Security Estimates for Lattice Problems
=======================================

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 :target: https://mybinder.org/v2/gh/malb/lattice-estimator/jupyter-notebooks?labpath=..%2F..%2Ftree%2Fprompt.ipynb
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 :target: https://lattice-estimator.readthedocs.io/en/latest/?badge=latest
 :alt: Documentation Status

This `Sage <http://sagemath.org>`__ module provides functions for estimating the concrete security of `Learning with Errors <https://en.wikipedia.org/wiki/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
-----------

We currently provide evaluators for the security of the `LWE`, `NTRU`, and `SIS` problems.
Our estimator integrates simulators for the best known attacks against these problems, and provides
bit-security estimates relying on heuristics to predict the cost and shape of lattice reduction algorithms. The default
models are configured in `conf.py <https://github.com/malb/lattice-estimator/blob/main/estimator/conf.py>`__.

It is possible to evaluate attacks cost individually, or using the helper functions:

- ``*.estimate.rough``: fast routine that evaluates the security of the problem only against the usually most efficient
  attacks. Note that it uses a non-default cost model for lattice reduction, most often used in the literature for ease of
  comparison, and will thus return different numbers than the rest of the API. Refer to 
  `its documentation <https://lattice-estimator.readthedocs.io/en/latest/_apidoc/estimator.lwe/estimator.lwe.Estimate/estimator.lwe.Estimate.rough.html>`__
  for details.
- ``*.estimate``: extended routine that evaluates the security of the problem against all supported attacks. This uses the
  default cost and shape model for lattice reduction.

Usage examples:

  .. code-block:: python
    
    >>> from estimator import *
    >>> schemes.Kyber512
    LWEParameters(n=512, q=3329, Xs=D(σ=1.22), Xe=D(σ=1.22), m=512, tag='Kyber 512')

    >>> LWE.primal_usvp(schemes.Kyber512)
    rop: ≈2^143.8, red: ≈2^143.8, δ: 1.003941, β: 406, d: 998, tag: usvp
    
    >>> r = LWE.estimate.rough(schemes.Kyber512)
    usvp                 :: rop: ≈2^118.6, red: ≈2^118.6, δ: 1.003941, β: 406, d: 998, tag: usvp
    dual_hybrid          :: rop: ≈2^115.5, red: ≈2^115.3, guess: ≈2^112.3, β: 395, p: 5, ζ: 0, t: 40, β': 395, N: ≈2^81.4, m: 512

    >>> r = LWE.estimate(schemes.Kyber512)
    bkw                  :: rop: ≈2^178.8, m: ≈2^166.8, mem: ≈2^167.8, b: 14, t1: 0, t2: 16, ℓ: 13, #cod: 448, #top: 0, #test: 64, tag: coded-bkw
    usvp                 :: rop: ≈2^143.8, red: ≈2^143.8, δ: 1.003941, β: 406, d: 998, tag: usvp
    bdd                  :: rop: ≈2^140.2, red: ≈2^139.1, svp: ≈2^139.3, β: 389, η: 422, d: 1005, tag: bdd
    dual                 :: rop: ≈2^149.9, mem: ≈2^97.1, m: 512, β: 424, d: 1024, ↻: 1, tag: dual
    dual_hybrid          :: rop: ≈2^139.7, red: ≈2^139.5, guess: ≈2^135.9, β: 387, p: 5, ζ: 0, t: 50, β': 391, N: ≈2^81.1, m: 512

  .. code-block:: python

    >>> from estimator import *
    >>> schemes.Dilithium2_MSIS_WkUnf
    SISParameters(n=1024, q=8380417, length_bound=350209, m=2304, norm=+Infinity, tag='Dilithium2_MSIS_WkUnf')

    >>> r = SIS.estimate.rough(schemes.Dilithium2_MSIS_WkUnf)
    lattice  :: rop: ≈2^123.5, red: ≈2^123.5, sieve: ≈2^-332.2, β: 423, η: 423, ζ: 1, d: 2303, prob: 1, ↻: 1, tag: infinity

    >>> r = SIS.estimate(schemes.Dilithium2_MSIS_WkUnf)
    lattice  :: rop: ≈2^152.2, red: ≈2^151.3, sieve: ≈2^151.0, β: 427, η: 433, ζ: 0, d: 2304, prob: 1, ↻: 1, tag: infinity

  .. code-block:: python

    >>> from estimator import *
    >>> schemes.Falcon512_SKR
    NTRUParameters(n=512, q=12289, Xs=D(σ=4.05), Xe=D(σ=4.05), m=512, tag='Falcon512_SKR', ntru_type='circulant')
   
    >>> r = NTRU.estimate.rough(schemes.Falcon512_SKR)
    usvp                 :: rop: ≈2^140.5, red: ≈2^140.5, δ: 1.003499, β: 481, d: 544, tag: usvp
   
