Abstract : This thesis investigates the problem of reverse-engineering a classical transmission scheme from an eavesdropped noisy communication. The two main parts of this work are successively focus on the reconstruction of the two main elements in the scheme: the scrambler and the error correcting code, in the order they have to be treated by an attacker, i.e. in the reverse order to that in which they appear in the transmission scheme.
The first part deals with the reconstruction of a binary linear code
from the knowledge of noisy codewords. First, we present and analyse an algorithm due to A. Valembois. The analysis leads us to a new statistical test for finding words that may belong to the dual of the error correcting code used during the transmission. Then, we present a new decoding algorithm based on classical techniques of iterative decoding. This algorithm enables us to correct some errors even if some parity check equations are not valid. Using this decoding algorithm, we then describe a new algorithm for
reconstructing a linear code.
The second part deals with the reconstruction of a linear scrambler. First, we assume that the attacker knows the exact output of the scrambler. We present different techniques for reconstructing a synchronous scrambler and a self-synchronized scrambler, depending on the assumptions we make on the input stream. Then, we are interested in the general case and we present an algebraic technique for reconstructing a synchronous scrambler when a part
of the input sequence is known but when we only know the image of the output sequence by a linear transformation per block.