Attribute‐based conditional proxy re‐encryption protocols (AB‐CPREs) enable a delegator to delegate his decryption rights via different policies and grant the data owner greater flexibility in allocating their encrypted private data stored in the cloud. However, existing lattice‐based AB‐CPREs suffer from some drawbacks such as large parameters and weak passive securities. To the best of our knowledge, the first quantum‐safe key‐policy AB‐CPREs with polynomially bounded parameters (for certain NC 0 circuits/policies) that is selective attribute secure against honest re‐encryption attacks (HRA) is presented. The security of our proposed AB‐CPREs is based on standard LWE assumptions. We further introduce the directly revocable AB‐CPREs, a primitive that enables a delegator to authorize and revoke his delegation of decryption rights dynamically and offers more flexible access control on externally stored encrypted data. Definition and security model of single‐hop directly revocable AB‐CPREs are given, and the first detailed construction of single‐hop directly revocable AB‐CPREs based on standard LWE assumptions is also proposed.

Lattice‐based encryption schemes are significant cryptographic primitives to defend information security against quantum menace, and the decryption failure rate is related to both theoretical and realistic security. We quantitatively analyze how the floating‐point arithmetic and neglecting small probabilities impact the precision, and propose a new effective and efficient test of the failure probability. Therein explicit criteria are given to select the floating‐point datatype and to decide which small probabilities should be abandoned. Furthermore, the outcome is theoretically ensured to meet a given precision. Moreover, by combining the heuristic estimate and the precise simulation, this test is more efficient than previously neglecting small probabilities in a practical way.

Identity-based cryptography is a type of public key cryptography with simple key management procedures. To our knowledge, till now, the existing identity-based cryptography based on NTRU is all over power-of-2 cyclotomic rings. Whether there is provably secure identity-based cryptography over more general fields is still open. In this paper, with the help of the results of collision resistance preimage sampleable functions (CRPSF) over cyclotomic fields, we give concrete constructions of provably secure identity-based encryption schemes (IBE) and identity-based signature schemes (IBS) based on NTRU over any cyclotomic field. Our IBE schemes are provably secure under adaptive chosen-plaintext and adaptive chosen-identity attacks, meanwhile, our IBS schemes are existentially unforgeable against adaptively chosen message and adaptively chosen identity attacks for any probabilistic polynomial time (PPT) adversary in the random oracle model. The securities of both schemes are based on the worst-case approximate shortest independent vectors problem (SIVPγ) over corresponding ideal lattices. The secret key size of our IBE (IBS) scheme is short—only one (two) ring element(s). The ciphertext (signature) is also short—only two (three) ring elements. Meanwhile, as the case of NTRUEncrypt, our IBE scheme could encrypt n bits in each encryption process. These properties may make our schemes have more advantages for some IoT applications over postquantum world in theory.