Joan-Josep Climent - Profile on Academia.edu (original) (raw)
Papers by Joan-Josep Climent
Linear Algebra and its Applications, Sep 1, 2008
In this paper, we characterize four models of concatenation of a block code and a convolutional c... more In this paper, we characterize four models of concatenation of a block code and a convolutional code from a linear systems theory viewpoint. We provide the input-state-output representation of these models and we give conditions in order to get a non-catastrophic concatenated convolutional code with minimal representation. Lower bounds on the free distances of the concatenated codes are also developed.
Linear Algebra and its Applications, Sep 1, 2007
This article focuses on the characterization of two models of concatenated convolutional codes fr... more This article focuses on the characterization of two models of concatenated convolutional codes from the perspective of linear systems theory. We present an inputstate-output representation of these models and study the conditions for obtaining a minimal input-state-output representation and non-catastrophic concatenated convolutional code. We also establish conditions so that the concatenated codes are observable and give a lower bound for their free distances.
El modelo Bulk Synchronous Parallel (BSP) Computing permite predecir el coste de algoritmos paral... more El modelo Bulk Synchronous Parallel (BSP) Computing permite predecir el coste de algoritmos paralelos. En este trabajo * se analizan, implementan según este modelo y comparan entre sí, tres algoritmos para la resolución de sistemas tridiagonales en paralelo: un método del tipo divide y vencerás, el método de las particiones superpuestas y el método de las particiones de Wang. Se realiza un estudio del coste computacional teórico comparándolo con los resultados experimentales, obtenidos al ejecutar dichos algoritmos en un cluster de estaciones de trabajo RS/6000 .
For a prime number p, Bergman (1974) established that End(Z p × Z p 2) is a semilocal ring with p... more For a prime number p, Bergman (1974) established that End(Z p × Z p 2) is a semilocal ring with p 5 elements that cannot be embedded in matrices over any commutative ring. We identify the elements of End(Z p × Z p 2) with elements in a new set, denoted by E p , of matrices of size 2 × 2, whose elements in the rst row belong to Z p and the elements in the second row belong to Z p 2 ; also, using the arithmetic in Z p and Z p 2 , we introduce the arithmetic in that ring and prove that the ring End(Z p × Z p 2) is isomorphic to the ring E p. Finally, we present a Die-Hellman key interchange protocol using some polynomial functions over E p dened by polynomial in Z[X]. x + y = (x + y) mod m and x • y = (xy) mod m, for all x, y ∈ Z m. Let us assume from now on that p is a prime number and consider the rings Z p and Z p 2. Clearly, we can also assume that Z p ⊆ Z p 2 , even though Z p is not a subring of Z p 2. Then, it follows that notation is utmost important to prevent errors like the following. Suppose that p = 5, then Z 5 = {0, 1, 2, 3, 4} and Z 5 2 = {0, 1, 2, 3,. .. , 23, 24}. Note that 2, 4 ∈ Z 5 and 2 + 4 = 1 ∈ Z 5 ; but 2, 4 ∈ Z 5 2 equally. However when 2, 4 ∈ Z 5 2 , 2 + 4 = 6 ∈ Z 5 2. Obviously, 1 = 6 in Z 5 2. Such error can be easily avoidable if we write, when necessary, x mod p and x mod p 2 to refer the element x when x ∈ Z p and x ∈ Z p 2 , respectively. In this light, the above example could be rewritten as (2 mod 5)+(4 mod 5) = 1 mod 5, whereas (2 mod 5 2) + (4 mod 5 2) = 6 mod 5 2. 2 The ring End(Z p × Z p 2) Consider the additive group Z p × Z p 2 of order p 3 , where the addition is dened componentwise, and the set End(Z p × Z p 2) of endomorphisms of such additive group. It is well known that End(Z p × Z p 2) is a noncommutative unitary ring with the usual addition and composition of endomorphisms, that are dened, for f, g ∈ End(Z p × Z p 2), as (f + g)(x, y) = f (x, y) + g(x, y) and (f • g)(x, y) = f (g(x, y)). The additive and multiplicative identities O and I are dened, obviously, by O(x, y) = (0, 0) and I(x, y) = (x, y) respectively. The additive identity is also called the null endomorphism. Te next result not only determines the cardinality of the ring End(Z p × Z p 2), but also introduces the primary property of such a ring: it cannot be embedded in matrices over any commutative ring. Theorem 1 (Theorem 3 of [2]) If p is a prime number, then the ring of endomorphisms End(Z p × Z p 2) has p 5 elements and is semilocal, but cannot be embedded in matrices over any commutative ring.