    >>> r = NTRU.estimate(schemes.Falcon512_SKR)
    usvp                 :: rop: ≈2^165.0, red: ≈2^165.0, δ: 1.003489, β: 483, d: 1020, tag: usvp
    bdd                  :: rop: ≈2^160.6, red: ≈2^159.5, svp: ≈2^159.6, β: 463, η: 496, d: 1022, tag: bdd
    bdd_hybrid           :: rop: ≈2^160.6, red: ≈2^159.5, svp: ≈2^159.6, β: 463, η: 496, ζ: 0, |S|: 1, d: 1024, prob: 1.0, ↻: 1, tag: hybrid
    bdd_mitm_hybrid      :: rop: ≈2^347.8, red: ≈2^347.8, svp: ≈2^202.7, β: 483, η: 2, ζ: 0, |S|: 1, d: 1024, prob: ≈2^-180.5, ↻: ≈2^182.7, tag: hybrid

    >>> schemes.Falcon512_Unf
    SISParameters(n=512, q=12289, length_bound=5833.9072, m=1024, norm=2, tag='Falcon512_Unf')
   
    >>> r = SIS.estimate.rough(schemes.Falcon512_Unf)
    lattice  :: rop: ≈2^121.2, red: ≈2^121.2, δ: 1.003882, β: 415, d: 1024, tag: euclidean
   
    >>> r = SIS.estimate(schemes.Falcon512_Unf)
    lattice  :: rop: ≈2^146.3, red: ≈2^146.3, δ: 1.003882, β: 415, d: 1024, tag: euclidean

- `Try it in your browser <https://mybinder.org/v2/gh/malb/lattice-estimator/jupyter-notebooks?labpath=..%2F..%2Ftree%2Fprompt.ipynb>`__.
- `Read the documentation <https://lattice-estimator.readthedocs.io/en/latest/>`__.
  
Status
------

We cover:

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

.. |lwe-primal-binder| image:: https://mybinder.org/badge_logo.svg
   :target: https://mybinder.org/v2/gh/malb/lattice-estimator/jupyter-notebooks?labpath=..%2F..%2Ftree%2Flwe-primal.ipynb

.. |lwe-dual-binder| image:: https://mybinder.org/badge_logo.svg
   :target: https://mybinder.org/v2/gh/malb/lattice-estimator/jupyter-notebooks?labpath=..%2F..%2Ftree%2Flwe-dual.ipynb

.. |lwe-bkw-binder| image:: https://mybinder.org/badge_logo.svg
   :target: https://mybinder.org/v2/gh/malb/lattice-estimator/jupyter-notebooks?labpath=..%2F..%2Ftree%2Flwe-bkw.ipynb

.. |gb-binder| image:: https://mybinder.org/badge_logo.svg
   :target: https://mybinder.org/v2/gh/malb/lattice-estimator/jupyter-notebooks?labpath=..%2F..%2Ftree%2Fgb.ipynb

.. |ntru-binder| image:: https://mybinder.org/badge_logo.svg
   :target: https://mybinder.org/v2/gh/malb/lattice-estimator/jupyter-notebooks?labpath=..%2F..%2Ftree%2Fntru.ipynb

.. |sis-lattice-binder| image:: https://mybinder.org/badge_logo.svg
   :target: https://mybinder.org/v2/gh/malb/lattice-estimator/jupyter-notebooks?labpath=..%2F..%2Ftree%2Fsis-lattice.ipynb
                     
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.

.. warning :: We give no API/interface stability guarantees. We try to be mindful but we may reorganize the code without advance warning.

Bugs
----

Please report bugs through the `GitHub issue tracker <https://github.com/malb/lattice-estimator/issues>`__.

Contributions
-------------

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

- `Benjamin Curtis <https://github.com/bencrts>`__
- `Cathie Yun <https://github.com/cathieyun>`__
- Cedric Lefebvre
- Fernando Virdia
- Florian Göpfert
- `Hamish Hunt <https://github.com/hamishun>`__
- `Hunter Kippen <https://github.com/hkippen-SBAQ>`__
- James Owen
- Léo Ducas
- `Ludo Pulles <https://github.com/ludopulles>`__
- Markus Schmidt
- `Martin Albrecht <https://github.com/malb>`__
- Michael Walter
- `Navid Abapour <https://github.com/navid-divan>`__
- Rachel Player
- Sam Scott

See `Contributing <https://lattice-estimator.readthedocs.io/en/latest/contributing.html>`__ 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 <https://pure.royalholloway.ac.uk/portal/files/29983580/2018playerrphd.pdf>`__.

License
-------

The estimator is licensed under the `LGPLv3+ <https://www.gnu.org/licenses/lgpl-3.0.en.html>`__ license.


Third Party Tools Using this Estimator
--------------------------------------

- Zama's TFHE Compiler: `Concrete <https://github.com/zama-ai/concrete>`__.

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 <https://zama.ai/>`__ and by `SandboxAQ <https://sandboxaq.com>`__.