Master Thesis
Security proofs for code-based cryptosystems
For one student
Domain
Cryptography and coding theory
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.
To prove the security of cryptographic protocols, we may use a reduction using random oracles.
Such reduction are widely proposed for number theory based scheme but they are rare for code- based cryptosystems. Some reduction already exists but they are not tight.
Purpose
After a state of the art of code-based cryptosystems and the construction of security proof in the random oracle and/or in the standard model, the student will have to propose a security proof of a code-based signature scheme and/or to signicantly improve an existing reduction like Courtois Finiasz and Sendrier signature scheme, McEliece cryptosystem or schemes combining dierent code-based schemes.
He will also have to write an article on his research in a LATEX format and give an english presentation to the team.
Goals
The outcome of the thesis is supposed to be a publishable result on provably secure code-based scheme.
Required Skills
The required skills, in order of importance, are:
High motivation and creativity;
Good knowledge of cryptographic constructions;
Experience with reading research papers.
Knowledge of the English language goes without saying.
Bibliography
[1] - L. Dallot : Towards a Concrete Security Proof of Courtois, Finiasz and Sendrier Signature Scheme, WEWoRC 2007.
[2] - P.-L. Cayrel, P.Gaborit, D. Galindo and M. Girault : Identity-based identication and signature schemes using error-correcting codes, preprint.
Institute
CASED : www.cased.de
Place : Darmstadt, Germany (4h30 from Paris by train)
Team : Cryptographic primitives
Master thesis supervisors : Dr. Pierre-Louis Cayrel and Markus Rückert 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: pierre-louis.cayrel@cased.de
e-mail laboratory director: buchmann@cdc.informatik.tu-darmstadt.de
web : http://www.cayrel.net/
