Hash functions based on the syndrome decoding problem

Hash functions based on the syndrome decoding problem

For one student Domain

Cryptography and coding theory

Presentation

In cryptography, the Fast Syndrome-based hash Functions (FSB) are a family of cryptographic hash functions introduced in 2003 by Daniel Augot, Matthieu Finiasz, and Nicolas Sendrier. Unlike most other cryptographic hash functions in use today, FSB can to a certain extent be proven to be secure. More exactly, it can be proven that breaking FSB is at least as dicult as solving a certain NP-complete problem known as Regular Syndrome Decoding. We call function with these properties provably secure. Though it is not known whether NP-complete problems are solvable in polynomial time, it is often assumed that they are not. Several versions of FSB have been proposed, the latest of which was submitted to the SHA-3 cryptography competition but was rejected in the rst round. Though all versions of FSB claim provable security, some preliminary versions were eventually broken. The design of the latest version of FSB has however taken this attack into account and remains secure to all currently known attacks. As usual, provably security does come at a cost. FSB is slower than traditional hash functions and uses quite a lot of memory, which makes it impractical on memory constrained environments. Furthermore, the compression function used in FSB needs a large output size to guarantee security.

Recently, Bernstein et al. introduces a new design for FSB which permits to reach the speed of 2 of the 5 SHA-3 nalists.

Purpose

The purpose of the thesis is to understand the recent improvements in the design of hash functions based on the syndrome decoding problem and design/implement an improved code- based stream cipher.

The students will have to write an article on his research in a L

TEX format and give an English presentation to the team.

Goals

The outcome of the thesis is supposed to be a publishable result on code-based secret key cryp- tosystem.

Required Skills

The required skills, in order of importance, are:

ˆ High motivation and creativity;

ˆ Some experience in L

TEX;

ˆ Skills in C, Java, (CUDA would be better);

ˆ Good knowledge of cryptographic constructions;

ˆ Experience with reading research papers.

Knowledge of the English language goes without saying.

Bibliography

[1] - 2008. Daniel Augot, Matthieu Finiasz, Philippe Gaborit, Stéphane Manuel, and Nicolas Sendrier. "SHA-3 proposal: FSB", Submission to the SHA3 NIST competition, 2008

[2] - 2011. Daniel J. Bernstein, Tanja Lange, Christiane Peters and Peter Schwabe. "Really fast syndrome-based hashing"

[3] - 2007. Eli Biham and Orr Dunkelman. "A Framework for Iterative Hash Functions HAIFA"

Institute

Laboratoire Hubert Curien : http://laboratoirehubertcurien.fr/spip.php?rubrique29

Place : Saint-Etienne - France

Team : Applied Cryptography and Telecom

Thesis supervisor : Pierre-Louis Cayrel (Maître de conférences)

Contact

If you are interested, please contact Pierre-Louis Cayrel Laboratoire Hubert Curien, UMR CNRS 5516

Bâtiment F 18 rue du professeur Benoît Lauras 42000 Saint-Etienne France

Phone: 0033-4 77 91 57 94

e-mail supervisor: pierre.louis.cayrel@univ-st-etienne.fr

web : http://www.cayrel.net/