You can download the complete text of my dissertation in pdf format. Warning: the text is in French.

My Ph.D. defence was held on Thursday, 10th November 2005. The members of the committee were:

• Tor Helleseth, referee, professor, University of Bergen
• Matt Robshaw, referee, senior security expert, France Telecom R&D
• Daniel Lazard, professor emeritus, University Paris 6
• Antoine Joux, DGA and associate professor, University of Versailles Saint Quentin-en-Yvelines
• Didier Alquié, DGA
• Anne Canteaut, advisor, researcher, INRIA-Rocquencourt
• Pascale Charpin, advisor, senior researcher, INRIA-Rocquencourt

Summary:

The work done during my thesis concerns two different aspects of the security of secret key ciphers. The first part is devoted to the study of the security of iterated block ciphers against last round attacks based on distinguishers. The results especially concern a generalisation of a higher order differential attack that was lead against MISTY1 algorithm. The origin of this attack and of its generalisation has been explained thanks to the properties of the Walsh spectra of the highly nonlinear functions used in the cipher. Hence, it has been possible to mount a generic attack against all Feistel ciphers using confusion functions whose Walsh spectra are divisible by a high power of 2. Indeed, this property leads to an upper bound for the degree of the composition of such functions which can be noticeably smaller than the trivial bound. Thus the attack we have mounted leads to a new security criterion for iterated block ciphers which lies on the divisibility of the Walsh spectra of the round functions. The second part of my work is a study of cryptographic properties of symmetric Boolean functions. Starting from a structural property of one representation of symmetric Boolean functions, we improve existing results concerning algebraic degree, balance, resiliency, propagation criterion and nonlinearity of such functions. Besides, we compute explicitly the Walsh spectra of all symmetric Boolean functions of degree 2 and 3. We also determine all the balance symmetric Boolean functions of degree less than or equal to 7, for all number of variables.