On the provable security of an efficient RSA-based pseudorandom generator

Pseudorandom Generators (PRGs) based on the RSA inversion (one-wayness) problem have been extensively studied in the literature over the last 25 years. These generators have the attractive feature of provable pseudorandomness security assuming the hardness of the RSA inversion problem. However, despite extensive study, the most efficient provably secure RSA-based generators output asymptotically only at most O(logn) bits per multiply modulo an RSA modulus of bitlength n, and hence are too slow to be used in many practical applications. To bring theory closer to practice, we present a simple modification to the proof of security by Fischlin and Schnorr of an RSA-based PRG, which shows that one can obtain an RSA-based PRG which outputs Ω(n) bits per multiply and has provable pseudorandomness security assuming the hardness of a well-studied variant of the RSA inversion problem, where a constant fraction of the plaintext bits are given. Our result gives a positive answer to an open question posed by Gennaro (J. of Cryptology, 2005) regarding finding a PRG beating the rate O(logn) bits per multiply at the cost of a reasonable assumption on RSA inversion.

Fast pseudorandom generator based on packed matrices

Pseudorandom generators are a basic foundation of many cryptographic services and information security protocols. We propose a modification of a previously published matricial pseudorandom generator that significantly improves performance and security. The resulting generator is successfully compared to world class standards.

An optimized pseudorandom generator using packed matrices

Most cryptographic services and information security protocols require a dependable source of random data; pseudorandom generators are convenient and efficient for this application working as one of the basic foundation blocks on which to build the required security infrastructure. We propose a modification of a previously published matricial pseudorandom generator that significantly improves performance and security by using word packed matrices and modifying key scheduling and bit extraction schemes. The resulting generator is then successfully compared to world class standards.

Contribución al estudio del criptoanálisis y diseño de los criptosistemas caóticos

