It is Friday and all teaching is done for the week. Also, it has been about 10 days since the FREAK attack was made public. Hence, *the* most natural idea is to scan the Internet for hosts that are still vulnerable and mining their Ps and Qs. After all, the tools for the job are readily available. Here’s what we found.

# Google Summer of Code 2015

Both Sage and the Lmonade project were selected for Google’s Summer of Code 2015. If you are an eligible student, you should consider applying. If you need ideas what to work on, there are many fine projects/project ideas on either the Lmonade or the Sage GSoC pages. In particular, here are the fplll project ideas, for which I could be one of the two mentors.

# Sage Development with Emacs

A while back I described my (then current) setup to develop C code with Emacs. The other programming language I tend to spend a lot of time with is Python, specifically Sage’s Python. Here’s my Emacs setup for writing Sage code. For starters, it makes sense to highlight indentation in Python.

(use-package highlight-indentation :ensure t)

I use anaconda-mode for auto-completion and stuff, it runs jedi for me. In particular it offers:

- M-. Goto definition for thing at point.
- M-, Switch to buffer of most recent marker.
- M-? Show documentation for context at point.
- M-r Show usage for thing at point.

(use-package anaconda-mode :ensure t :diminish anaconda-mode :config (bind-key "M-," #'anaconda-nav-pop-marker anaconda-mode-map))

# On the concrete hardness of Learning with Errors

Together with Rachel Player and Sam Scott (both also from the Information Security Group at Royal Holloway, University of London) we finally managed to put our survey on solving the Learning with Errors problem out. Here’s the abstract:

The Learning with Errors (LWE) problem has become a central building block of modern cryptographic constructions. This work collects and presents hardness results for concrete instances of LWE. In particular, we discuss algorithms proposed in the literature and give the expected resources required to run them. We consider both generic instances of LWE as well as small secret variants. Since for several methods of solving LWE we require a lattice reduction step, we also review lattice reduction algorithms and use a refined model for estimating their running times. We also give concrete estimates for various families of LWE instances, provide a Sage module for computing these estimates and highlight gaps in the knowledge about algorithms for solving the Learning with Errors problem.

Continue reading “On the concrete hardness of Learning with Errors”

# Looking Back and Forward for Open-Source Mathematics Software (2014)

When a year ends people make lists. I can only guess that several people are currently busy with writing “The 5 most revised papers on eprint ” and “The 8 best IACR flagship conference rump session presentations of 2014”. Since all the good lists are taken, my list has to be a little bit more personal. Alas, here is my list of stuff that happened in open-source computational mathematics in 2014 around me. That is, below I list what developments happened in 2014 and try to provide an outlook for 2015 (so that I can come back in a year to notice that nothing played out as planned).

If you are interested in any of the projects below feel invited to get involved. Also, if you are student and you are interested in working on one of the (bigger) projects listed below over the summer, get in touch: we could try to turn it into a Google Summer of Code 2015 project.

Continue reading “Looking Back and Forward for Open-Source Mathematics Software (2014)”

# Sage 6.4

Sage 6.4 is out. Here are some (to me) particularly exciting changes.

# Improved Parameters and an Implementation of Graded Encoding Schemes from Ideal Lattices

Our paper (with Catalin Cocis, Fabien Laguillaumie and Adeline Langlois) on picking parameters and implementing GGHLite just hit eprint. Here’s the abstract:

We discuss how to set parameters for GGH-like graded encoding schemes approximating cryptographic multilinear maps from ideal lattices and propose a strategy which reduces parameter sizes for concrete instances. Secondly, we discuss a first software implementation of a graded encoding scheme based on GGHLite, an improved variant of Garg, Gentry and Halevi’s construction (GGH) due to Langlois, Stehlé and Steinfeld. Thirdly, we provide an implementation of non-interactive N-partite Diffie-Hellman key exchange. We discuss our implementation strategies and show that our implementation outperforms previous work.