fplll 5.1 and fpylll 0.2.4dev

New versions of fplll and fpylll were released today. I’ve reproduced release notes below for greater visibility. The biggest user-visible changes for fplll are probably that

  • CVP enumeration is not experimental any more,
  • support for external enumeration libraries (go write that GPU implementation of enumeration) was added and
  • support for OSX was greatly improved.

On the fpylll side, the biggest user-visible changes are probably various API updates and a much nicer strategy/framework for gathering statistics about BKZ.

The next version of fplll will contain support for LLL reduction on Gram matrices.

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On dual lattice attacks against small-secret LWE and parameter choices in HElib and SEAL

My paper on solving small, sparse secret instances is now on ePrint. Here’s the abstract:

We present novel variants of the dual-lattice attack against LWE in the presence of an unusually short secret. These variants are informed by recent progress in BKW-style algorithms for solving LWE. Applying them to parameter sets suggested by the homomorphic encryption libraries HElib and SEAL yields revised security estimates. Our techniques scale the exponent of the dual-lattice attack by a factor of (2\,L)/(2\,L+1) when \log q = \Theta{\left(L \log n\right)}, when the secret has constant hamming weight h and where L is the maximum depth of supported circuits. They also allow to half the dimension of the lattice under consideration at a multiplicative cost of 2^{h} operations. Moreover, our techniques yield revised concrete security estimates. For example, both libraries promise 80 bits of security for LWE instances with n=1024 and \log_2 q \approx {47}, while the techniques described in this work lead to estimated costs of 68 bits (SEAL) and 62 bits (HElib).

If you want to see what its effect would be on your favourite small, sparse secret instance of LWE, the code for estimating the running time is included in our LWE estimator. The integration into the main function estimate_lwe is imperfect, though. To get you started, here’s the code used to produce the estimates for the rolling example in the paper.

  • Our instance’s secret has hamming weight h=64 and a ternary secret. We always use sieving as the SVP oracle in BKZ:

    sage: n, alpha, q = fhe_params(n=2048, L=2)
    sage: kwds = {"optimisation_target": "sieve", "h":64, "secret_bounds":(-1,1)}
    
  • We establish a base line:

    sage: print cost_str(sis(n, alpha, q, optimisation_target="sieve"))
    
  • We run the scaled normal form approach from Section 4 and enable amortising costs from Section 3 by setting use_lll=True:

    sage: print cost_str(sis_small_secret_mod_switch(n, alpha, q, use_lll=True, **kwds))
    
  • We run the approach from Section 5 for sparse secrets. Setting postprocess=True enables the search for solutions \mathbf{s}_1 with very low hamming weight (page 17):

    sage: print cost_str(drop_and_solve(sis, n, alpha, q, postprocess=True, **kwds))
    
  • We combine everything:

    sage: f = sis_small_secret_mod_switch
    sage: print cost_str(drop_and_solve(f, n, alpha, q, postprocess=True, **kwds))
    

fpylll

fpylll is a Python library for performing lattice reduction on lattices over the Integers. It is based on the fplll, a C++ library which describes itself as follows:

fplll contains several algorithms on lattices that rely on floating-point computations. This includes implementations of the floating-point LLL reduction algorithm, offering different speed/guarantees ratios. It contains a ‘wrapper’ choosing the estimated best sequence of variants in order to provide a guaranteed output as fast as possible. In the case of the wrapper, the succession of variants is oblivious to the user. It also includes a rigorous floating-point implementation of the Kannan-Fincke-Pohst algorithm that finds a shortest non-zero lattice vector, and the BKZ reduction algorithm.

fplll is distributed under the GNU Lesser General Public License (either version 2.1 of the License, or, at your option, any later version) as published by the Free Software Foundation.

In short, fplll is your best bet at a publicly available fast lattice-reduction library and fpylll provides a convenient interface for it — for experimentation, development and extension — from Python.

For the rest of this post, I’ll give you a tour of the features currently implemented in fpylll and point out some areas where we could do with some help.

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Cysignals

If you’ve written a fair amount of Cython code in your time, chances are that you got frustrated by

  1. buggy C/C++ code crashing your Python shell and
  2. the fact that you cannot interrupt C/C++ functions.

