## Section: Partnerships and Cooperations

### Regional Initiatives

#### PEPS Aije-bitcoin

Within the group PAIP (Pour une Approche Interdisciplinaire de la Privacy), D. Augot presented the cryptographic and peer-to-peer principles at the heart of the Bitcoin protocol (electronic signature, hash functions, and so on). Most of the information is publicly available: the history of all transactions, evolution of the source code, developers' mailing lists, and the Bitcoin exchange rate. It was recognized by the economists in our group that such an amount of data is very rare for an economic phenomenon, and it was decided to start research on the history of Bitcoin, to study the interplay between the development of protocol and the development of the economical phenomenon.

The project
**Aije-Bitcoin** (analyse
informatique, juridique et economique de Bitcoin) was accepted as
interdisciplinary research for a PEPS (Projet exploratoire Premier
Soutien) cofunded by the CNRS and Universite de Paris-Saclay. This
one-year preliminary program will enable the group to master the
understanding of Bitcoin from various angles, allowing more advanced
research in the following years.

One M2 intern, E. Palazzollo, was intern in Sceaux, with aim to qualify the nature of bitcoin, as an asset, curency, etc.

This project ended in March 2016

#### IDEALCODES

Idealcodes is a two-year Digiteo research project, started in October 2014. The partners involved are the École Polytechnique (X) and the Université de Versailles–Saint-Quentin-en-Yvelines (Luca de Feo, UVSQ). After hiring J. Nielsen the first year, we have hired V. Ducet for the second year, both working at the boundary between coding theory, cryptography, and computer algebra

Idealcodes spans the three research areas of algebraic coding theory, cryptography, and computer algebra, by investigating the problem of lattice reduction (and root-finding). In algebraic coding theory this is found in Guruswami and Sudan's list decoding of algebraic geometry codes and Reed–Solomon codes. In cryptography, it is found in Coppersmith's method for finding small roots of integer equations. These topics were unified and generalised by H. Cohn and N. Heninger [25], by considering algebraic geometry codes and number field codes under the deep analogy between polynomials and integers. Sophisticated results in coding theory could be then carried over to cryptanalysis, and vice-versa. The generalized view raises problems of computing efficiently, which is one of the main research topics of Idealcodes.

The last year of the one-year project aims to find matrices with good diffusion properties over small finite fields. The principle is to find non-maximal matrices, but with better coefficients and implementation properties. The relevant cryptographic properties to be studied correspond to the weight distribution of the associated code. Since we use Algebraic-Geometry codes, much more powerful techniques can be used for computing these weight distribution, using and improving Duursma's ideas [28].

#### IRT System-X

D. Augot is co-advising a PhD candidate, H.-M. Bisserier, on “les relations contractuelles de droit privé à l'épreuve de la technologie des blockchains”, i.e. on (French) law and so-called “smart contracts”. D. Augot will mainly help H.-M. Bisserier to clarify the essential computer science topics and issues relevant to the most important blockchains (bitcoin, ethereum). Then H.-M. Bisserier will be advised by C. Zolynksi for remaining two years, fixing research directions.