Master Thesis Code-based cryptanalysis of lattice-based constructions

Master Thesis

Code-based cryptanalysis of lattice-based constructions

For one student

Domain

Cryptography, coding theory and lattice-based cryptography

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.

Lattice-based and code-based cryptography have a lot in common, and the use of code-based tools to attack lattice-based constructions seems quite obvious but never deeply studied so far.

Purpose

After a state of the art of code-based attacks and lattice-based constructionss the student will search how to apply theese attacks to some 'famous' lattice-based schemes like NTRU or SWIFFTX.

Both practical and theoretical, this thesis proposes to study the code-based attacks and how to apply them against lattice-based schemes. An implementation on GPU or CPU of a practical attack against a scheme would be appreciate.

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

TEX format and give an english presentation to the team. With specialists in both areas, the student could work with dierent teams and improve his background in the two areas.

Goals

The outcome of the thesis is supposed to be a publishable result on cryptanalysis of a lattice-based

scheme.

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] - D. J. Bernstein, T. Lange and C. Peters : Attacking and defending the McEliece cryptosystem, Post-Quantum Cryptography Workshop, PQCrypto'2008,

[2] - A. Canteaut and F. Chabaud : A new algorithm for nding minimum-weight words in a linear code : application to primitive narrow-sense BCH-codes of length 511, IEEE Transactions on Information Theory, vol 44, number 1, 1998

Institute

CASED : www.cased.de

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

Team : Cryptographic primitives

Master thesis supervisors : Dr. Pierre-Louis Cayrel and Richard Lindner 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/