For example, the following Cython code cannot be interrupted:

while True:
    pass

On the other hand, if you have written Cython code in Sage, then you might have come across its nifty sig_on(), sig_off() and sig_check() macros which prevent crashes and allow your calls to C/C++ code to be interrupted. Sage had signal handling — crashes, interrupts — forever (see below).

Cysignals is Sage’s signal handling reborn as a stand-alone module, i.e. it allows to wrap C/C++ code blocks in sig_on() and sig_off() pairs which catch signals such as SIGSEGV. Using it is straight-forward. Simply add

include "cysignals/signals.pxi"

to each Cython module and then wrap long-running computations in sig_on() / sig_off() pairs or check for signals with sig_check(). See the cysignals documentation for details.

We have a first pre-release out. Pre-release because we haven’t switched Sage to the new, stand-alone code yet. Once this is done, we’ll publish version 1.0 since some version of this code has been in use on many different systems for at least decade.

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First CoDiMa Training School in Computational Discrete Mathematics

This winter school sounds excellent:

We have just finalised the date and location for the First CoDiMa Training School in Computational Discrete Mathematics which will take place at the University of Manchester on November 16th-20th, 2015. This school is intended for post-graduate students and researchers from UK institutions. It will start with the 2-days hands-on Software Carpentry workshop covering basic concepts and tools, including working with the command line, version control and task automation, continued with introductions to GAP and SageMath systems, and followed by the series of lectures and exercise classes on a selection of topics in computational discrete mathematics.

The School’s website and the registration details will be announced shortly. In the meantime, if you’re interested in attending, please keep the dates in your diary and check for updates on our website and on our Twitter @codima_project, or tell us about your interest writing to contact at codima.ac.uk so that we will be able to notify you when the registration will begin.

PolyBoRi is dead, it needs your help

On the Sage development list a discussion is going on what to do about PolyBoRi. For those who do not know PolyBoRi, for computing Gröbner bases for Boolean polynomials it is pretty much the only (open-source) game in town (as far as I know):

The core of PolyBoRi is a C++ library, which provides high-level data types for Boolean polynomials and monomials, exponent vectors, as well as for the underlying polynomial rings and subsets of the powerset of the Boolean variables. As a unique approach, binary decision diagrams are used as internal storage type for polynomial structures.

On top of this C++-library we provide a Python interface. This allows parsing of complex polynomial systems, as well as sophisticated and extendable strategies for Gröbner base computation. PolyBoRi features a powerful reference implementation for Gröbner basis computation.

Boolean polynomials show up a lot in cryptography and other areas of computer science.

The trouble with PolyBoRi is that both authors of PolyBoRi – Alexander Dreyer and Michael Brickenstein – left academia and have jobs now which have nothing to do with PolyBoRi. Hence, PolyBoRi is currently not maintained. This is a big problem. In particular, there are some issues with PolyBoRi which cannot be ignored forever:

  • PolyBoRi uses Python (yay) but only Python 2. At some point the world – i.e. Sage – will switch to Python 3 and PolyBoRi is the only obstacle to that switch except for the Sage Python library itself.
  • PolyBoRi uses Scons as a build system. Everybody would be a lot happier if it was switched to using autotools (which are a lot more awesome than many people realise).

In the long-term the Singular team might get involved and keep PolyBoRi alive, but this is not certain. Also, there is a push for a decision about what to do with PolyBoRi in Sage now.

The current proposal on the table is to drop PolyBoRi from the default Sage installation, i.e. to demote it to an optional package. In my mind, this would be very bad as Sage and PolyBoRi benefit from the tight integration that currently exists. Also, in my experience, optional packages tend to simply not work that well as they are not tested in each release.

Hence, if you care about PolyBoRi you should consider to

  1. let us know in the relevant thread on the mailing list if you use PolyBoRi in Sage.
  2. volunteer to help to autotool-ify PolyBoRi if you speak autotools. (If you don’t speak autotools, you should learn, they are awesome.)
  3. volunteer to help to port PolyBoRi from Python 2 to Python 3.

I’m up for getting involved, but I don’t want to take on the responsibility alone.

Update (2015-06-13): A fair share of work has already been done by Andrew. Still, anyone up for helping out?