In this work, we propose the first adaptively secure IPE based on the learning with errors (LWE) assumption with sub-exponential modulus size (without resorting to complexity leveraging). Concretely, our IPE supports inner-products over the integers $\mathbb{Z}$ with polynomial sized entries and satisfies adaptively weakly-attribute-hiding security. We also show how to convert such an IPE to an IPE supporting inner-products over $\mathbb{Z}_p$ for a polynomial-sized $p$ and a fuzzy identity-based encryption (FIBE) for small and large universes. Our result builds on the ideas presented in Tsabary (CRYPTO'19), which uses constrained pseudorandom functions (CPRF) in a semi-generic way to achieve adaptively secure ABEs, and the recent lattice-based adaptively secure CPRF for inner-products by Davidson et al. (CRYPTO'20). Our main observation is realizing how to weaken the conforming CPRF property introduced in Tsabary (CRYPTO'19) by taking advantage of the specific linearity property enjoyed by the lattice evaluation algorithms by Boneh et al. (EUROCRYPT'14).
Category / Keywords: public-key cryptography / inner product encryption, adaptive security, LWE Original Publication (with minor differences): IACR-ASIACRYPT-2020 Date: received 17 Sep 2020 Contact author: takashi yamakawa obf at gmail com Available format(s): PDF | BibTeX Citation Version: 20200921:082408 (All versions of this report) Short URL: ia.cr/2020/1135