Generation of pseudorandom binary sequences by means of linear feedback shift registers (LFSRs) with dynamic feedback

Peinado, Alberto; Fúster‐Sabater, Amparo

doi:10.1016/j.mcm.2011.07.023

Cited by 25 publications

(18 citation statements)

References 8 publications

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“…The term, w 0 ( t + n ), can be written [33,34] as a linear combination of the previous n terms, and consequently, the linear span of the sequence, w 0 , is at most n . The same reasoning applies to any of the other decimated sequences, w j , whose generic terms are defined as:

\begin{matrix} w_{j} (t) = s (t \cdot m + j), & 0 \leq j \leq (m - 1) \end{matrix}

…”

Section: An Epcg2-compliant Prng: J3genmentioning

confidence: 99%

EPCGen2 Pseudorandom Number Generators: Analysis of J3Gen

Peinado

Munilla

Fúster‐Sabater

2014

Sensors

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This paper analyzes the cryptographic security of J3Gen, a promising pseudo random number generator for low-cost passive Radio Frequency Identification (RFID) tags. Although J3Gen has been shown to fulfill the randomness criteria set by the EPCglobal Gen2 standard and is intended for security applications, we describe here two cryptanalytic attacks that question its security claims: (i) a probabilistic attack based on solving linear equation systems; and (ii) a deterministic attack based on the decimation of the output sequence. Numerical results, supported by simulations, show that for the specific recommended values of the configurable parameters, a low number of intercepted output bits are enough to break J3Gen. We then make some recommendations that address these issues.

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\begin{matrix} w_{j} (t) = s (t \cdot m + j), & 0 \leq j \leq (m - 1) \end{matrix}

…”

Section: An Epcg2-compliant Prng: J3genmentioning

confidence: 99%

EPCGen2 Pseudorandom Number Generators: Analysis of J3Gen

Peinado

Munilla

Fúster‐Sabater

2014

Sensors

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“…Most keystream generators are based on maximal-length Linear Feedback Shift Registers (LFSRs) [8] whose output sequences, the so-called m-sequences, are combined by means of nonlinear functions to produce pseudorandom sequences for cryptographic applications. Desirable properties for such sequences can be enumerated as follows: a) Long Period, b) Good statistical properties, c) Large Linear Complexity [15].…”

Section: Introductionmentioning

confidence: 99%

Recovering Decimation-Based Cryptographic Sequences by Means of Linear CAs

Cardell

Aranha

Fúster‐Sabater

2019

Logic Journal of the IGPL

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The sequences produced by the cryptographic sequence generator known as the shrinking generator can be modelled as the output sequences of linear elementary cellular automata. These sequences are composed of interleaved m-sequences produced by linear structures based on feedback shifts. This profitable characteristic can be used in the cryptanalysis of this generator. In this work we propose an algorithm that takes advantage of the inherent linearity of these cellular automata and the interleaved m-sequences. Although irregularly decimated generators have been conceived and designed as non-linear sequence generators, in practice they can be easily analysed in terms of simple linear structures.

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“…On the other hand, PRNGs can generate pseudo-random numbers depending on deterministic sources by inputting an initial seed to a given algorithm, such as the Linear Congruential Generator (LCG) [22,42], the Mersenne Twister [31], nonlinear LCG [12], Linear Feedback Shift Registers (LFSR) [40], among other numerical algorithms. The main advantage of PRNGs is their determinism (repeatability of the pseudo-random sequences), which for certain purposes is a desirable characteristic specially considering cryptography and one-way functions (hashing algorithms).…”

Section: Introductionmentioning

confidence: 99%

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

Machicao

Bruno

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a "deep-zoom" manner by using k-digits to the right from the decimal separator of a given point from the underlying chaotic map. Interesting phenomena have been identified. Rapid randomization was observed, i.e., chaotic patterns tend to become indistinguishable when compared to the original orbits of the underlying chaotic map. Our results were presented using different graphical analyses (i.e., time-evolution, bifurcation diagram, Lyapunov exponent, Poincaré diagram, and frequency distribution). Moreover, taking advantage of this randomization improvement, we propose a Pseudo-Random Number Generator (PRNG) based on the k-logistic map. The pseudo-random qualities of the proposed PRNG passed both tests successfully, i.e., DIEHARD and NIST, and were comparable with other traditional PRNGs such as the Mersenne Twister. The results suggest that simple maps such as the logistic map can be considered as good PRNG methods.

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Generation of pseudorandom binary sequences by means of linear feedback shift registers (LFSRs) with dynamic feedback

Cited by 25 publications

References 8 publications

EPCGen2 Pseudorandom Number Generators: Analysis of J3Gen

EPCGen2 Pseudorandom Number Generators: Analysis of J3Gen

Recovering Decimation-Based Cryptographic Sequences by Means of Linear CAs

Improving the pseudo-randomness properties of chaotic maps using deep-zoom

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