Concatenation of convolutional and block codes Final report

Comparison of concatenated and sequential decoding systems and convolutional code structural propertie

Deterministic Chaos in Digital Cryptography

This thesis studies the application of deterministic chaos to digital cryptography. Cryptographic systems such as pseudo-random generators (PRNG), block ciphers and hash functions are regarded as a dynamic system (X, j), where X is a state space (Le. message space) and f : X -+ X is an iterated function. In both chaos theory and cryptography, the object of study is a dynamic system that performs an iterative nonlinear transformation of information in an apparently unpredictable but deterministic manner. In terms of chaos theory, the sensitivity to the initial conditions together with the mixing property ensures cryptographic confusion (statistical independence) and diffusion (uniform propagation of plaintext and key randomness into cihertext). This synergetic relationship between the properties of chaotic and cryptographic systems is considered at both the theoretical and practical levels: The theoretical background upon which this relationship is based, includes discussions on chaos, ergodicity, complexity, randomness, unpredictability and entropy. Two approaches to the finite-state implementation of chaotic systems (Le. pseudo-chaos) are considered: (i) floating-point approximation of continuous-state chaos; (ii) binary pseudo-chaos. An overview is given of chaotic systems underpinning cryptographic algorithms along with their strengths and weaknesses. Though all conventional cryposystems are considered binary pseudo-chaos, neither chaos, nor pseudo-chaos are sufficient to guarantee cryptographic strength and security. A dynamic system is said to have an analytical solution Xn = (xo) if any trajectory point Xn can be computed directly from the initial conditions Xo, without performing n iterations. A chaotic system with an analytical solution may have a unpredictable multi-valued map Xn+l = f(xn). Their floating-point approximation is studied in the context of pseudo-random generators. A cryptographic software system E-Larm ™ implementing a multistream pseudo-chaotic generator is described. Several pseudo-chaotic systems including the logistic map, sine map, tangent- and logarithm feedback maps, sawteeth and tent maps are evaluated by means of floating point computations. Two types of partitioning are used to extract pseudo-random from the floating-point state variable: (i) combining the last significant bits of the floating-point number (for nonlinear maps); and (ii) threshold partitioning (for piecewise linear maps). Multi-round iterations are produced to decrease the bit dependence and increase non-linearity. Relationships between pseudo-chaotic systems are introduced to avoid short cycles (each system influences periodically the states of other systems used in the encryption session). An evaluation of cryptographic properties of E-Larm is given using graphical plots such as state distributions, phase-space portraits, spectral density Fourier transform, approximated entropy (APEN), cycle length histogram, as well as a variety of statistical tests from the National Institute of Standards and Technology (NIST) suite. Though E-Larm passes all tests recommended by NIST, an approach based on the floating-point approximation of chaos is inefficient in terms of the quality/performance ratio (compared with existing PRNG algorithms). Also no solution is known to control short cycles. In conclusion, the role of chaos theory in cryptography is identified; disadvantages of floating-point pseudo-chaos are emphasized although binary pseudo-chaos is considered useful for cryptographic applications.Durand Technology Limite

The hardware implementation of an artificial neural network using stochastic pulse rate encoding principles

In this thesis the development of a hardware artificial neuron device and artificial neural network using stochastic pulse rate encoding principles is considered. After a review of neural network architectures and algorithmic approaches suitable for hardware implementation, a critical review of hardware techniques which have been considered in analogue and digital systems is presented. New results are presented demonstrating the potential of two learning schemes which adapt by the use of a single reinforcement signal. The techniques for computation using stochastic pulse rate encoding are presented and extended with new novel circuits relevant to the hardware implementation of an artificial neural network. The generation of random numbers is the key to the encoding of data into the stochastic pulse rate domain. The formation of random numbers and multiple random bit sequences from a single PRBS generator have been investigated. Two techniques, Simulated Annealing and Genetic Algorithms, have been applied successfully to the problem of optimising the configuration of a PRBS random number generator for the formation of multiple random bit sequences and hence random numbers. A complete hardware design for an artificial neuron using stochastic pulse rate encoded signals has been described, designed, simulated, fabricated and tested before configuration of the device into a network to perform simple test problems. The implementation has shown that the processing elements of the artificial neuron are small and simple, but that there can be a significant overhead for the encoding of information into the stochastic pulse rate domain. The stochastic artificial neuron has the capability of on-line weight adaption. The implementation of reinforcement schemes using the stochastic neuron as a basic element are discussed

