the public parameters is reduced from O(n)to O((?)),where n is the bit length of arbitrary identity and p(p≥2)is a flexible constant.The larger the n and p,the more observable of our proposal.Typically,comparing to the related scheme,the size of public parameters in our proposal is reduced by at least 88%.Finally,our lattice-based IB-DRE scheme is proved to be secure indistinguishable against adaptively chosen identity and plaintext attacks(IND-ID-CPA).(2)An attribute based encryption scheme with two-dimensional attributes and privacy protection from lattice is proposed.In order to solve the problem of attribute space limitation and attribute privacy disclosure in lattice-based attribute encryption scheme,we extend the traditional onedimensional attribute structure to two-dimensional attribute structure.It can add new attribute values at any time without reconstructing the system.The attribute space is no longer bounded.In addition,by doing that the attribute labels are used to set the access policy while the actual values are hidden.It can protect the attribute privacy.Besides,a new trapdoor generation algorithm is introduced to generate the master secret key and remove the dependency of the master secret key on the total number of system’s attributes,and solves the security problem of the leakage of the master secret key.Finally,the space cost in our scheme is remarkably reduced and it is proved to be secure in the standard model.(3)An attribute based encryption scheme with flexible access policy and multi-authority from lattice is proposed.In order to improve the flexibility of access policy and solve the problem of single point bottleneck,Shamir’s secret sharing mechanism and monotonic access tree structure are used to express a clearer and flexible access policy,which can support the"and","or" and "threshold" operations between attributes at the same time.Besides,we construct an optimized sampling algorithm to generate an invertible matrix with a lower runtime.Based on it,we designed multiple attribute authorities which can manage different attribute sets and generate private keys for the user independently.Compared with the existing related schemes,the proposed scheme can improve the functional agility and flexibility of the access policy prominently,and it also can achieve a better performance with less lattice dimension and trapdoor storage cost and ciphertext size.(4)An attribute based fully homomorphic encryption scheme with short ciphertext from lattice is proposed.To reduce the ciphertext size which leads to a high communication overhead and a long running time of encryption and decryption,we use the same two-dimensional attribute structure and the special structure matrix with tag to remove the dependency of ciphertext size on system’s attributes and the ciphertext size is no longer increased with the total number of system’s attributes.In addition,the gadget matrix G’s inverse function is introduced into the homomorphic operations on the ciphertext to re-randomize the noise in the new ciphertext.The sub-Gaussian nature of the G’s inverse function makes the parameters setting and error analysis in the scheme more compact.Besides,performance analysis shows that the size of ciphertext in our scheme is reduced by at least 73.3%.Finally,our scheme is proved to be secure in the standard model.