Amparo Fúster-Sabater - Academia.edu (original) (raw)

Papers by Amparo Fúster-Sabater

Open Mathematics, 2018

Decimation-based sequence generators are a class of non-linear cryptographic generators designed ... more Decimation-based sequence generators are a class of non-linear cryptographic generators designed to be used in hardware implementations. An inherent characteristic of such generators is that their output sequences are interleaved sequences. This pro table characteristic can be used in the cryptanalysis of those generators. In this work, emphasis is on the most representative decimation-based generator, the shrinking generator, which has been cryptanalyzed just by solving linear equation systems. Compared with previous cryptanalysis, computational complexity and intercepted sequence requirements are dramatically reduced. Although irregularly decimated generators have been conceived and designed as non-linear sequence generators, in practice they can be easily analyzed in terms of simple linear structures.

Logic Journal of the IGPL, Feb 18, 2022

Advances in intelligent systems and computing, Apr 28, 2019

The generalized self-shrinking generator (or generalized generator) produces binary sequences (ge... more The generalized self-shrinking generator (or generalized generator) produces binary sequences (generalized sequences) with good cryptographic properties. On the other hand, the binomial sequences can be obtained considering infinite successions of binomial coefficients modulo 2. It is possible to see that the generalized sequences can be computed as a finite binary sum of binomial sequences. Besides, the cryptographic parameters of the generalized sequences can be studied in terms of the binomial sequences.

This book offers a broad survey of all information made public - from 1993 until today - on keyst... more This book offers a broad survey of all information made public - from 1993 until today - on keystream sequence generators based on irregular decimation, which are referred to as shrinking generators. Starting with an overview of cryptography, it describes each type of generator - shrinking, self-shrinking, modified self-shrinking, generalized self-shrinking and the DECIM algorithm - with examples and references. Further, the book discusses several attacks on these generators and applications. It concludes by demonstrating how the output sequences can be modeled by means of different families of one-dimensional cellular automata, rendering the generators vulnerable to attacks. Intended for researchers and graduate students, the book will hopefully inspire them to search for more details on this family of generators and to address the open problems in this field.

Lecture Notes in Computer Science, 2016

The modified self-shrinking generator is a non-linear cryptographic sequence generator designed t... more The modified self-shrinking generator is a non-linear cryptographic sequence generator designed to be used in hardware implementations. In this work, the output sequence of such a generator is obtained as one of the output sequences of a linear model based on Cellular Automata. Although irregularly decimated generators have been conceived and designed as non-linear sequence generators, in practice they can be easy modelled in terms of simple linear structures.

Lecture Notes in Computer Science, 2018

In this work, we present a method of computing the linear complexity of the sequences produced by... more In this work, we present a method of computing the linear complexity of the sequences produced by the cryptographic sequence generator known as generalized self-shrinking generator. This approach is based on the comparison of different shifted versions of a single PN-sequence. Just the analysis of binary digits in these shifted sequences allows one to determine the linear complexity of those generalized sequences. The method is simple, direct and efficient. Furthermore, the concept of linear recurrence relationship and the rows of the Sierpinski’s triangle are the basic tools in this computation.

SpringerBriefs in Mathematics, 2019

In this chapter, we study the definition and the principal characteristics of the main keystream ... more In this chapter, we study the definition and the principal characteristics of the main keystream generators based on irregular decimation: the shrinking generator, the self-shrinking generator, the modified self-shrinking generator and the generalized self-shrinking generator.

J. Cell. Autom., 2016

The self-shrinking generator is a non-linear cryptographic sequence generator designed to be used... more The self-shrinking generator is a non-linear cryptographic sequence generator designed to be used in stream cipher applications. In this work, its output sequence, the self-shrunken sequence, is computed as one of the output sequences of a linear model based on Cellular Automata. Such Automata are uniform, null, one-dimensional and use rules 102 or 60 for their computations. The linearity of these structures can be advantageous exploited to recover the complete selfshrunken sequence from a number of intercepted bits. Indeed, a Cellular Automata-based reconstruction procedure that is deterministic, does not need the knowledge of the LFSR characteristic polynomial and is performed exclusively by means of XOR operations has been proposed. © 2016 Old City Publishing, Inc.1119521

Computational Science and Its Applications – ICCSA 2017, 2017

Different binary sequence generators produce sequences whose period is a power of 2. Although the... more Different binary sequence generators produce sequences whose period is a power of 2. Although these sequences exhibit good cryptographic properties, in this work it is proved that such sequences can be obtained as output sequences from simple linear structures. More precisely, every one of these sequences is a particular solution of a linear difference equation with binary coefficients. This fact allows one to analyze the structural properties of the sequences with such a period from the point of view of the linear difference equations. In addition, a new application of the Pascal’s triangle to the cryptographic sequences has been introduced. In fact, it is shown that all these binary sequences can be obtained by XORing a finite number of binomial sequences that correspond to the diagonals of the Pascal’s triangle reduced modulo 2.

