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View article: A computational approach for the study of linear complexity of shrunken sequences
A computational approach for the study of linear complexity of shrunken sequences Open
The shrinking generator is a pseudorandom bit generator based on the combination of two linear feedback shift registers of maximum period. These registers are synchronized with a common clock and produce binary sequences with good statisti…
View article: A New Representation of Binary Sequences by means of Boolean Functions
A New Representation of Binary Sequences by means of Boolean Functions Open
Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a connecti…
View article: Spread Codes from Abelian non-cyclic groups
Spread Codes from Abelian non-cyclic groups Open
Given the finite field $\mathbb{F}_{q}$, for a prime power $q$, in this paper we present a way of constructing spreads of $\mathbb{F}_{q}^{n}$. They will arise as orbits under the action of an Abelian non-cyclic group. First, we construct …
View article: Weighted Reed–Solomon convolutional codes
Weighted Reed–Solomon convolutional codes Open
In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed–Solomon block codes to…
View article: Computational Analysis of Interleaving PN-Sequences with Different Polynomials
Computational Analysis of Interleaving PN-Sequences with Different Polynomials Open
Binary PN-sequences generated by LFSRs exhibit good statistical properties; however, due to their intrinsic linearity, they are not suitable for cryptographic applications. In order to break such a linearity, several approaches can be impl…
View article: An Efficient Algorithm to Compute the Linear Complexity of Binary Sequences
An Efficient Algorithm to Compute the Linear Complexity of Binary Sequences Open
Binary sequences are algebraic structures currently used as security elements in Internet of Things devices, sensor networks, e-commerce, and cryptography. In this work, a contribution to the evaluation of such sequences is introduced. In …
View article: Randomness study of the concatenation of generalized sequences
Randomness study of the concatenation of generalized sequences Open
Keystream sequences should look as random as possible, i.e. should present no logical pattern to be exploited in cryptographic attacks. The generalized self-shrinking generator, a sequence generator based on irregular decimation, produces …
View article: Minimal State-Space Representation of Convolutional Product Codes
Minimal State-Space Representation of Convolutional Product Codes Open
In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes.…
View article: Interleaving Shifted Versions of a PN-Sequence
Interleaving Shifted Versions of a PN-Sequence Open
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 its…
View article: Weighted Reed-Solomon convolutional codes
Weighted Reed-Solomon convolutional codes Open
In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to…
View article: Randomness Analysis for GSS-sequences Concatenated
Randomness Analysis for GSS-sequences Concatenated Open
Binary sequences produced by a generator should appear as random as possible, that is, have no logical pattern to be used in cryptographic applications. In this paper, we give a detailed analysis of the randomness of a family of binary seq…
View article: Representations of Generalized Self-Shrunken Sequences
Representations of Generalized Self-Shrunken Sequences Open
Output sequences of the cryptographic pseudo-random number generator, known as the generalized self-shrinking generator, are obtained self-decimating Pseudo-Noise (PN)-sequences with shifted versions of themselves. In this paper, we presen…
View article: Randomness Analysis for the Generalized Self-Shrinking Sequences
Randomness Analysis for the Generalized Self-Shrinking Sequences Open
In cryptography, the property of randomness in pseudo-random generators is very important to avoid any pattern in output sequences, to provide security against attacks, privacy and anonymity. In this article, the randomness of the family o…