Abstract
The functional encryption scheme designed using the lattice can realize fine-grained encryption and it can resist quantum attacks. Unfortunately, the sizes of the keys and ciphertexts in cryptographic applications based on learning with errors are large, which makes the algorithm inefficient. Therefore, we construct a functional encryption for inner product predicates scheme by improving the learning with errors scheme of Agrawal et al. [Asiacrypt 2011], and its security relies on the difficulty assumption of ring learning with errors. Our construction can reduce the sizes of the keys and ciphertexts compared with the learning with errors scheme.
Highlights
Traditional public key encryption is “all or nothing” in accessing data, that is, a user can decrypt successfully or know nothing about the plaintexts
The n samples from the learning with errors (LWE) distribution can be replaced by a sample from the R-LWE distribution, which will reduce the size of the public key by a factor of n
We present an inner product encryption (IPE) scheme that is secure under the R-LWE hardness assumption
Summary
Traditional public key encryption is “all or nothing” in accessing data, that is, a user can decrypt successfully or know nothing about the plaintexts. We generate the secret key associated with the predicate g using of ring-SIS (R-SIS) and the ciphertext c associated with the attribute I using of R-LWE. A predicate encryption scheme with respect to G and is attribute hiding if for any PPT adversaries A, the advantage of A in the following experiment is negligible in the security parameter κ: 1.
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