Identity-Based Encryption from Lattices Using Approximate Trapdoors

Practical implementations of advanced lattice-based constructions have received much attention since the first practical scheme instantiated over $$\textsf{NTRU}$$ lattices, proposed by Prest et al. (Asiacrypt 2014). They are using powerful lattice-based building blocks which allow to build Gaussian preimage sampling and trapdoor generation efficiently. In this paper, we propose two different constructions and implementations of identity-based encryption schemes (IBE) using approximate variants of “gadget-based” trapdoors introduced by Chen et al. (Asiacrypt 2019). Both constructions are proven secure. Our first IBE scheme is an adaptation of the Bert et al. scheme (PQCrypto 2021) to the approximate setting, relying on the $$\textsf{Module}\text {-}\textsf{LWE}$$ hardness assumption and making use of the Micciancio-Peikert paradigm with approximate trapdoors. The second IBE relies on a variant of the $$\textsf{NTRU}$$ hardness assumption. We provide several timings and a comparison analysis to explain our results. The two different instantiations give interesting trade-offs in terms of security and efficiency and both benefit from the use of approximate trapdoors. Though our second IBE construction is less efficient than other $$\textsf{NTRU}$$ -based IBEs, we believe our work provides useful insights into efficient advanced lattice-based constructions.