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.