Mejora de las asignaturas de Álgebra Lineal y Geometría Lineal en los Grados en Matemáticas y Física de la Universidad de Alicante
Esta red de investigacion en docencia es una continuacion natural de una labor que comenzo ya en ... more Esta red de investigacion en docencia es una continuacion natural de una labor que comenzo ya en el curso academico 2015-2016 por parte de los profesores responsables de las asignaturas de Algebra Lineal y Geometria Lineal del Grado en Matematicas de la Facultad de Ciencias de la Universidad de Alicante y cuyo objetivo principal era analizar el desarrollo de las asignaturas Algebra Lineal I, Algebra Lineal II y Geometria Lineal. Durante este curso academico 2017-2018 el Grado en Fisica de la Universidad de Alicante tambien ha alcanzado su segundo ano de imparticion. Aunque este grado sigue siendo muy joven y no ha completado un ciclo completo, hasta el segundo curso comparte una cantidad importante de asignaturas y contenidos con el Grado en Matematicas. Mas concretamente, estos dos grados comparten las asignaturas de Algebra Lineal I, Algebra Lineal II y Geometria Lineal, que son de las que nos ocupamos en esta red. Durante este curso hemos continuado con el minucioso analisis inic...
International Journal of Control, 2018
In this paper we investigate the properties of two-dimensional (2D) convolutional codes which are... more In this paper we investigate the properties of two-dimensional (2D) convolutional codes which are obtained from series concatenation of two 2D convolutional codes. For this purpose we confine ourselves to dealing with finite-support 2D convolutional codes and make use of the so-called Fornasini-Marchesini input-stateoutput (ISO) model representations. Within these ISO representations we study when the structural properties of modal reachability and modal observability of the two given ISO representations carry over to the resulting 2D convolutional code. Moreover, we provide necessary conditions for obtaining a systematic concatenated convolutional code. Finally, we present a lower bound on its free distance.
Starting with a basis of F2k2, we define some sets in F2k2 that are the supports of bent function... more Starting with a basis of F2k2, we define some sets in F2k2 that are the supports of bent functions of 2k variables. We also establish some results in order to count the number of bent functions we can construct, and we provide a complete classification of all bases of F2k2 (for k = 2) providing the same supports of bent functions.
On the arithmetic of the endomorphisms ring [FORMULA]
Applicable Algebra in Engineering Communication and Computing, 2011
For a prime number p, Bergman (Israel J Math 18:257–277, 1974) established that [FORMULA] is a se... more For a prime number p, Bergman (Israel J Math 18:257–277, 1974) established that [FORMULA] is a semilocal ring with p 5 elements that cannot be embedded in matrices over any commutative ring. We identify the elements of [FORMULA] with elements in a new set, denoted by E p , of matrices of size 2 × 2, whose elements in the first row belong to [FORMULA] and the elements in the second row belong to [FORMULA]; also, using the arithmetic in [FORMULA] and [FORMULA], we introduce the arithmetic in that ring and prove that the ring [FORMULA] is isomorphic to the ring E p . Finally, we present a Diffie-Hellman key interchange protocol using some polynomial functions over E p defined by polynomials in [FORMULA].
