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A Python interface for

Project description

A Python (2 and 3) wrapper for fplll.
>>> from fpylll import *

>>> A = IntegerMatrix(50, 50)
>>> A.randomize("ntrulike", bits=50, q=127)
>>> A[0].norm()

>>> M = GSO.Mat(A)
>>> M.update_gso()
>>> M.get_mu(1,0)

>>> L = LLL.Reduction(M)
>>> L()
>>> M.get_mu(1,0)
>>> A[0].norm()

The basic BKZ algorithm can be implemented in about 60 pretty readable lines of Python code (cf. For a quick tour of the library, you can check out the tutorial.


fpylll relies on the following C/C++ libraries:

  • GMP or MPIR for arbitrary precision integer arithmetic.
  • MPFR for arbitrary precision floating point arithmetic.
  • QD for double double and quad double arithmetic (optional).
  • fplll for pretty much everything.

fpylll also relies on

  • Cython for linking Python and C/C++.
  • cysignals for signal handling such as interrupting C++ code.
  • py.test for testing Python.
  • flake8 for linting.

We also suggest

  • virtualenv to build and install fpylll in
  • IPython for interacting with Python
  • Numpy for numerical computations (e.g. with Gram-Schmidt values)


fpylll ships with Sage 7.4. Thus, it is available via SageMathCell and SageMathCloud (select a Jupyter notebook with a Sage 7.4 kernel, the default Sage worksheet still runs Sage 7.3 at the time of writing). You can also fire up a virtual server with the latest fpylll/fplll preinstalled (it takes perhaps 15 minutes until everything is compiled).

Getting Started

Note: fpylll is also available via PyPI and Conda-Forge for Conda. In what follows, we explain manual installation.

We recommend virtualenv for isolating Python build environments and virtualenvwrapper to manage virtual environments. We indicate active virtualenvs by the prefix (fpylll).

Automatic install

  1. Run

    $ ./
    $ source ./activate

Manual install

  1. Create a new virtualenv and activate it:

    $ virtualenv env
    $ ln -s ./env/bin/activate ./
    $ source ./activate
  2. Install the required libraries - GMP or MPIR and MPFR - if not available already. You may also want to install QD.

  3. Install fplll:

    $ (fpylll) ./ $VIRTUAL_ENV

    Some OSX users report that they required export CXXFLAGS="-stdlib=libc++ -mmacosx-version-min=10.7" and export CXX=clang++ (after installing a recent clang with brew) since the default GCC installed by Apple does not have full C++11 support.

  4. Then, execute:

    $ (fpylll) pip install Cython
    $ (fpylll) pip install -r requirements.txt

    to install the required Python packages (see above).

  5. If you are so inclined, run:

    $ (fpylll) pip install -r suggestions.txt

    to install suggested Python packages as well (optional).

  6. Build the Python extension:

    $ (fpylll) export PKG_CONFIG_PATH="$VIRTUAL_ENV/lib/pkgconfig:$PKG_CONFIG_PATH"
    $ (fpylll) python build_ext
    $ (fpylll) python install
  7. To run fpylll, you will need to:

    $ (fpylll) export LD_LIBRARY_PATH="$VIRTUAL_ENV/lib"

    so that Python can find fplll and friends.

    Note that you can also patch activate to set LD_LIBRRY_PATH. For this, add:

    export LD_LIBRARY_PATH
    export PKG_CONFIG_PATH

    towards the end and:

    if ! [ -z ${_OLD_LD_LIBRARY_PATH+x} ] ; then
        export LD_LIBRARY_PATH
        unset _OLD_LD_LIBRARY_PATH
    if ! [ -z ${_OLD_PKG_CONFIG_PATH+x} ] ; then
        export PKG_CONFIG_PATH
        unset _OLD_PKG_CONFIG_PATH

    in the deactivate function in the activate script.

Running fpylll

  1. To (re)activate the virtual environment, simply run:

    $ source ./activate
  2. Start Python:

    $ (fpylll) ipython

Multicore Support

fpylll supports parallelisation on multiple cores. For all C++ support to drop the GIL is enabled, allowing the use of threads to parallelise. Fplll is thread safe as long as each thread works on a separate object such as IntegerMatrix or MatGSO. Also, fpylll does not actually drop the GIL in all calls to C++ functions yet. In many scenarios using multiprocessing, which sidesteps the GIL and thread safety issues by using processes instead of threads, will be the better choice.

The example below calls LLL.reduction on 128 matrices of dimension 30 on four worker processes.

from fpylll import IntegerMatrix, LLL
from multiprocessing import Pool

d, workers, tasks = 30, 4, 128

def run_it(p, f, A, prefix=""):
    """Print status during parallel execution."""
    import sys
    r = []
    for i, retval in enumerate(p.imap_unordered(f, A, 1)):
        sys.stderr.write('\r{0} done: {1:.2%}'.format(prefix, float(i)/len(A)))
    sys.stderr.write('\r{0} done {1:.2%}\n'.format(prefix, float(i+1)/len(A)))
    return r

A = [IntegerMatrix.random(d, "uniform", bits=30) for _ in range(tasks)]
A = run_it(Pool(workers), LLL.reduction, A)

To test threading simply replace the line from multiprocessing import Pool with from multiprocessing.pool import ThreadPool as Pool. For calling BKZ.reduction this way, which expects a second parameter with options, using functools.partial is a good choice.


fpylll welcomes contributions, cf. the list of open issues. To contribute, clone this repository, commit your code on a separate branch and send a pull request. Please write tests for your code. You can run them by calling:

$ (fpylll) PY_IGNORE_IMPORTMISMATCH=1 py.test

from the top-level directory which runs all tests in tests/test_*.py. We run flake8 on every commit automatically, In particular, we run:

$ (fpylll) flake8 --max-line-length=120 --max-complexity=16 --ignore=E22,E241 src

Note that fpylll supports Python 2 and 3. In particular, tests are run using Python 2.7 and 3.5. See .travis.yml for details on automated testing.

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