London-ish Lattice & Coding Meeting: 10 May 2017 – Titles & Abstracts

[Martin R. Albrecht]

Hi all,

we now have finalised the programme:

## 10:30 - 12:00 | Robert Fischer: Lattice Reduction and
Factorization for Equalization

In digital communications, signal constellations are usually drawn
from a regular grid. Consequently, the mathematical tool of
lattices is of great interest. Since more than one decade,
equalization schemes based on the principle of lattice reduction,
i.e., the selection of a suited basis, in which the equalization
is carried out, are known to achieve the optimum diversity order
with very low complexity. Recently, in the field of relaying,
integer-forcing schemes have been proposed. Both approaches are
tightly related to each other.

In the talk, an introduction to the concepts of
lattice-reduction-aided and integer-forcing equalization is given.
The respective mathematical background is studied and an overview
on the different criteria and algorithms for solving the
respective factorization problem is given.

## 13:00 - 14:30 | Alexander May: Recent Advances in Decoding
Random Binary Linear Codes – and Their Implications to Crypto

This survey talk gives an overview of algorithms for decoding
random linear codes. We start with Pranges information set
decoding and Stern's meet-in-the-middle technique, and building on
these algorithms we explain recent advances by May, Meurer, Thomae
(Asiacrypt 2011), Becker, Joux, May, Meurer (Eurocrypt 2012) and
May, Ozerov (Eurocrypt 2015) that led to significant improvements
in the run time exponent. Moreover, we discuss implications for
choosing cryptographic keys in code-based cryptography, also in
the quantum setting.

## 15:00 - 16:30 | Joseph Jean Boutros: Construction-A Lattices
with Number Fields

Lattices are discrete sets of points in real or complex Euclidean
spaces with a group structure. Lattices are an important tool for
information processing in many areas such as cryptography, vector
quantization, and channel coding. The recent success of building
high-dimensional fast-decodable lattices from non-binary codes
motivated us to investigate methods for building full-diversity
lattices via Construction A (Leech & Sloane 1971). On the Gaussian
channel, in absence of fading, low-density lattices from
Construction A (LDA) can achieve Shannon capacity under lattice
decoding (di Pietro 2014). Generalized low-density (GLD) lattices
and LDA lattices are built from an error-correcting code over a
finite field which is embedded and shifted in all directions in
the Euclidean space to create a discrete group structure. Under
iterative decoding, the finite field size is selected large enough
to guarantee that the LDA/GLD lattice is not perturbed by its
integer cubic sub-lattice. In presence of fading, cubic integer
lattices are replaced by lattices from number fields. The LDA/GLD
lattice for diversity forms a partition chain starting with the
lattice from the ring of integers in the number field and ending
with a lattice from an ideal in the ring of integers. The lattice
diversity order is directly related to the signature of the number
field. For fields of degree two and above, we show how to select
the number field and the ideal for Construction A in order to make
lattices that are good for both Gaussian and fading channels.

## 16:45 - 18:15 | Thomas Johansson: Combinatorial Methods for
Solving LWE

This survey talk gives an overview of combinatorial algorithms for
solving the learning with errors (LWE) problem. We will discuss
various problem instances of interest and then overview the BKW
algorithm. We will present various improvements to BKW, including
lazy modulus switching and coded-BKW (Albrecht, Faugère,
Fitzpatrick, Perret, PKC 2014; Kirchner Fouque, Crypto 2015; Guo,
Johansson, Stankovski, Crypto 2015).

# URL

http://malb.io/discrete-subgroup/2017/05/10/

# Venue

MPEB 1.20
UCL
Department of Computer Science
Gower St
Kings Cross
London WC1E 6BT

## Directions

Follow directions at http://www.cs.ucl.ac.uk/getting_here/ but go
to 1st floor instead of 5th floor.

# Registration

Everyone is welcome. Two caveats:

1. Speakers are told the audience is somewhat familiar with
lattices.

2. Please send us an email at
<martin....@royalholloway.ac.uk>, so that the size of the
room fits with the number of participants.

Best,
Cong Ling and Martin Albrecht
--

_pgp: https://keybase.io/martinralbrecht
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_jab: martinr...@jabber.ccc.de
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