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019
In this paper we study a problem in the area of coding theory. In particular, we focus on a class... more In this paper we study a problem in the area of coding theory. In particular, we focus on a class of error-correcting codes called convolutional codes. We characterize convolutional codes that can correct bursts of erasures with the lowest possible delay. This characterization is given in terms of a block Toeplitz matrix with entries in a finite field that is built upon a given generator matrix of the convolutional code. This result allows us to provide a concrete construction of a generator matrix of a convolutional code with entries being only zeros or ones that can recover bursts of erasures with low delay. This construction admits a very simple decoding algorithm and, therefore, simplifies the existing schemes proposed recently in the literature.
SeMA Journal, 2015
Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduce... more Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ F n 2 | w(f ⊕l a) = 2 n−1 + 2 n 2 −1 } and {a ∈ F n 2 | w(f ⊕ l a) = 2 n−1 − 2 n 2 −1 } respectively, where w(f ⊕ l a) denotes the Hamming weight of the Boolean function f (x) ⊕ l a (x) and l a (x) is the linear function defined by a ∈ F n 2. f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple (f 0 (x), f 1 (x), f 2 (x), f 3 (x)) of bent functions of n variables such that f 0 (x) ⊕ f 1 (x) ⊕ f 2 (x) ⊕ f 3 (x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.
Journal of Computational and Applied Mathematics, 1997
In this paper we develop a semi-iterative method for computing the Drazin-inverse solution of a s... more In this paper we develop a semi-iterative method for computing the Drazin-inverse solution of a singular linear system Ax = b, where the spectrum of A is real, but its index (i.e., the size of its largest Jordan block corresponding to the eigenvalue zero) is arbitrary. The method employs a set of polynomials that satisfy certain normalization conditions and minimize some well-defined least-squares norm. We develop an efficient recursive algorithm for implementing this method that has a fixed length independent of the index of A. Following that, we give a complete theory of convergence, in which we provide rates of convergence as well. We conclude with a numerical application to determine eigenprojections onto generalized eigenspaces. Our treatment extends the work of Hanke and Hochbruck (1993) that considers the case in which the index of A is 1.
Construcción de funciones bent a partir de una función bent y de sus traslaciones cíclicas basadas en bases de gauss-jordan de cardinalidad 2
In this paper we present a public key cryptosystem based on the McEliece scheme, but using a conv... more In this paper we present a public key cryptosystem based on the McEliece scheme, but using a convolutional code, instead of a block code. Firstly we present some conditions about the convolutional code C to construct the public key cryptosystem and then, starting with the parity check matrix H of a good block code, we find an input-state-output representation of C such that the controllability matrix of C is H t. This cryptosystem is constructed so that any user can encrypt a message by introducing the largest number of possible errors.
Abstract: The objective of this paper is to develop a method to hide information inside a binary ... more Abstract: The objective of this paper is to develop a method to hide information inside a binary image. An algorithm to embed data in scanned text or figures is proposed, based on the detection of suitable pixels, which verify some conditions in order to be not detected. In broad terms, the algorithm locates those pixels placed at the contours of the figures or in those areas where some scattering of the two colors can be found. The hidden information is independent from the values of the pixels where this information is embedded. Notice that, depending on the sequence of bits to be hidden, around half of the used pixels to keep bits of data will not be modified. The other basic characteristic of the proposed scheme is that it is necessary to take into consideration the bits that are modified, in order to perform the recovering process of the information, which consists on recovering the sequence of bits placed in the proper positions. An application to banking sector is proposed fo...
Applicable Algebra in Engineering, Communication and Computing, 2014
For a prime number p, Bergman (Israel J Math 18:257-277, 1974) established that End(Z p × Z p 2 )... more For a prime number p, Bergman (Israel J Math 18:257-277, 1974) established that End(Z p × Z p 2 ) is a semilocal ring with p 5 elements that cannot be embedded in matrices over any commutative ring. In an earlier paper Climent et al. (Appl Algebra Eng Commun Comput 22(2):91-108, 2011), the authors presented an efficient implementation of this ring, and introduced a key exchange protocol based on it. This protocol was cryptanalyzed by Kamal and Youssef (Appl Algebra Eng Commun Comput 23(3-4):143-149, 2012) using the invertibility of most elements in this ring. In this paper we introduce an extension of Bergman's ring, in which only a negligible fraction of elements are invertible, and propose to consider a key exchange protocol over this ring.