Computational Science and Its Applications – ICCSA 2021, 2021

SpringerBriefs in Mathematics, 2019

The irregular decimation was introduced to break the linearity of the PN-sequences. However, in t... more The irregular decimation was introduced to break the linearity of the PN-sequences. However, in this chapter we will see that there exist linear structures that describe the behaviour of the shrinking generators, designed as non-linear. The inherent linearity of these structures can be used to cryptanalyse such generators as described in Chap. 4.

Finite Fields and Their Applications, 2017

Lecture Notes in Computer Science, 2015

Logic Journal of IGPL, 2016

Mathematical and Computer Modelling, 2013

In 2002, Mita et al. [1] proposed a pseudorandom bit generator based on a dynamic linear feedback... more In 2002, Mita et al. [1] proposed a pseudorandom bit generator based on a dynamic linear feedback shift register (DLFSR) for cryptographic application. The particular topology there proposed is now analyzed, allowing us to extend the results to more general cases. Maximum period and linear span values are obtained for the generated sequences, while several estimations for autocorrelation and cross-correlation of such sequences are also presented. Furthermore, the sequences produced by DLFSRs can be considered as interleaved sequences. This fact allows us to apply the general interleaved sequence model proposed by Gong and consequently simplify their study. Finally, several remarks are stated regarding DLFSR utilization for cryptographic or code division multiple access (CDMA) applications.

Lecture notes in networks and systems, Dec 31, 2022

Acta Applicandae Mathematicae, Aug 15, 2006

In this work, pseudorandom sequence generators based on finite fields have been analyzed from the... more In this work, pseudorandom sequence generators based on finite fields have been analyzed from the point of view of their cryptographic application. In fact, a class of nonlinear sequence generators has been modelled in terms of linear cellular automata. The algorithm that converts the given generator into a linear model based on automata is very simple and is based on the concatenation of a basic structure. Once the generator has been linearized, a cryptanalytic attack that exploits the weaknesses of such a model has been developed. Linear cellular structures easily model sequence generators with application in stream cipher cryptography.

Open Mathematics, 2018

Decimation-based sequence generators are a class of non-linear cryptographic generators designed ... more Decimation-based sequence generators are a class of non-linear cryptographic generators designed to be used in hardware implementations. An inherent characteristic of such generators is that their output sequences are interleaved sequences. This pro table characteristic can be used in the cryptanalysis of those generators. In this work, emphasis is on the most representative decimation-based generator, the shrinking generator, which has been cryptanalyzed just by solving linear equation systems. Compared with previous cryptanalysis, computational complexity and intercepted sequence requirements are dramatically reduced. Although irregularly decimated generators have been conceived and designed as non-linear sequence generators, in practice they can be easily analyzed in terms of simple linear structures.

Logic Journal of the IGPL, Feb 18, 2022

Advances in intelligent systems and computing, Apr 28, 2019

The generalized self-shrinking generator (or generalized generator) produces binary sequences (ge... more The generalized self-shrinking generator (or generalized generator) produces binary sequences (generalized sequences) with good cryptographic properties. On the other hand, the binomial sequences can be obtained considering infinite successions of binomial coefficients modulo 2. It is possible to see that the generalized sequences can be computed as a finite binary sum of binomial sequences. Besides, the cryptographic parameters of the generalized sequences can be studied in terms of the binomial sequences.

This book offers a broad survey of all information made public - from 1993 until today - on keyst... more This book offers a broad survey of all information made public - from 1993 until today - on keystream sequence generators based on irregular decimation, which are referred to as shrinking generators. Starting with an overview of cryptography, it describes each type of generator - shrinking, self-shrinking, modified self-shrinking, generalized self-shrinking and the DECIM algorithm - with examples and references. Further, the book discusses several attacks on these generators and applications. It concludes by demonstrating how the output sequences can be modeled by means of different families of one-dimensional cellular automata, rendering the generators vulnerable to attacks. Intended for researchers and graduate students, the book will hopefully inspire them to search for more details on this family of generators and to address the open problems in this field.

Lecture Notes in Computer Science, 2016

The modified self-shrinking generator is a non-linear cryptographic sequence generator designed t... more The modified self-shrinking generator is a non-linear cryptographic sequence generator designed to be used in hardware implementations. In this work, the output sequence of such a generator is obtained as one of the output sequences of a linear model based on Cellular Automata. Although irregularly decimated generators have been conceived and designed as non-linear sequence generators, in practice they can be easy modelled in terms of simple linear structures.

