Interleaving Shifted Versions of a PN-Sequence

The output sequence of the shrinking generator can be considered as an interleaving of determined shifted versions of a single PN -sequence. In this paper, we present a study of the interleaving of a PN-sequence and shifted versions of itself. We analyze some important cryptographic properties as the period and the linear complexity in terms of the shifts. Furthermore, we determine the total number of the interleaving sequences that achieve each possible value of the linear complexity.This research is 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. It is also supported by Comunidad de Madrid (Spain) under project CYNAMON (P2018/TCS-4566), co-funded by FSE and European Union FEDER funds. Finally, the third author is partially supported by Spanish grant VIGROB-287 of the Universitat d’Alacant

New Attack Strategy for the Shrinking Generator

ACM Classification: E.3 (Data Encryption), B.6.1 (Design Styles)This work shows that the cryptanalysis of the shrinking generator requires fewer intercepted bits than that indicated by the linear complexity. Indeed, whereas the linear complexity of shrunken sequences is between A ⋅ 2(S-2) and A ⋅ 2(S-1), we claim that the initial states of both component registers are easily computed with less than A ⋅ S shrunken bits. Such a result is proven thanks to the definition of shrunken sequences as interleaved sequences. Consequently, it is conjectured that this statement can be extended to all interleaved sequences. Furthermore, this paper confirms that certain bits of the interleaved sequences have a greater strategic importance than others, which may be considered as a proof of weakness of interleaved generators.This research has been supported by the Spanish Ministry of Science and Innovation under Project TIN2008-02236/TSI, and developed in the frame of the project HESPERIA (www.proyectohesperia. org) under program CENIT supported by Centro para el Desarrollo Tecnológico Industrial (CDTI) and the companies: Soluziona, Unión Fenosa, Tecnobit, Visual-Tools, BrainStorm, SAC and TechnoSafe.Peer reviewe