Linear complexity is a much used metric of the security of any binary sequence with application in communication systems and cryptography. In this work, we propose a method of computing the linear complexity of a popular family of cryptographic sequences, the so-called generalized sequences. Such a family is generated by means of the irregular decimation of a single Pseudo Noise sequence (PN-sequence). The computation method is based on the comparison of the PN-sequence with shifted versions of itself. The concept of linear recurrence relationship and the rows of the Sierpinski triangle play a leading part in this computation.
This research has been partially supported by Ministerio de Economía, Industria y Competitividad (MINECO), Agencia Estatal de Investigación (AEI), and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project COPCIS, reference TIN2017-84844-C2-1-R, and by Comunidad de Madrid (Spain) under project CYNAMON, reference P2018/TCS-4566, also co-funded by European Union FEDER funds. Sara D. Cardell was supported by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), Brazil, and Sao Paulo Research Foundation (FAPESP), grant 2013/25977-7.
