Attribute-Based Fully Homomorphic Encryption Scheme from Lattices with Short Ciphertext

Attribute-based encryption (ABE) is a good choice for one-to-many communication and fine-grained access control of the encryption data in a cloud environment. Fully homomorphic encryption (FHE) allows cloud servers to make valid operations on encrypted data without decrypting. Attribute-based fully homomorphic encryption (ABFHE) from lattices not only combines the bilateral advantages/facilities of ABE and FHE but also can resist quantum attacks. However, in the most previous ABFHE schemes, the growth of ciphertext size usually depends on the total number of system's attributes which leads to high communication overhead and long running time of encryption and decryption. In this paper, based on the LWE problem on lattices, we propose an attribute-based fully homomorphic scheme with short ciphertext. More specifically, by classifying the system's attributes and using the special structure matrix in MP12, we remove the dependency of ciphertext size on system's attributes l and the ciphertext size is no longer increased with the total number of system's attributes. In addition, by introducing the function G-1 in the homomorphic operations, we completely rerandomize the error term in the new ciphertext and have a very tight and simple error analysis using sub-Gaussianity. Besides, performance analysis shows that when l=2 and n=284 according to the parameter suggestion given by Micciancio and Dai et al., the size of ciphertext in our scheme is reduced by at least 73.3%, not to mention l>2. The larger the l, the more observable of our scheme. The short ciphertext in our construction can not only reduce the communication overhead but also reduce the running time of encryption and decryption. Finally, our scheme is proved to be secure in the standard model.