Lecture Notes in Computer Science, 2003
The popularity of the Web has created a great marketplace for businesses to sell and showcase the... more The popularity of the Web has created a great marketplace for businesses to sell and showcase their products increasing the need for secure Web services such as SSL, TLS or SET. We propose a pseudorandom bit generator that can be used to create a stream cipher directly applicable to these secure systems; it is based on the powers of a block upper triangular matrix achieving great statistical results and efficiency.
International Journal of Computer Mathematics, 2012
In this paper we introduce some key exchange protocols over noncommutative rings. These protocols... more In this paper we introduce some key exchange protocols over noncommutative rings. These protocols use some polynomials with coefficients in the center of the ring as part of the private keys. We give some examples over the ring End(Z p × Z p 2), where p is a prime number. We also give a security analysis of the proposed protocols and conclude that the only possible attack is by brute force.
Applied Mathematics and Computation, 2004
The parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Ne... more The parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra Appl. 103 (1988) 175-192] for solving nonsingular linear system Ax ¼ b using a weak nonnegative multisplitting of the first type. In this paper new results using a weak nonnegative multisplitting of the second type are introduced when A is a monotone matrix, and using P -regular multisplitting when A is a symmetric positive definite matrix. Combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. It is shown that when matrix A is monotone and the multisplittings are weak nonnegative of the first or second type, both models lead to convergent schemes. When matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent.
Applied Mathematics and Computation, 2005
In this paper we present a new overlapped two-way parallel method for solving tridiagonal linear ... more In this paper we present a new overlapped two-way parallel method for solving tridiagonal linear systems on a bulk-synchronous parallel (BSP) computer. We develop a theoretical study of the computational cost for this new method and we compare it with the experimental times measured on an IBM SP2 using switch hardware for the communications between processors. Using the cost model, we also obtain theoretical results on a CRAY T3E and we achieve a study on the optimum number of processors.
Linear Algebra and its Applications, Sep 1, 2008
In this paper, we characterize four models of concatenation of a block code and a convolutional c... more In this paper, we characterize four models of concatenation of a block code and a convolutional code from a linear systems theory viewpoint. We provide the input-state-output representation of these models and we give conditions in order to get a non-catastrophic concatenated convolutional code with minimal representation. Lower bounds on the free distances of the concatenated codes are also developed.
Linear Algebra and its Applications, Sep 1, 2007
This article focuses on the characterization of two models of concatenated convolutional codes fr... more This article focuses on the characterization of two models of concatenated convolutional codes from the perspective of linear systems theory. We present an inputstate-output representation of these models and study the conditions for obtaining a minimal input-state-output representation and non-catastrophic concatenated convolutional code. We also establish conditions so that the concatenated codes are observable and give a lower bound for their free distances.
El modelo Bulk Synchronous Parallel (BSP) Computing permite predecir el coste de algoritmos paral... more El modelo Bulk Synchronous Parallel (BSP) Computing permite predecir el coste de algoritmos paralelos. En este trabajo * se analizan, implementan según este modelo y comparan entre sí, tres algoritmos para la resolución de sistemas tridiagonales en paralelo: un método del tipo divide y vencerás, el método de las particiones superpuestas y el método de las particiones de Wang. Se realiza un estudio del coste computacional teórico comparándolo con los resultados experimentales, obtenidos al ejecutar dichos algoritmos en un cluster de estaciones de trabajo RS/6000 .
