Identity-based encryption (IBE), and its hierarchical extension (HIBE), are interesting cryptographic primitives that aim at the implicit authentication on the users’ public keys by using users’ identities directly. During the past several decades, numerous elegant pairing-based (H)IBE schemes were proposed. However, most pairing-related security assumptions suffer from known quantum algorithmic attacks. Therefore, the construction of lattice-based (H)IBE became one of the hot directions in recent years. In the setting of most existing lattice-based (H)IBE schemes, each bit of a user’s identity is always associated with a parameter matrix. This always leads to drastic but unfavorable increases in the sizes of the system public parameters. To overcome this issue, we propose a flexible trade-off mechanism between the size of the public parameters and the involved computational cost using the blocking technique. More specifically, we divide an identity into l′ segments and associate each segment with a matrix, while increasing the lattice modulo slightly for maintaining the same security level. As a result, for the setting of 160-bit identities, we show that the size of the public parameters can be reduced by almost 89.7% (resp. 93.8%) while increasing the computational cost by merely 5.2% (resp. 12.25%) when l′ is a set of 16 (resp. 8). Finally, our IBE scheme is extended to an HIBE scheme, and both of them are proved to achieve the indistinguishability of ciphertexts against adaptively chosen identity and chosen plaintext attack (IND-ID-CPA) in the standard model, assuming that the well-known ring learning with error (RLWE) problem over the involved ideal lattices is intractable, even in the post-quantum era.

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.