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Security Estimates for Lattice Problems

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Documentation Status

This Sage module provides functions for estimating the concrete security of Learning with Errors instances.

The main purpose of this estimator is to give designers an easy way to choose parameters resisting known attacks and to enable cryptanalysts to compare their results and ideas with other techniques known in the literature.

Quick Start

Status

We cover:

  • [x] lwe-primal-binder primal attacks on LWE <../algorithms/lwe-primal>
  • [X] lwe-dual-binder dual attacks on LWE <../algorithms/lwe-dual>
  • [x] lwe-bkw-binder Coded-BKW attack on LWE <../algorithms/lwe-bkw>
  • [X] gb-binder Arora-GB attack on LWE <../algorithms/gb>
  • [x] ntru-binder attacks on NTRU public keys (using overstretched parameters) <../algorithms/ntru>

We are planning:

  • [ ] attack on SIS instances

Evolution

This code is evolving, new results are added and bugs are fixed. Hence, estimations from earlier versions might not match current estimations. This is annoying but unavoidable. We recommend to also state the commit that was used when referencing this project.

Bugs

Please report bugs through the GitHub issue tracker.

Contributions

At present, this estimator is maintained by Martin Albrecht. Contributors are:

  • Benjamin Curtis
  • Cathie Yun
  • Cedric Lefebvre
  • Fernando Virdia
  • Florian Göpfert
  • Hamish Hunt
  • Hunter Kippen
  • James Owen
  • Léo Ducas
  • Ludo Pulles
  • Markus Schmidt
  • Martin Albrecht
  • Michael Walter
  • Rachel Player
  • Sam Scott

See Contributing <../contributing> for details on how to contribute.

Citing

If you use this estimator in your work, please cite

Martin R. Albrecht, Rachel Player and Sam Scott. On the concrete hardness of Learning with Errors.
Journal of Mathematical Cryptology. Volume 9, Issue 3, Pages 169–203, ISSN (Online) 1862-2984,
ISSN (Print) 1862-2976 DOI: 10.1515/jmc-2015-0016, October 2015

A pre-print is available as

Cryptology ePrint Archive, Report 2015/046, 2015. https://eprint.iacr.org/2015/046

An updated version of the material covered in the above survey is available in Rachel Player's PhD thesis.

License

The estimator is licensed under the LGPLv3+ license.

Third Party Tools Using this Estimator

Acknowledgements

This project was supported through the European Union PROMETHEUS project (Horizon 2020 Research and Innovation Program, grant 780701), EPSRC grant EP/P009417/1 and EPSRC grant EP/S020330/1, by Zama and by SandboxAQ.

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An attempt at a new LWE estimator

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