For a prime number p, Bergman (1974) established that End(Z p × Z p 2) is a semilocal ring with p... more For a prime number p, Bergman (1974) established that End(Z p × Z p 2) is a semilocal ring with p 5 elements that cannot be embedded in matrices over any commutative ring. We identify the elements of End(Z p × Z p 2) with elements in a new set, denoted by E p , of matrices of size 2 × 2, whose elements in the rst row belong to Z p and the elements in the second row belong to Z p 2 ; also, using the arithmetic in Z p and Z p 2 , we introduce the arithmetic in that ring and prove that the ring End(Z p × Z p 2) is isomorphic to the ring E p. Finally, we present a Die-Hellman key interchange protocol using some polynomial functions over E p dened by polynomial in Z[X]. x + y = (x + y) mod m and x • y = (xy) mod m, for all x, y ∈ Z m. Let us assume from now on that p is a prime number and consider the rings Z p and Z p 2. Clearly, we can also assume that Z p ⊆ Z p 2 , even though Z p is not a subring of Z p 2. Then, it follows that notation is utmost important to prevent errors like the following. Suppose that p = 5, then Z 5 = {0, 1, 2, 3, 4} and Z 5 2 = {0, 1, 2, 3,. .. , 23, 24}. Note that 2, 4 ∈ Z 5 and 2 + 4 = 1 ∈ Z 5 ; but 2, 4 ∈ Z 5 2 equally. However when 2, 4 ∈ Z 5 2 , 2 + 4 = 6 ∈ Z 5 2. Obviously, 1 = 6 in Z 5 2. Such error can be easily avoidable if we write, when necessary, x mod p and x mod p 2 to refer the element x when x ∈ Z p and x ∈ Z p 2 , respectively. In this light, the above example could be rewritten as (2 mod 5)+(4 mod 5) = 1 mod 5, whereas (2 mod 5 2) + (4 mod 5 2) = 6 mod 5 2. 2 The ring End(Z p × Z p 2) Consider the additive group Z p × Z p 2 of order p 3 , where the addition is dened componentwise, and the set End(Z p × Z p 2) of endomorphisms of such additive group. It is well known that End(Z p × Z p 2) is a noncommutative unitary ring with the usual addition and composition of endomorphisms, that are dened, for f, g ∈ End(Z p × Z p 2), as (f + g)(x, y) = f (x, y) + g(x, y) and (f • g)(x, y) = f (g(x, y)). The additive and multiplicative identities O and I are dened, obviously, by O(x, y) = (0, 0) and I(x, y) = (x, y) respectively. The additive identity is also called the null endomorphism. Te next result not only determines the cardinality of the ring End(Z p × Z p 2), but also introduces the primary property of such a ring: it cannot be embedded in matrices over any commutative ring. Theorem 1 (Theorem 3 of [2]) If p is a prime number, then the ring of endomorphisms End(Z p × Z p 2) has p 5 elements and is semilocal, but cannot be embedded in matrices over any commutative ring.
Mejora de las asignaturas de Álgebra Lineal y Geometría Lineal en los Grados en Matemáticas y Física de la Universidad de Alicante
Esta red de investigacion en docencia es una continuacion natural de una labor que comenzo ya en ... more Esta red de investigacion en docencia es una continuacion natural de una labor que comenzo ya en el curso academico 2015-2016 por parte de los profesores responsables de las asignaturas de Algebra Lineal y Geometria Lineal del Grado en Matematicas de la Facultad de Ciencias de la Universidad de Alicante y cuyo objetivo principal era analizar el desarrollo de las asignaturas Algebra Lineal I, Algebra Lineal II y Geometria Lineal. Durante este curso academico 2017-2018 el Grado en Fisica de la Universidad de Alicante tambien ha alcanzado su segundo ano de imparticion. Aunque este grado sigue siendo muy joven y no ha completado un ciclo completo, hasta el segundo curso comparte una cantidad importante de asignaturas y contenidos con el Grado en Matematicas. Mas concretamente, estos dos grados comparten las asignaturas de Algebra Lineal I, Algebra Lineal II y Geometria Lineal, que son de las que nos ocupamos en esta red. Durante este curso hemos continuado con el minucioso analisis inic...