STATISTICAL PROPERTIES OF PSEUDORANDOM SEQUENCES

Random numbers (in one sense or another) have applications in computer simulation, Monte Carlo integration, cryptography, randomized computation, radar ranging, and other areas. It is impractical to generate random numbers in real life, instead sequences of numbers (or of bits) that appear to be ``random yet repeatable are used in real life applications. These sequences are called pseudorandom sequences. To determine the suitability of pseudorandom sequences for applications, we need to study their properties, in particular, their statistical properties. The simplest property is the minimal period of the sequence. That is, the shortest number of steps until the sequence repeats. One important type of pseudorandom sequences is the sequences generated by feedback with carry shift registers (FCSRs). In this dissertation, we study statistical properties of N-ary FCSR sequences with odd prime connection integer q and least period (q-1)/2. These are called half-ℓ-sequences. More precisely, our work includes: The number of occurrences of one symbol within one period of a half-ℓ-sequence; The number of pairs of symbols with a fixed distance between them within one period of a half-ℓ-sequence; The number of triples of consecutive symbols within one period of a half-ℓ-sequence. In particular we give a bound on the number of occurrences of one symbol within one period of a binary half-ℓ-sequence and also the autocorrelation value in binary case. The results show that the distributions of half-ℓ-sequences are fairly flat. However, these sequences in the binary case also have some undesirable features as high autocorrelation values. We give bounds on the number of occurrences of two symbols with a fixed distance between them in an ℓ-sequence, whose period reaches the maximum and obtain conditions on the connection integer that guarantee the distribution is highly uniform. In another study of a cryptographically important statistical property, we study a generalization of correlation immunity (CI). CI is a measure of resistance to Siegenthaler\u27s divide and conquer attack on nonlinear combiners. In this dissertation, we present results on correlation immune functions with regard to the q-transform, a generalization of the Walsh-Hadamard transform, to measure the proximity of two functions. We give two definitions of q-correlation immune functions and the relationship between them. Certain properties and constructions for q-correlation immune functions are discussed. We examine the connection between correlation immune functions and q-correlation immune functions

Cellular Automata in Cryptographic Random Generators

Cryptographic schemes using one-dimensional, three-neighbor cellular automata as a primitive have been put forth since at least 1985. Early results showed good statistical pseudorandomness, and the simplicity of their construction made them a natural candidate for use in cryptographic applications. Since those early days of cellular automata, research in the field of cryptography has developed a set of tools which allow designers to prove a particular scheme to be as hard as solving an instance of a well-studied problem, suggesting a level of security for the scheme. However, little or no literature is available on whether these cellular automata can be proved secure under even generous assumptions. In fact, much of the literature falls short of providing complete, testable schemes to allow such an analysis. In this thesis, we first examine the suitability of cellular automata as a primitive for building cryptographic primitives. In this report, we focus on pseudorandom bit generation and noninvertibility, the behavioral heart of cryptography. In particular, we focus on cyclic linear and non-linear automata in some of the common configurations to be found in the literature. We examine known attacks against these constructions and, in some cases, improve the results. Finding little evidence of provable security, we then examine whether the desirable properties of cellular automata (i.e. highly parallel, simple construction) can be maintained as the automata are enhanced to provide a foundation for such proofs. This investigation leads us to a new construction of a finite state cellular automaton (FSCA) which is NP-Hard to invert. Finally, we introduce the Chasm pseudorandom generator family built on this construction and provide some initial experimental results using the NIST test suite

