Classical Hardness of Learning with Errors

Zvika Brakerski; Adeline Langlois; Chris Peikert; Oded Regev; Damien Stehlé

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arXiv · 1306.0281

Classical Hardness of Learning with Errors

Zvika Brakerski·Adeline Langlois·Chris Peikert·Oded Regev·Damien Stehlé

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Abstract

We show that the Learning with Errors (LWE) problem is classically at least as hard as standard worst-case lattice problems, even with polynomial modulus. Previously this was only known under quantum reductions. Our techniques capture the tradeoff between the dimension and the modulus of LWE instances, leading to a much better understanding of the landscape of the problem. The proof is inspired by techniques from several recent cryptographic constructions, most notably fully homomorphic encryption schemes.

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Zvika Brakerski, Adeline Langlois, Chris Peikert, Oded Regev, Damien Stehlé. 2013-06-03. Classical Hardness of Learning with Errors. https://arxiv.org/abs/1306.0281

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