International Journal of Control, 2018
In this paper we investigate the properties of two-dimensional (2D) convolutional codes which are... more In this paper we investigate the properties of two-dimensional (2D) convolutional codes which are obtained from series concatenation of two 2D convolutional codes. For this purpose we confine ourselves to dealing with finite-support 2D convolutional codes and make use of the so-called Fornasini-Marchesini input-stateoutput (ISO) model representations. Within these ISO representations we study when the structural properties of modal reachability and modal observability of the two given ISO representations carry over to the resulting 2D convolutional code. Moreover, we provide necessary conditions for obtaining a systematic concatenated convolutional code. Finally, we present a lower bound on its free distance.
Starting with a basis of F2k2, we define some sets in F2k2 that are the supports of bent function... more Starting with a basis of F2k2, we define some sets in F2k2 that are the supports of bent functions of 2k variables. We also establish some results in order to count the number of bent functions we can construct, and we provide a complete classification of all bases of F2k2 (for k = 2) providing the same supports of bent functions.
On the arithmetic of the endomorphisms ring [FORMULA]
Applicable Algebra in Engineering Communication and Computing, 2011
For a prime number p, Bergman (Israel J Math 18:257–277, 1974) established that [FORMULA] is a se... more For a prime number p, Bergman (Israel J Math 18:257–277, 1974) established that [FORMULA] is a semilocal ring with p 5 elements that cannot be embedded in matrices over any commutative ring. We identify the elements of [FORMULA] with elements in a new set, denoted by E p , of matrices of size 2 × 2, whose elements in the first row belong to [FORMULA] and the elements in the second row belong to [FORMULA]; also, using the arithmetic in [FORMULA] and [FORMULA], we introduce the arithmetic in that ring and prove that the ring [FORMULA] is isomorphic to the ring E p . Finally, we present a Diffie-Hellman key interchange protocol using some polynomial functions over E p defined by polynomials in [FORMULA].
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019
In this paper we study a problem in the area of coding theory. In particular, we focus on a class... more In this paper we study a problem in the area of coding theory. In particular, we focus on a class of error-correcting codes called convolutional codes. We characterize convolutional codes that can correct bursts of erasures with the lowest possible delay. This characterization is given in terms of a block Toeplitz matrix with entries in a finite field that is built upon a given generator matrix of the convolutional code. This result allows us to provide a concrete construction of a generator matrix of a convolutional code with entries being only zeros or ones that can recover bursts of erasures with low delay. This construction admits a very simple decoding algorithm and, therefore, simplifies the existing schemes proposed recently in the literature.
SeMA Journal, 2015
Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduce... more Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ F n 2 | w(f ⊕l a) = 2 n−1 + 2 n 2 −1 } and {a ∈ F n 2 | w(f ⊕ l a) = 2 n−1 − 2 n 2 −1 } respectively, where w(f ⊕ l a) denotes the Hamming weight of the Boolean function f (x) ⊕ l a (x) and l a (x) is the linear function defined by a ∈ F n 2. f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple (f 0 (x), f 1 (x), f 2 (x), f 3 (x)) of bent functions of n variables such that f 0 (x) ⊕ f 1 (x) ⊕ f 2 (x) ⊕ f 3 (x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.
Journal of Computational and Applied Mathematics, 1997
In this paper we develop a semi-iterative method for computing the Drazin-inverse solution of a s... more In this paper we develop a semi-iterative method for computing the Drazin-inverse solution of a singular linear system Ax = b, where the spectrum of A is real, but its index (i.e., the size of its largest Jordan block corresponding to the eigenvalue zero) is arbitrary. The method employs a set of polynomials that satisfy certain normalization conditions and minimize some well-defined least-squares norm. We develop an efficient recursive algorithm for implementing this method that has a fixed length independent of the index of A. Following that, we give a complete theory of convergence, in which we provide rates of convergence as well. We conclude with a numerical application to determine eigenprojections onto generalized eigenspaces. Our treatment extends the work of Hanke and Hochbruck (1993) that considers the case in which the index of A is 1.
