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Lecture notes in computer science

Feel the Quantum Functioning: Instantiating Generic Multi-Input Functional Encryption from Learning with Errors

Alexandros Bakas, Antonis Michalas, Eugene Frimpong, Reyhaneh Rabaninejad

Published Jan 1, 2022• 4 citations
Publisher
DOI
10.1007/978-3-031-10684-2_16

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There only exists one deterministic identity-based encryption (DIBE) scheme which is adaptively secure in the auxiliary-input setting, under the learning with errors (LWE) assumption. However, the master public key consists of basic matrices. In this paper, we consider to construct adaptively secure DIBE schemes with more compact public parameters from the LWE problem. (i) On the one hand, we gave a generic DIBE construction from lattice-based programmable hash functions with high min-entropy. (ii) On the other hand, when instantiating our generic DIBE construction with four LPHFs with high min-entropy, we can get four adaptively secure DIBE schemes with more compact public parameters. In one of our DIBE schemes, the master public key only consists of basic matrices.
There only exists one deterministic identity-based encryption (DIBE) scheme which is adaptively secure in the auxiliary-input setting, under the learning with errors (LWE) assumption. However, the master public key consists of O(λ) basic matrices. In this paper, we consider to construct adaptively secure DIBE schemes with more compact public parameters from the LWE problem. (i) On the one hand, we gave a generic DIBE construction from lattice-based programmable hash functions with high min-entropy. (ii) On the other hand, when instantiating our generic DIBE construction with four LPHFs with high min-entropy, we can get four adaptively secure DIBE schemes with more compact public parameters. In one of our DIBE schemes, the master public key only consists of ω(log⁡λ) basic matrices.
We construct a general-purpose multi-input functional encryption scheme in the private-key setting. Namely, we construct a scheme where a functional key corresponding to a function f enables a user holding encryptions of x1; : : : ; xt to compute f(x1; : : : ; xt) but nothing else. This is achieved starting from any general-purpose private-key single-input scheme (without any additional assumptions), and is proven to be adaptively secure for any constant number of inputs t. Moreover, it can be extended to a super-constant number of inputs assuming that the underlying single-input scheme is sub-exponentially secure. Instantiating our construction with existing single-input schemes, we obtain multi-input schemes that are based on a variety of assumptions (such as indistinguishability obfuscation, multilinear maps, learning with errors, and even one-way functions), offering various trade-offs between security and efficiency. Previous and concurrent constructions of multi-input functional encryption schemes either rely on stronger assumptions and provided weaker security guarantees (Goldwasser et al. [EU-ROCRYPT '14], and Ananth and Jain [CRYPTO '15]), or relied on multilinear maps and could