On lattices, learning with errors, random linear codes, and cryptography

@inproceedings{Regev2005OnLL,
title={On lattices, learning with errors, random linear codes, and cryptography},
author={O. Regev},
booktitle={STOC '05},
year={2005}
}

Our main result is a reduction from worst-case lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the 'learning from parity with error' problem to higher moduli. It can also be viewed as the problem of decoding from a random linear code. This, we believe, gives a strong indication that these problems are hard. Our reduction, however, is quantum. Hence, an efficient solution to the learning problem implies a <i>quantum</i… CONTINUE READING