Linearity in decimation-based generators: an improved cryptanalysis on the shrinking generator

Cardell, Sara D.; Fúster‐Sabater, Amparo; Ranea, Adrián

doi:10.1515/math-2018-0058

Cited by 9 publications

(3 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [18], the authors determined how to compute the shifts of the interleaved sequences that compose the shrunken sequence. This fact can be used advantageously to design cryptanalytic attacks against this generator [18,[21][22][23][24]. A natural way to deal with this vulnerability is to alter the shifts or interleave PN-sequences of different primitive polynomials.…”

Section: Introductionmentioning

confidence: 99%

Interleaving Shifted Versions of a PN-Sequence

Cardell¹,

Fúster‐Sabater

Requena

2021

Mathematics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Interleaving Shifted Versions of a PN-Sequence

Cardell¹,

Fúster‐Sabater

Requena

2021

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The analogue of n-fold interleaving for finite codes is referred to by coding theorists as block interleaving of depth n. Decimation and interleaving operators together have been considered both in cryptography and cryptanalysis, cf. Rueppel [39] and Cardell et al [10]. Since methods of encoding and decoding can be viewed as dynamical processes, it is of interest to view these operations in a dynamical context.…”

Section: Introductionmentioning

confidence: 99%

Decimation and Interleaving Operations in One-Sided Symbolic Dynamics

Abram¹,

Lagarias²,

Slonim³

2020

Preprint

View full text Add to dashboard Cite

This paper studies subsets of one-sided shift spaces on a finite alphabet. Such subsets arise in symbolic dynamics, in fractal constructions, and in number theory. We study a family of decimation operations, which extract subsequences of symbol sequences in infinite arithmetic progressions, and show they are closed under composition. We also study a family of n-ary interleaving operations, one for each n ≥ 1. Given subsets X0, X1, ..., Xn−1 of the shift space, the n-ary interleaving operator produces a set whose elements combine individual elements xi, one from each Xi, by interleaving their symbol sequences cyclically in arithmetic progressions (mod n). We determine algebraic relations between decimation and interleaving operators and the shift operator. We study set-theoretic n-fold closure operations X → X [n] , which interleave decimations of X of modulus level n. A set is n-factorizable if X = X [n] . The n-fold interleaving operators are closed under composition and are idempotent. To each X we assign the set N (X) of all values n ≥ 1 for which X = X [n] . We characterize the possible sets N (X) as nonempty sets of positive integers that form a distributive lattice under the divisibility partial order and are downward closed under divisibility. We show that all sets of this type occur. We introduce a class of weakly shift-stable sets and show that this class is closed under all decimation, interleaving, and shift operations. This class includes all shift-invariant sets. We study two notions of entropy for subsets of the full one-sided shift and show that they coincide for weakly shift-stable X, but can be different in general. We give a formula for entropy of interleavings of weakly shift-stable sets in terms of individual entropies.

show abstract

“…Among the different examples of decimation-based generators we can enumerate: (1) the shrinking generator [23] with two LFSRs for a mutual decimation, (2) the self-shrinking generator [24] with just one LFSR that decimates itself and (3) the generalized self-shrinking generator [25] that outputs a family of pseudo-random sequences, the so-called generalized self-shrunken sequences (GSS-sequences). Different cryptanalytic attacks against the previous generators can be found in the literature [26][27][28][29][30].…”

mentioning

confidence: 99%

Review of the Lineal Complexity Calculation through Binomial Decomposition-Based Algorithms

Martín-Navarro

Fúster‐Sabater

2021

Mathematics

Self Cite

View full text Add to dashboard Cite

The ubiquity of smart devices and IoT are the main forces behind the development of cryptographic primitives that preserve the security of this devices, with the resources constraints they face. In this sense, the development of lightweight cryptographic algorithms, where PRNGs are an essential part of them, provides security to all these interconnected devices. In this work, a family of sequence generators with hard characteristics to be analyzed by standard methods is described. Moreover, we introduce an innovative technique for sequence decomposition that allows one to extract useful information on the sequences under study. In addition, diverse algorithms to evaluate the strength of such binary sequences have been introduced and analyzed to show which performs better.

show abstract

Linearity in decimation-based generators: an improved cryptanalysis on the shrinking generator

Cited by 9 publications

References 24 publications

Interleaving Shifted Versions of a PN-Sequence

Interleaving Shifted Versions of a PN-Sequence

Decimation and Interleaving Operations in One-Sided Symbolic Dynamics

Review of the Lineal Complexity Calculation through Binomial Decomposition-Based Algorithms

Contact Info

Product

Resources

About