Quasi-dyadic constructions of code-based cryptosytems

Master Thesis

Quasi-dyadic constructions of code-based cryptosytems

For one student

Domain

Cryptography, coding theory and key-size reduction

Presentation

Most of the cryptographic schemes used and studied today are based on number theory problems as factorisation or discrete logarithm. In 1994, Shor proposed an algorithm which can factorise in polynomial time using a quantum computer. So RSA and several others schemes are threatened by the quantum computer.

Code-based cryptography is one of the branches of post-quantum cryptography with lattice- based, multivariate-based and hash-based cryptography. Schemes based on problems as syndrome decoding or decoding random codes are well studied for years and there doesn't exist polynomial time algorithm to solve those problems even in a post quantum world. McEliece was the rst to propose a code-based cryptosystem and several improvements and derivation have been proposed so far.

An important problem in code-based cryptography is the size of the public key. In order to reduce this size, several constructions have been proposed and most of them are broken (generally due to their structure). Recently, a family of codes, the quasi-dyadic codes have been proposed in order to reduce this size. Up to date, there is no structural attack against such a construction for codes dened over F

.

Purpose

In code-based cryptography there is essentially two kinds of attacks against a scheme, the decoding one (decode directly) and the structural one (use the structure to nd the secret key).

After a state of the art of possibilities to reduce the public key size of the McEliece scheme and all the dierent structural attacks against such schemes. The purpose of this thesis is to study how can we adapt existing attacks to this kind of construction and/or can we use quasi-dyadic codes to improve some code-based cryptosystems as the hash function FSB or the stream cipher SYND.

The student could compare the quasi-cyclic construction to the quasi-dyadic one and their security faces structural attacks.

The student 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 quasi-dyadic constructions in code-based cryptography.

Required Skills

The required skills, in order of importance, are:

ˆ High motivation and creativity;

ˆ Skills in C;

ˆ Good knowledge of cryptographic constructions;

ˆ Experience with reading research papers.

Knowledge of the English language goes without saying.

Bibliography

[1] - R. Misoczki and P. S. L. M. Barreto Compact McEliece Keys from Goppa Codes Cryptology ePrint Archive, Report 2009/187, 2009.

[2] - D. Augot, M. Finiasz, P. Gaborit, S. Manuel, and N. Sendrier. Sha-3 proposal : FSB.

Submission to the SHA3 NIST competition, 2008.

Institute

CASED : www.cased.de

Place : Darmstadt, Germany (4h30 from Paris by train)

Team : Cryptographic primitives

Master thesis supervisors : Dr. Pierre-Louis Cayrel and Robert Niebuhr Laboratory director : Pr. Johannes Buchmann

Contact

If you are interested, please contact Dr. Pierre-Louis Cayrel (french speaker) CASED : Center for Advanced Security Research Darmstadt

Mornewegstrasse, 32 64293 Darmstadt Germany

Phone: 0049-6151-16-64821

e-mail supervisor: [email protected]

e-mail laboratory director: [email protected]

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