Linear solutions for cryptographic nonlinear sequence generators

This letter shows that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are pseudo-random noise sequences with application in cryptography: the sequences generated by the class of shrinking generators. Consequently, this contribution show that shrinking generators do not provide enough guarantees to be used for encryption purposes. Furthermore, the linearization is achieved through a simple algorithm about which a full description is provided

Analysis of the generalized self-shrinking generator

AbstractThis work shows that the output sequences of a well-known cryptographic generator, the so-called generalized self-shrinking generator, are particular solutions of homogeneous linear difference equations with binary coefficients. In particular, all those generated sequences are just linear combinations of primary sequences weighted by binary values. Furthermore, the complete class of solutions of these difference equations includes other balanced sequences with the same period and even greater linear complexity than that of the generalized self-shrinking sequences. Cryptographic parameters of all above mentioned sequences are here analyzed in terms of linear equation solutions. In addition, this work describes an efficient algorithm to synthesize the component primary sequences as well as to compute the linear complexity and period of any generalized self-shrinking sequence

Estudio de algunas Secuencias pseudoaleatorias de aplicación criptográfica

Sin resume

A Simple Attack on Some Clock-Controlled Generators

We present a new approach to edit distance attacks on certain clock-controlled generators, which applies basic concepts of Graph Theory to simplify the search trees of the original attacks in such a way that only the most promising branches are analyzed. In particular, the proposed improvement is based on cut sets defined on some graphs so that certain shortest paths provide the edit distances. The strongest aspects of the proposal are that the obtained results from the attack are absolutely deterministic, and that many inconsistent initial states of the target registers are recognized beforehand and avoided during search

Synthesis of Cryptographic Interleaved Sequences by means of Linear Cellular Automata

This work shows that a class of pseudorandom binary sequences, the so-called interleaved sequences, can be generated by means of linear multiplicative polynomial cellular automata. In fact, these linear automata generate all the solutions of a type of linear difference equations with binary coefficients. Interleaved sequences are just particular solutions of such equations. In this way, popular nonlinear sequence generators with cryptographic application can be linearized in terms of simple cellular automata.This work has been developed in the frame of the project HESPERIA under programme CENIT and supported by CDTI as well as by the companies: Soluziona, Unión Fenosa, Tecnobit, Visual-Tools, BrainStorm, SAC and TechnoSafe.Peer reviewe

Generation of Cryptographic Sequences by means of Difference Equations

Abstract: In the present work, it is shown that the sequences obtained from cryptographic generators based on decimation are just particular solutions of a kind of linear difference equations. Moreover, all these sequences are simple linear combinations of a class of basic sequences (binomial sequences). Cryptographic parameters of decimated sequences, e.g. period, linear complexity or balancedness, can be analyzed in terms of solutions to linear equations. In brief, difference equations are useful tools for the generation of new cryptographic sequences with application in stream ciphers

Deterministic Cryptanalysis of some Stream Ciphers

A new graph-based approach to edit distance cryptanalysis of some clock-controlled generators is here presented in order to simplify search trees of the original attacks. In particular, the proposed improve- ment is based on cut sets de¯ned on some graphs so that only the most promising branches of the search tree have to be analyzed because cer- tain shortest paths provide the edit distances. The strongest aspects of the proposal are: a) the obtained results from the attack are absolutely deterministic and b) many inconsistent initial states are recognized be- forehand and avoided during search.Peer reviewe

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

Binomial characterization of cryptographic sequences

The generalized self-shrinking generator is a sequence generator that produces binary sequences with good cryptographic properties. On the other hand, the binomial sequences are a well-defined class of sequences that can be obtained considering infinite successions of binomial coefficients modulo 2. In this work, we see that the generalized sequences can be computed as a finite binary sum of binomial sequences. Moreover, the cryptographic parameters of the generalized sequences can be studied in terms of the binomial sequences.1161980381619. International Conference on Computational Science and Its Applications2019-07-01Saint Petersbur