The extraordinary increase of new information technologies, the development of Internet, the electronic commerce, the e-government, mobile telephony and future cloud computing and storage, have provided great benefits in all areas of society. Besides these, there are new challenges for the protection of information, such as the loss of confidentiality and integrity of electronic documents. Cryptography plays a key role by providing the necessary tools to ensure the safety of these new media. It is imperative to intensify the research in this area, to meet the growing demand for new secure cryptographic techniques. The theory of chaotic nonlinear dynamical systems and the theory of cryptography give rise to the chaotic cryptography, which is the field of study of this thesis. The link between cryptography and chaotic systems is still subject of intense study. The combination of apparently stochastic behavior, the properties of sensitivity to initial conditions and parameters, ergodicity, mixing, and the fact that periodic points are dense, suggests that chaotic orbits resemble random sequences. This fact, and the ability to synchronize multiple chaotic systems, initially described by Pecora and Carroll, has generated an avalanche of research papers that relate cryptography and chaos. The chaotic cryptography addresses two fundamental design paradigms. In the first paradigm, chaotic cryptosystems are designed using continuous time, mainly based on chaotic synchronization techniques; they are implemented with analog circuits or by computer simulation. In the second paradigm, chaotic cryptosystems are constructed using discrete time and generally do not depend on chaos synchronization techniques. The contributions in this thesis involve three aspects about chaotic cryptography. The first one is a theoretical analysis of the geometric properties of some of the most employed chaotic attractors for the design of chaotic cryptosystems. The second one is the cryptanalysis of continuos chaotic cryptosystems and finally concludes with three new designs of cryptographically secure chaotic pseudorandom generators. The main accomplishments contained in this thesis are: v Development of a method for determining the parameters of some double scroll chaotic systems, including Lorenz system and Chua’s circuit. First, some geometrical characteristics of chaotic system have been used to reduce the search space of parameters. Next, a scheme based on the synchronization of chaotic systems was built. The geometric properties have been employed as matching criterion, to determine the values of the parameters with the desired accuracy. The method is not affected by a moderate amount of noise in the waveform. The proposed method has been applied to find security flaws in the continuous chaotic encryption systems. Based on previous results, the chaotic ciphers proposed by Wang and Bu and those proposed by Xu and Li are cryptanalyzed. We propose some solutions to improve the cryptosystems, although very limited because these systems are not suitable for use in cryptography. Development of a method for determining the parameters of the Lorenz system, when it is used in the design of two-channel cryptosystem. The method uses the geometric properties of the Lorenz system. The search space of parameters has been reduced. Next, the parameters have been accurately determined from the ciphertext. The method has been applied to cryptanalysis of an encryption scheme proposed by Jiang. In 2005, Gunay et al. proposed a chaotic encryption system based on a cellular neural network implementation of Chua’s circuit. This scheme has been cryptanalyzed. Some gaps in security design have been identified. Based on the theoretical results of digital chaotic systems and cryptanalysis of several chaotic ciphers recently proposed, a family of pseudorandom generators has been designed using finite precision. The design is based on the coupling of several piecewise linear chaotic maps. Based on the above results a new family of chaotic pseudorandom generators named Trident has been designed. These generators have been specially designed to meet the needs of real-time encryption of mobile technology. According to the above results, this thesis proposes another family of pseudorandom generators called Trifork. These generators are based on a combination of perturbed Lagged Fibonacci generators. This family of generators is cryptographically secure and suitable for use in real-time encryption. Detailed analysis shows that the proposed pseudorandom generator can provide fast encryption speed and a high level of security, at the same time. El extraordinario auge de las nuevas tecnologías de la información, el desarrollo de Internet, el comercio electrónico, la administración electrónica, la telefonía móvil y la futura computación y almacenamiento en la nube, han proporcionado grandes beneficios en todos los ámbitos de la sociedad. Junto a éstos, se presentan nuevos retos para la protección de la información, como la suplantación de personalidad y la pérdida de la confidencialidad e integridad de los documentos electrónicos. La criptografía juega un papel fundamental aportando las herramientas necesarias para garantizar la seguridad de estos nuevos medios, pero es imperativo intensificar la investigación en este ámbito para dar respuesta a la demanda creciente de nuevas técnicas criptográficas seguras. La teoría de los sistemas dinámicos no lineales junto a la criptografía dan lugar a la ((criptografía caótica)), que es el campo de estudio de esta tesis. El vínculo entre la criptografía y los sistemas caóticos continúa siendo objeto de un intenso estudio. La combinación del comportamiento aparentemente estocástico, las propiedades de sensibilidad a las condiciones iniciales y a los parámetros, la ergodicidad, la mezcla, y que los puntos periódicos sean densos asemejan las órbitas caóticas a secuencias aleatorias, lo que supone su potencial utilización en el enmascaramiento de mensajes. Este hecho, junto a la posibilidad de sincronizar varios sistemas caóticos descrita inicialmente en los trabajos de Pecora y Carroll, ha generado una avalancha de trabajos de investigación donde se plantean muchas ideas sobre la forma de realizar sistemas de comunicaciones seguros, relacionando así la criptografía y el caos. La criptografía caótica aborda dos paradigmas de diseño fundamentales. En el primero, los criptosistemas caóticos se diseñan utilizando circuitos analógicos, principalmente basados en las técnicas de sincronización caótica; en el segundo, los criptosistemas caóticos se construyen en circuitos discretos u ordenadores, y generalmente no dependen de las técnicas de sincronización del caos. Nuestra contribución en esta tesis implica tres aspectos sobre el cifrado caótico. En primer lugar, se realiza un análisis teórico de las propiedades geométricas de algunos de los sistemas caóticos más empleados en el diseño de criptosistemas caóticos vii continuos; en segundo lugar, se realiza el criptoanálisis de cifrados caóticos continuos basados en el análisis anterior; y, finalmente, se realizan tres nuevas propuestas de diseño de generadores de secuencias pseudoaleatorias criptográficamente seguros y rápidos. La primera parte de esta memoria realiza un análisis crítico acerca de la seguridad de los criptosistemas caóticos, llegando a la conclusión de que la gran mayoría de los algoritmos de cifrado caóticos continuos —ya sean realizados físicamente o programados numéricamente— tienen serios inconvenientes para proteger la confidencialidad de la información ya que son inseguros e ineficientes. Asimismo una gran parte de los criptosistemas caóticos discretos propuestos se consideran inseguros y otros no han sido atacados por lo que se considera necesario más trabajo de criptoanálisis. Esta parte concluye señalando las principales debilidades encontradas en los criptosistemas analizados y algunas recomendaciones para su mejora. En la segunda parte se diseña un método de criptoanálisis que permite la identificaci ón de los parámetros, que en general forman parte de la clave, de algoritmos de cifrado basados en sistemas caóticos de Lorenz y similares, que utilizan los esquemas de sincronización excitador-respuesta. Este método se basa en algunas características geométricas del atractor de Lorenz. El método diseñado se ha empleado para criptoanalizar eficientemente tres algoritmos de cifrado. Finalmente se realiza el criptoanálisis de otros dos esquemas de cifrado propuestos recientemente. La tercera parte de la tesis abarca el diseño de generadores de secuencias pseudoaleatorias criptográficamente seguras, basadas en aplicaciones caóticas, realizando las pruebas estadísticas, que corroboran las propiedades de aleatoriedad. Estos generadores pueden ser utilizados en el desarrollo de sistemas de cifrado en flujo y para cubrir las necesidades del cifrado en tiempo real. Una cuestión importante en el diseño de sistemas de cifrado discreto caótico es la degradación dinámica debida a la precisión finita; sin embargo, la mayoría de los diseñadores de sistemas de cifrado discreto caótico no ha considerado seriamente este aspecto. En esta tesis se hace hincapié en la importancia de esta cuestión y se contribuye a su esclarecimiento con algunas consideraciones iniciales. Ya que las cuestiones teóricas sobre la dinámica de la degradación de los sistemas caóticos digitales no ha sido totalmente resuelta, en este trabajo utilizamos algunas soluciones prácticas para evitar esta dificultad teórica. Entre las técnicas posibles, se proponen y evalúan varias soluciones, como operaciones de rotación de bits y desplazamiento de bits, que combinadas con la variación dinámica de parámetros y con la perturbación cruzada, proporcionan un excelente remedio al problema de la degradación dinámica. Además de los problemas de seguridad sobre la degradación dinámica, muchos criptosistemas se rompen debido a su diseño descuidado, no a causa de los defectos esenciales de los sistemas caóticos digitales. Este hecho se ha tomado en cuenta en esta tesis y se ha logrado el diseño de generadores pseudoaleatorios caóticos criptogr áficamente seguros.

