Classical Hardness of Learning with Errors
Résumé
We show that the Learning with Errors (LWE) problem is classically at least as hard as standard worst-case lattice problems. 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.