Construcción de funciones bent a partir de una función bent y de sus traslaciones cíclicas basadas en bases de gauss-jordan de cardinalidad 2
In this paper we present a public key cryptosystem based on the McEliece scheme, but using a conv... more In this paper we present a public key cryptosystem based on the McEliece scheme, but using a convolutional code, instead of a block code. Firstly we present some conditions about the convolutional code C to construct the public key cryptosystem and then, starting with the parity check matrix H of a good block code, we find an input-state-output representation of C such that the controllability matrix of C is H t. This cryptosystem is constructed so that any user can encrypt a message by introducing the largest number of possible errors.
Abstract: The objective of this paper is to develop a method to hide information inside a binary ... more Abstract: The objective of this paper is to develop a method to hide information inside a binary image. An algorithm to embed data in scanned text or figures is proposed, based on the detection of suitable pixels, which verify some conditions in order to be not detected. In broad terms, the algorithm locates those pixels placed at the contours of the figures or in those areas where some scattering of the two colors can be found. The hidden information is independent from the values of the pixels where this information is embedded. Notice that, depending on the sequence of bits to be hidden, around half of the used pixels to keep bits of data will not be modified. The other basic characteristic of the proposed scheme is that it is necessary to take into consideration the bits that are modified, in order to perform the recovering process of the information, which consists on recovering the sequence of bits placed in the proper positions. An application to banking sector is proposed fo...
Applicable Algebra in Engineering, Communication and Computing, 2014
For a prime number p, Bergman (Israel J Math 18:257-277, 1974) established that End(Z p × Z p 2 )... more For a prime number p, Bergman (Israel J Math 18:257-277, 1974) established that End(Z p × Z p 2 ) is a semilocal ring with p 5 elements that cannot be embedded in matrices over any commutative ring. In an earlier paper Climent et al. (Appl Algebra Eng Commun Comput 22(2):91-108, 2011), the authors presented an efficient implementation of this ring, and introduced a key exchange protocol based on it. This protocol was cryptanalyzed by Kamal and Youssef (Appl Algebra Eng Commun Comput 23(3-4):143-149, 2012) using the invertibility of most elements in this ring. In this paper we introduce an extension of Bergman's ring, in which only a negligible fraction of elements are invertible, and propose to consider a key exchange protocol over this ring.
Lecture Notes in Computer Science, 2003
The popularity of the Web has created a great marketplace for businesses to sell and showcase the... more The popularity of the Web has created a great marketplace for businesses to sell and showcase their products increasing the need for secure Web services such as SSL, TLS or SET. We propose a pseudorandom bit generator that can be used to create a stream cipher directly applicable to these secure systems; it is based on the powers of a block upper triangular matrix achieving great statistical results and efficiency.
International Journal of Computer Mathematics, 2012
In this paper we introduce some key exchange protocols over noncommutative rings. These protocols... more In this paper we introduce some key exchange protocols over noncommutative rings. These protocols use some polynomials with coefficients in the center of the ring as part of the private keys. We give some examples over the ring End(Z p × Z p 2), where p is a prime number. We also give a security analysis of the proposed protocols and conclude that the only possible attack is by brute force.
Applied Mathematics and Computation, 2004
The parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Ne... more The parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra Appl. 103 (1988) 175-192] for solving nonsingular linear system Ax ¼ b using a weak nonnegative multisplitting of the first type. In this paper new results using a weak nonnegative multisplitting of the second type are introduced when A is a monotone matrix, and using P -regular multisplitting when A is a symmetric positive definite matrix. Combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. It is shown that when matrix A is monotone and the multisplittings are weak nonnegative of the first or second type, both models lead to convergent schemes. When matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent.
Applied Mathematics and Computation, 2005
In this paper we present a new overlapped two-way parallel method for solving tridiagonal linear ... more In this paper we present a new overlapped two-way parallel method for solving tridiagonal linear systems on a bulk-synchronous parallel (BSP) computer. We develop a theoretical study of the computational cost for this new method and we compare it with the experimental times measured on an IBM SP2 using switch hardware for the communications between processors. Using the cost model, we also obtain theoretical results on a CRAY T3E and we achieve a study on the optimum number of processors.