Lecture Notes in Computer Science, 2018

In this work, we present a method of computing the linear complexity of the sequences produced by... more In this work, we present a method of computing the linear complexity of the sequences produced by the cryptographic sequence generator known as generalized self-shrinking generator. This approach is based on the comparison of different shifted versions of a single PN-sequence. Just the analysis of binary digits in these shifted sequences allows one to determine the linear complexity of those generalized sequences. The method is simple, direct and efficient. Furthermore, the concept of linear recurrence relationship and the rows of the Sierpinski’s triangle are the basic tools in this computation.

SpringerBriefs in Mathematics, 2019

In this chapter, we study the definition and the principal characteristics of the main keystream ... more In this chapter, we study the definition and the principal characteristics of the main keystream generators based on irregular decimation: the shrinking generator, the self-shrinking generator, the modified self-shrinking generator and the generalized self-shrinking generator.

J. Cell. Autom., 2016

The self-shrinking generator is a non-linear cryptographic sequence generator designed to be used... more The self-shrinking generator is a non-linear cryptographic sequence generator designed to be used in stream cipher applications. In this work, its output sequence, the self-shrunken sequence, is computed as one of the output sequences of a linear model based on Cellular Automata. Such Automata are uniform, null, one-dimensional and use rules 102 or 60 for their computations. The linearity of these structures can be advantageous exploited to recover the complete selfshrunken sequence from a number of intercepted bits. Indeed, a Cellular Automata-based reconstruction procedure that is deterministic, does not need the knowledge of the LFSR characteristic polynomial and is performed exclusively by means of XOR operations has been proposed. © 2016 Old City Publishing, Inc.1119521

Computational Science and Its Applications – ICCSA 2017, 2017

Different binary sequence generators produce sequences whose period is a power of 2. Although the... more Different binary sequence generators produce sequences whose period is a power of 2. Although these sequences exhibit good cryptographic properties, in this work it is proved that such sequences can be obtained as output sequences from simple linear structures. More precisely, every one of these sequences is a particular solution of a linear difference equation with binary coefficients. This fact allows one to analyze the structural properties of the sequences with such a period from the point of view of the linear difference equations. In addition, a new application of the Pascal’s triangle to the cryptographic sequences has been introduced. In fact, it is shown that all these binary sequences can be obtained by XORing a finite number of binomial sequences that correspond to the diagonals of the Pascal’s triangle reduced modulo 2.

Computational Science and Its Applications – ICCSA 2021, 2021

SpringerBriefs in Mathematics, 2019

The irregular decimation was introduced to break the linearity of the PN-sequences. However, in t... more The irregular decimation was introduced to break the linearity of the PN-sequences. However, in this chapter we will see that there exist linear structures that describe the behaviour of the shrinking generators, designed as non-linear. The inherent linearity of these structures can be used to cryptanalyse such generators as described in Chap. 4.

Finite Fields and Their Applications, 2017

Lecture Notes in Computer Science, 2015

Logic Journal of IGPL, 2016

Mathematical and Computer Modelling, 2013

In 2002, Mita et al. [1] proposed a pseudorandom bit generator based on a dynamic linear feedback... more In 2002, Mita et al. [1] proposed a pseudorandom bit generator based on a dynamic linear feedback shift register (DLFSR) for cryptographic application. The particular topology there proposed is now analyzed, allowing us to extend the results to more general cases. Maximum period and linear span values are obtained for the generated sequences, while several estimations for autocorrelation and cross-correlation of such sequences are also presented. Furthermore, the sequences produced by DLFSRs can be considered as interleaved sequences. This fact allows us to apply the general interleaved sequence model proposed by Gong and consequently simplify their study. Finally, several remarks are stated regarding DLFSR utilization for cryptographic or code division multiple access (CDMA) applications.

Lecture notes in networks and systems, Dec 31, 2022

Acta Applicandae Mathematicae, Aug 15, 2006

In this work, pseudorandom sequence generators based on finite fields have been analyzed from the... more In this work, pseudorandom sequence generators based on finite fields have been analyzed from the point of view of their cryptographic application. In fact, a class of nonlinear sequence generators has been modelled in terms of linear cellular automata. The algorithm that converts the given generator into a linear model based on automata is very simple and is based on the concatenation of a basic structure. Once the generator has been linearized, a cryptanalytic attack that exploits the weaknesses of such a model has been developed. Linear cellular structures easily model sequence generators with application in stream cipher cryptography.