London-ish Lattice Coding & Crypto Meeting: 26 March 2018

[Martin R. Albrecht]

Hi all,

our next meeting will take place next Monday at Imperial, details
below.

http://malb.io/discrete-subgroup/2018/01/15/lattice-meeting/

## Program ##

### 10:30 - 12:00 | [Carl
Bootland](https://www.esat.kuleuven.be/cosic/carl-bootland/):
Using non-integral bases to make better use of the plaintext
space in homomorphic encryption schemes ###

In this talk I will present an encoding method for real numbers
tailored for homomorphic function evaluation. Using a somewhat
homomorphic encryption scheme allows one to compute simple
arithmetic functions on encrypted data securely. Security
constraints in all popular somewhat homomorphic encryption schemes
necessitate the degree of the polynomial modulus to be large but
with current encoding techniques the correctness requirement
allows for much smaller values. As a result much of the plaintext
space is left unused when using these encoding techniques. Our new
generic encoding method uses expansions with respect to a
non-integral base which allows one to exploit the full extent of
the available plaintext space and reduces the growth of the
coefficients when performing operations. This leads to better
parameters and faster homomorphic function evaluation.

Joint work with Charlotte Bonte, Joppe W. Bos, Wouter Castryk,
Ilia Iliashenko, Frederik Vercauteren:

Charlotte Bonte, Carl Bootland, Joppe W. Bos, Wouter Castryck,
Ilia Iliashenko, Frederik Vercauteren, [Faster Homomorphic
Function Evaluation using Non-Integral Base
Encoding](https://eprint.iacr.org/2017/333), In Workshop on
Cryptographic Hardware and Embedded Security, Lecture Notes in
Computer Science, Springer-Verlag, pages 579–600, 2017.

### 13:00 - 14:30 | [Xiaojun
Yuan](http://sist.shanghaitech.edu.cn/faculty/yuanxj/):
Fundamental Limits of Compute-Compress-and-Forward ###

Compute-and-forward (CF) harnesses interference by exploiting
structured coding in wireless communication networks. The key idea
of CF is to compute integer combinations of codewords from
multiple source nodes, rather than to decode individual codewords
by treating others as noise. Nested lattice codes are commonly
used for efficient realization of CF. In this talk, we focus on
how to forward the computed messages at relays in a wireless relay
network. In general, these computed messages are correlated since
they are combinations of a common set of source messages. As such,
compression operations can be employed to enhance the spectral
efficiency of the network. We show that the compression can be
efficiently realized in a nested-lattice-coded network.
Specifically, we present a compute-compress-and-forward (CCF)
scheme where each relay compresses its computed message by taking
quantization and modulo (QM) lattice operations. As an
application, we explore the fundamental limits of CCF in a two-hop
relay network with a single sink node. We show that CCF with
multiple QM operations is optimal in the sense of achieving the
minimum total compression rate. We also show that CCF is able to
achieve the Slepian-Wolf rate region under certain conditions. We
further show that most of the QM-operations involved in CCF can be
realized in finite fields, so as to reduce the complexity involved
in CCF. Numerical results are demonstrated to verify the
superiority of CCF over CF.

### 15:00 - 16:30 | [Thomas
Prest](https://www.di.ens.fr/~prest/): The Rényi Divergence
and Security Proofs ###

The Rényi divergence has recently found several applications in
lattice-based cryptography, in which it often produces tighter
proofs than the more classical statistical distance. However, it
remains somewhat arcane to use because to its properties (or lack
thereof, such as symmetry and triangle inequality).

In this talk, I will review recent advances regarding the Rényi
divergence and provide an easy framework for establishing tight
proofs using it. As an illustration, I will present examples in
lattice-based cryptography for which the Rényi divergence allows
significant gains. Finally, I will discuss open problems and
potential future applications.

### 16:45 - 18:15 | [Qifu
Sun](https://www.researchgate.net/profile/Qifu_Sun): Lattice
partition based physical-layer network coding ###

Physical-layer network coding (PNC) is a means to improve the
throughput in wireless communication models. This talk will review
the study of PNC based on the algebraic structure of lattice
partitions. First, from an information-theoretical point of view,
we compare the performance of lattice partition based PNC (LNC)
with other transmission schemes such as routing, network-layer
network coding, and analog network coding in a two-way relay
network. Next, we revisit the classical algebraic framework of LNC
in a more general wireless multiple-access relay network, in which
two important research lines are the practical code design and the
optimal selection of coding coefficients. For the practical code
design, we emphasize on the LNC constructed from complex lattices
over the ring of Gaussian integers and the ring of Eisenstein
integers, and demonstrate its advantage over the LNC based on
integer lattices by illustrating some particular design instances.
For the optimal selection of coding coefficients, one main
approach is to reduce it to the shortest vector problem (SVP) of a
lattice. Though it is well known that a general SVP is NP-hard, we
summarize the recent advances in the study of SVPs for LNC in the
community, so that the particular SVPs can be efficiently solved.

### 18:30 - | Workshop Dinner ###

## Venue ##

Room 611
Department of Electrical and Electronic Engineering
[Imperial College
London](http://www.imperial.ac.uk/visit/campuses/south-kensington/)
South Kensington
London SW7 2AZ

## Registration ##

Everyone is welcome. Two caveats:

1. Speakers are told the audience is somewhat familiar with
lattices.
2. Please send us an email at <c.l...@imperial.ac.uk>, so that the
size of the room fits with the number of participants.

Cheers,
Martin
--

Please note that I am currently taking action short of a strike as
part
of the University and College Union’s (UCU) industrial action to
defend
our pension. Response times may be slower for the duration of the
dispute, especially outside of normal working hours.
Please support university staff by writing to university
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asking them to resume negotiations with UCU immediately.

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[Martin R. Albrecht]

Dang, wrong link:

it should be
http://malb.io/discrete-subgroup/2018/03/26/lattice-meeting/

Thanks, CJ, for bringing it to my attention.