A simple algorithm to compute the linear complexity of binary sequences with period a power of 2 has been proposed. The algorithm exploits the fractal structure of the binomial representation in this kind of binary sequences. The application of the general algorithm to a particular family of cryptographic sequences (generalized sequences) improves its performance as decreases the amount of sequence to be processed.
Research partially supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación, and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project COPCIS (TIN2017-84844-C2-1-R) and by Comunidad de Madrid (Spain) under project CYNAMON (P2018/TCS-4566), also co-funded by European Union FEDER funds. The first author was supported by JAE INTRO’19.
