Better Key Sizes (and Attacks) for LWE-Based Encryption

Richard Lindner; Chris Peikert

Paper 2010/613

Better Key Sizes (and Attacks) for LWE-Based Encryption

Richard Lindner and Chris Peikert

Abstract

We analyze the concrete security and key sizes of theoretically sound lattice-based encryption schemes based on the ``learning with errors'' (LWE) problem. Our main contributions are: (1)~a new lattice attack on LWE that combines basis reduction with an enumeration algorithm admitting a time/success tradeoff, which performs better than the simple distinguishing attack considered in prior analyses; (2)~concrete parameters and security estimates for an LWE-based cryptosystem that is more compact and efficient than the well-known schemes from the literature. Our new key sizes are up to $10$ times smaller than prior examples, while providing even stronger concrete security levels.

Note: Contains corrected final security estimates from (withdrawn) eprint report 2010/592.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Full version of paper in CT-RSA 2011
Keywords: lattice-based cryptography basis reduction learning with errors
Contact author(s): cpeikert @ cc gatech edu
History: 2010-11-30: received
Short URL: https://ia.cr/2010/613
License: CC BY

BibTeX

@misc{cryptoeprint:2010/613,
      author = {Richard Lindner and Chris Peikert},
      title = {Better Key Sizes (and Attacks) for {LWE}-Based Encryption},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/613},
      year = {2010},
      url = {https://eprint.iacr.org/2010/613}
}