.. image:: https://mybinder.org/badge_logo.svg :target: https://mybinder.org/v2/gh/malb/lattice-estimator/jupyter-notebooks?labpath=..%2F..%2Ftree%2Fprompt.ipynb .. image:: https://readthedocs.org/projects/lattice-estimator/badge/?version=latest :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.
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: ≈2^140.3, red: ≈2^139.7, svp: ≈2^138.8, β: 391, η: 421, d: 1013, 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: ≈2^139.6, 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: ≈2^151.1, 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: ≈2^165.1, red: ≈2^165.1, δ: 1.003489, β: 483, d: 1020, tag: usvp
bdd :: rop: ≈2^160.6, red: ≈2^159.6, svp: ≈2^159.6, β: 463, η: 496, d: 1022, tag: bdd
bdd_hybrid :: rop: ≈2^160.6, red: ≈2^159.6, svp: ≈2^159.6, β: 463, η: 496, ζ: 0, |S|: 1, d: 1024, prob: 1, ↻: 1, tag: hybrid
bdd_mitm_hybrid :: rop: ≈2^349.3, red: ≈2^349.3, svp: ≈2^204.8, β: 481, η: 2, ζ: 0, |S|: 1, d: 1024, prob: ≈2^-182.6, ↻: ≈2^184.8, 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: ≈2^146.4, red: ≈2^146.4, δ: 1.003882, β: 415, d: 1024, tag: euclideanTry 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/>__.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> .. |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
We are planning:
[ ] attack on SIS <https://en.wikipedia.org/wiki/Short_integer_solution_problem>__ instancesThis 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.
Please report bugs through the GitHub issue tracker <https://github.com/malb/lattice-estimator/issues>__.
At present, this estimator is maintained by Martin Albrecht. Contributors are:
See Contributing <https://lattice-estimator.readthedocs.io/en/latest/contributing.html>__ for details on how
to contribute.
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 2015A pre-print is available as
| Cryptology ePrint Archive, Report 2015/046, 2015. https://eprint.iacr.org/2015/046An 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>__.
The estimator is licensed under the LGPLv3+ <https://www.gnu.org/licenses/lgpl-3.0.en.html>__ license.
Concrete <https://github.com/zama-ai/concrete>__.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>.