Dear ECRYPT-NET fellows and readers,

I have some news from CWI @ Science Park in Amsterdam where

fplll-days-3, organized by

Leo Ducas and

Marc Stevens, are currently taking place!

Previously held at ENS Lyon, this is the third time already for such a combined effort to enhance the fplll OpenSource project. fplll has become a lively project with many suggestions that help to debug and feature requests for continuously improving the code-base in various directions.

As a brief history of fplll it can be noted that the first code was written by

Damien Stehlé. It is now written by many active contributors (according to GitHub, the

most active developers are: Martin Albrecht, Shi Bai, Damien Stehlé, Guillaume Bonnoron, Marc Stevens and Koen de Boer) and maintained by

Martin Albrecht and

Shi Bai.

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What does fplll do?

What fplll does, depending on additionally specified parameters, is performing its implementation of the

LLL algorithm using fast floating-point arithmetic under the hood. Other available lattice reduction algorithms are HKZ, BKZ reduction and variants. These algorithms can be applied on an input lattice represented by a matrix, given i.e. in a file as a set of row vectors, to obtain a reduced representation --- a versatile starting point of numerous applications. Furthermore, fplll allows to solve (arbitrarily adjustable approximate-)

SVP and

CVP instances, when used to find a shortest lattice vector relative to a user-chosen center.

To get started, one can not only use and compile the

fplll C++ sources to run experiments, but the often dubbed 'user-friendlier variant'

fpylll which provides Python access to the underlying, fast C++ functions. Finally, every mathematician's dear, Sage, (at least for anyone who isn't fully satisfied by pure Python) benefits from an improved fpylll as well, because importing the fpylll module seamlessly allows direct usage within Sage. Soon a new Sage version,

SageMath 8.0, will be released, which ships the current fpylll module that accesses said, fast C++ routines.

The significance of lattice-based cryptography is repeatedly mentioned in paper's abstracts and has been explored in past ECRYPT-NET blog posts i.e. on

'What are lattices?' and

'Learning problems and cryptography: LPN, LWE and LWR'.

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Significance for cryptanalysis

From a cryptanalysts point of view, the significance lies in the fact that most security models of lattice-based cryptography typically assume lattice reduction to be the most promising attack-vector against the underlying lattice-based primitive. Some security models are able to immediately (and provably) rule out certain classes of attacks and, for instance, a few others can be argued to be less promising than known formulations as lattice problems. Such arguing hence leads to fplll basically representing the SVP/CVP-oracle and it's performance is deemed as a lower bound for the practical performance of an attack. Typically attacks require many calls to such an oracle function, thus such an approach of taking the time of a single run as a lower bound is used to set parameters in experimental cryptosystems, when commonly a more conservative

lower bound including a security margin is chosen. Specifically, many proposed lattice-based crypto-schemes have been parametrized such that these best known-attacks are taken into account.

I suppose, I do not need to point out the numerous

advantages of OpenSource software (over closed-source projects) but and its value to the research community the significance of having freely-available, fast lattice reduction routines is manifold.

To begin with, there is a discrepancy between what theory predicts and algorithmic performance in practice. Techniques described in the literature, summarized as BKZ2.0, leave a broad range of implementation choices. Different groups using different software and metrics where their approach is supreme, naturally lead to results that are hard to compare. If there was software that comes with meaningful defaults for many standard lattice tasks, is customizable, and extensible to individual lattice solutions, then there is hope that the community can agree on problem instances. Ideally, problem instances should cover deployed or model experimental cryptosystems such that they embody a meaningful benchmark for new designs.

Originally, fplll was trying to provide such algorithms with reasonable speed. Recently, developers broadened theirs goals and try to fill gaps of cryptanalytic research. Concretely, now
fplll strives for speed from low level optimizations, and by implementing
diverse techniques from the literature hence catching up with the state of
the art. Additionally, it can be easily tweaked on a high algorithmic level with the Python layer fpylll, yet easily exploiting all the available optimized routines boosting the performance. One can argue that together with diverse lattice challanges this project helps to benchmark and compare various efforts to cryptanalyze cryptographic primitives used in cryptosystem's constructions.

A couple of

Lattice Challenges have been proposed (

SVP-,

Ideal-,

LWE- and

Ring-Challenges) and it seems that researchers also test their code on these instances, which aids a comparison of approaches.

Having them conveniently accessible and high-level, fast lattice operations allows to quickly try out a new idea, or slightly different approach which saves time and hopefully makes researchers willing to share their tweaks and algorithmic tricks more often in the future.

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The workshop

To come back to the start, the fplll-days are meant to be a hands-on, work-oriented workshop that enables direct discussions with core developers and with the goal to improve existing functions and the many algorithms involved. The general idea behind this meeting is to optimize often used routines, make it user-friendlier and accessible to cryptanalysts, for example.

By using code profiling tools, performance and memory usage bottlenecks can be spotted in a first overview, which allows to direct efforts where they might lead to significant speed-ups. After discussing know issues and useful features, this workshop tries to provide an implementation of numerically stable algorithmic variants to push the dimension LLL can handle (like Givens rotations while resorting only to machine floating point type), sophisticated pruning strategies to speed-up enumeration, and implementing sieving algorithms --- all as a promising new direction in finding short vectors faster.

It is exciting to join and shape such a project so let's hope for many interesting projects that got started and delegated here to be completed during this week and further interested researchers turning into active users joining the party and coming up with meaningful, reproducible research results. Remember that Newton "

has seen further, by standing on the shoulders of giants" thus achieving progress, and so you too are encouraged to become active, using an already established framework!