This thesis is dedicated to the study of cryptographic objects
connected with combinatorics and coding theory. We especially focus on the
public-key systems relying on the hardness of finding a minimum-weight
word in any linear code, and on the correlation-immune and resilient
functions which are essential tools to the generation of pseudo-random
sequences and to the conception of conventional cryptographic
We develop a probabilistic algorithm for finding low-weight words in a large linear code which improves all the previously known attacks on the cryptosystems using low-weight codewords. Studying its complexity with the Markov chain theory notably shows that McEliece's cipher with its original parameters does usually not provide a sufficient security-level. This algorithm also enables us to determine the minimum distance of some BCH codes of length 511.
On the other hand we generalize the notions of correlation-immune and resilient functions to the functions defined on any finite alphabet and we characterize these properties in different ways. We then point out the existence of a trade-off between the degree of the algebraic normal form and the correlation-immunity order of any function defined on a finite field and we construct some infinite families of t-resilient functions with optimal degree. This result implies a new security criterion for conventional cryptographic primitives, which enriches the concept of multipermutation introduced by Schnorr and Vaudenay. We finally develop a general construction which provides new resilient functions with a great number of variables.