Classical hardness of learning with errors

@inproceedings{Brakerski2013ClassicalHO,
  title={Classical hardness of learning with errors},
  author={Zvika Brakerski and Adeline Langlois and Chris Peikert and Oded Regev and Damien Stehl{\'e}},
  booktitle={STOC '13},
  year={2013}
}
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. 
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