## CryptoDB

### Paper: Lattice Trapdoors and IBE from Middle-Product LWE

Authors: Alex Lombardi Vinod Vaikuntanathan Thuy Duong Vuong DOI: 10.1007/978-3-030-36030-6_2 Search ePrint Search Google Middle-product learning with errors (MP-LWE) was recently introduced by Rosca, Sakzad, Steinfeld and Stehlé (CRYPTO 2017) as a way to combine the efficiency of Ring-LWE with the more robust security guarantees of plain LWE. While Ring-LWE is at the heart of efficient lattice-based cryptosystems, it involves the choice of an underlying ring which is essentially arbitrary. In other words, the effect of this choice on the security of Ring-LWE is poorly understood. On the other hand, Rosca et al. showed that a new LWE variant, called MP-LWE, is as secure as Polynomial-LWE (another variant of Ring-LWE) over any of a broad class of number fields. They also demonstrated the usefulness of MP-LWE by constructing an MP-LWE based public-key encryption scheme whose efficiency is comparable to Ring-LWE based public-key encryption. In this work, we take this line of research further by showing how to construct Identity-Based Encryption (IBE) schemes that are secure under a variant of the MP-LWE assumption. Our IBE schemes match the efficiency of Ring-LWE based IBE, including a scheme in the random oracle model with keys and ciphertexts of size $\tilde{O}(n)$ (for n-bit identities).We construct our IBE scheme following the lattice trapdoors paradigm of [Gentry, Peikert, and Vaikuntanathan, STOC’08]; our main technical contributions are introducing a new leftover hash lemma and instantiating a new variant of lattice trapdoors compatible with MP-LWE.This work demonstrates that the efficiency/security tradeoff gains of MP-LWE can be extended beyond public-key encryption to more complex lattice-based primitives.
##### BibTeX
@article{tcc-2019-29966,
title={Lattice Trapdoors and IBE from Middle-Product LWE},
booktitle={Theory of Cryptography},
series={Lecture Notes in Computer Science},
publisher={Springer},
volume={11891},
pages={24-54},
doi={10.1007/978-3-030-36030-6_2},
author={Alex Lombardi and Vinod Vaikuntanathan and Thuy Duong Vuong},
year=2019
}