Design of a reconfigurable pseudorandom number generator for use in intelligent systems

This paper deals with the design of a network-on-chip reconfigurable pseudorandom number generation unit that can map and execute meta-heuristic algorithms in hardware. The unit can be configured to implement one of the following five linear generator algorithms: a multiplicative congruential, a mixed congruential, a standard multiple recursive, a mixed multiple recursive, and a multiply-with-carry. The generation unit can be used both as a pseudorandom and a message passing-based server, which is able to produce pseudorandom numbers on demand, sending them to the network-on-chip blocks that originate the service request. The generator architecture has been mapped to a field programmable gate array, and showed that millions of numbers in 32-, 64-, 96-, or 128-bit formats can be produced in tens of milliseconds. (C) 2011 Elsevier B.V. All rights reserved.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis.

A new family of Marx generator based on resonant converter

This paper presents a novel topology to generate high voltage with utilization of slow and fast power switches. New concepts used in this topology include numbers of diode-capacitor units in parallel with resonant circuits which are connected to a positive buck-boost converter. The resonant circuit reverses the voltage polarity of the capacitors. This configuration has capability of generating a flexible high voltage with certain number of capacitors. The advantage of this topology is to use slow switches, less number of diodes and capacitors compare to Marx generator. Simulations have been performed to verify the proposed topology.

A resonant based Marx generator

The configuration proposed in this paper aims to generate high voltage for pulsed power applications. The main idea is to charge two groups of capacitors in parallel through an inductor and take the advantage of resonant phenomena in charging each capacitor up to a double input voltage level. In each resonant half a cycle, one of those capacitor groups are charged, and finally the charged capacitors will be connected together in series and the summation of the capacitor voltages can be appeared at the output of the topology. This topology can be considered as a modified Marx generator which works based on the resonant concept. Simulation models of this converter have been investigated in Matlab/SIMULINK platform and the attained results fully satisfy the proper operation of the converter.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis

A solid state Marx generator with a novel configuration

The new configuration proposed in this paper for Marx Generator (MG) aims to generate high voltage for pulsed power applications through reduced number of semiconductor components with a more efficient load supplying process. The main idea is to charge two groups of capacitors in parallel through an inductor and take advantage of resonant phenomenon in charging each capacitor up to a double input voltage level. In each resonant half a cycle, one of those capacitor groups are charged, and eventually the charged capacitors will be connected in series and the summation of the capacitor voltages can be appeared at the output of the topology. This topology can be considered as a modified Marx generator which works based on the resonant concept. Simulated models of this converter have been investigated in Matlab/SIMULINK platform and a prototype set up has been implemented in laboratory. The acquired results of either fully satisfy the anticipations in proper operation of the converter.

A solid state Marx generator with a novel configuration

The new configuration proposed in this paper for Marx Generator (MG.) aims to generate high voltage for pulsed power applications through reduced number of semiconductor components with a more efficient load supplying process. The main idea is to charge two groups of capacitors in parallel through an inductor and take the advantage of resonant phenomenon in charging each capacitor up to a double input voltage level. In each resonant half a cycle, one of those capacitor groups are charged, and eventually the charged capacitors will be connected in series and the summation of the capacitor voltages can be appeared at the output of the topology. This topology can be considered as a modified Marx generator which works based on the resonant concept. Simulated models of this converter have been investigated in Matlab/SIMULINK platform and the acquired results fully satisfy the anticipations in proper operation of the converter.

Generator interconnection procedures at the Midwest ISO

The Midwestern US is a wind-rich resource and wind power is being developed in this region at a very brisk pace. Transporting this energy resource to load centers invariably requires massive transmission lines. This issue of developing additional transmission to support reliable integration of wind on to the power grid provides a multitude of interesting challenges spanning various areas of power systems such as transmission planning, real-time operations and cost-allocation for new transmission. The Midwest ISO as a regional transmission provider is responsible for processing requests to interconnect proposed generation on to the transmission grid under its purview. This paper provides information about some of the issues faced in performing interconnection planning studies and Midwest ISO's efforts to improve its generator interconnection procedures. Related cost-allocation efforts currently ongoing at the Midwest ISO to streamline integration of bulk quantities of wind power in to the transmission grid are also presented.