  Recent years have shown that more than ever governments and intelligence
agencies try to control and bypass the cryptographic means used for the
protection of data. Backdooring encryption algorithms is considered as the best
way to enforce cryptographic control. Implementation backdoors (at the
protocol/implementation/ma\-nagement level) are generally considered. In this
paper we propose to address the most critical issue of backdoors: mathematical
backdoors or by-design backdoors, which are put directly at the mathematical
design of the encryption algorithm. Considering a particular family (among all
the possible ones) of backdoors, we present BSEA-1, a stream cipher algorithm
which contains a design backdoor enabling an effective cryptanalysis. The
BSEA-1 algorithm uses a 120-bit key. The exploitation of the backdoor enables
to break the cipher with around 2 Kbits of knowplaintext in a few seconds.
