Lattice Trapdoors and IBE from Middle-Product LWE
Name
2019-1067.pdf
Description
Accepted version
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607.82 KB
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Adobe PDF
Checksum (MD5)
20ed0c46a94ca2d288f9a9d03349b002
Author(s)
Lombardi, Alex
Vaikuntanathan, Vinod
Vuong, Thuy Duong
Date Issued
November 2019
Journal
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher
Springer International Publishing
Citation
Lombardi, Alex, Vaikuntanathan, Vinod and Vuong, Thuy Duong. 2019. "Lattice Trapdoors and IBE from Middle-Product LWE." Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 11891.
Version
Author's final manuscript
Abstract
© 2019, International Association for Cryptologic Research. 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 (formula presented) (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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/978-3-030-36030-6_2