Public keys quality

Dissertação de mestrado em Matemática e ComputaçãoThe RSA cryptosystem, invented by Ron Rivest, Adi Shamir and Len Adleman ([Rivest et al., 1978]) is the most commonly used cryptosystem for providing privacy and ensuring authenticity of digital data. RSA is usually used in contexts where security of digital data is priority. RSA is used worldwide by web servers and browsers to secure web traffic, to ensure privacy and authenticity of e-mail, to secure remote login sessions and to provide secure electronic creditcard payment systems. Given its importance in the protection of digital data, vulnerabilities of RSA have been analysed by many researchers. The researches made so far led to a number of fascinating attacks. Although the attacks helped to improve the security of this cryptosystem, showing that securely implementing RSA is a nontrivial task, none of them was devastating. This master thesis discusses the RSA cryptosystem and some of its vulnerabilities as well as the description of some attacks, both recent and old, together with the description of the underlying mathematical tools they use. Although many types of attacks exist, in this master thesis only a few examples were analysed. The ultimate attack, based in the batch-GCD algorithm, was implemented and tested in the RSA keys produced by a certificated Hardware Security Modules Luna SA and the results were commented. The random and pseudorandom numbers are fundamental to many cryptographic applications, including the RSA cryptosystems. In fact, the produced keys must be generated in a specific random way. The National Institute of Standards and Technology, responsible entity for specifying safety standards, provides a package named "A Statistical Test Suit for Random and Pseudorandom Number Generators for Cryptography Applications" which was used in this work to test the randomness of the Luna SA generated numbers. All the statistical tests were tested in different bit sizes number and the results commented. The main purpose of this thesis is to study the previous subjects and create an applications capable to test the Luna SA generated numbers randomness, a well as evaluate the security of the RSA. This work was developed in partnership with University of Minho and Multicert.O RSA, criado por Ron Rivest, Adi Shamir e Len Adleman ([Rivest et al., 1978]) é o sistema criptográfico mais utilizado para providenciar segurança e assegurar a autenticação de dados utilizados no mundo digital. O RSA é usualmente usado em contextos onde a segurança é a grande prioridade. Hoje em dia, este sistema criptográfico é utilizado mundialmente por servidores web e por browsers, por forma a assegurar um tráfego seguro através da Internet. É o sistema criptográfico mais utilizado na autenticação de e-mails, nos inícios de sessões remotos, na utilização de pagamentos através de cartões multibanco, garantindo segurança na utilização destes serviços. Dada a importância que este sistema assume na proteção da informação digital, as suas vulnerabilidades têm sido alvo de várias investigações. Estas investigações resultaram em vários ataques ao RSA. Embora nenhum destes ataques seja efetivamente eficaz, todos contribuíram para um aumento da segurança do RSA, uma vez que as implementações de referência deste algoritmo passaram a precaver-se contra os ataques descobertos. Esta tese de mestrado aborda o sistema criptográfico RSA, discutindo algumas das suas vulnerabilidades, assim como alguns ataques efetuados a este sistema, estudando todos os métodos matemáticos por estes usados. Embora existam diversos ataques, apenas alguns serão abordados nesta tese de mestrado. O último ataque, baseado no algoritmo batch-GCD foi implementado e foram feitos testes em chaves RSA produzidas por um Hardware Security Module Luna SA certificado e os resultados obtidos foram discutidos. Os números aleatórios e pseudoaleatórios são fundamentais a todas as aplicações criptográficas, incluindo, portanto, o sistema criptográfico RSA. De facto, as chaves produzidas deverão ser geradas com alguma aleatoriedade intrínseca ao sistema. O Instituto Nacional de Standards e Tecnologia, entidade responsável pela especificação dos standards de segurança, disponibiliza um pacote de testes estatísticos, denominado por "A Statistical Test Suit for Random and Pseudorandom Number Generators for Cryptography Applications". Estes testes estatísticos foram aplicados a números gerados pelo Luna SA e os resultados foram, também, comentados. O objetivo desta tese de mestrado é desenvolver capacidade de compreensão sobre os assuntos descritos anteriormente e criar uma aplicação capaz de testar a aleatoriedade dos números gerados pelo Luna SA, assim como avaliar a segurança do sistema criptográfico RSA. Este foi um trabalho desenvolvido em parceria com a Universidade do Minho e com a Multicert

Design and Analysis of Cryptographic Pseudorandom Number/Sequence Generators with Applications in RFID

This thesis is concerned with the design and analysis of strong de Bruijn sequences and span n sequences, and nonlinear feedback shift register (NLFSR) based pseudorandom number generators for radio frequency identification (RFID) tags. We study the generation of span n sequences using structured searching in which an NLFSR with a class of feedback functions is employed to find span n sequences. Some properties of the recurrence relation for the structured search are discovered. We use five classes of functions in this structured search, and present the number of span n sequences for 6 <= n <= 20. The linear span of a new span n sequence lies between near-optimal and optimal. According to our empirical studies, a span n sequence can be found in the structured search with a better probability of success. Newly found span n sequences can be used in the composited construction and in designing lightweight pseudorandom number generators. We first refine the composited construction based on a span n sequence for generating long de Bruijn sequences. A de Bruijn sequence produced by the composited construction is referred to as a composited de Bruijn sequence. The linear complexity of a composited de Bruijn sequence is determined. We analyze the feedback function of the composited construction from an approximation point of view for producing strong de Bruijn sequences. The cycle structure of an approximated feedback function and the linear complexity of a sequence produced by an approximated feedback function are determined. A few examples of strong de Bruijn sequences with the implementation issues of the feedback functions of an (n+16)-stage NLFSR are presented. We propose a new lightweight pseudorandom number generator family, named Warbler family based on NLFSRs for smart devices. Warbler family is comprised of a combination of modified de Bruijn blocks (CMDB) and a nonlinear feedback Welch-Gong (WG) generator. We derive the randomness properties such as period and linear complexity of an output sequence produced by the Warbler family. Two instances, Warbler-I and Warbler-II, of the Warbler family are proposed for passive RFID tags. The CMDBs of both Warbler-I and Warbler-II contain span n sequences that are produced by the structured search. We analyze the security properties of Warbler-I and Warbler-II by considering the statistical tests and several cryptanalytic attacks. Hardware implementations of both instances in VHDL show that Warbler-I and Warbler-II require 46 slices and 58 slices, respectively. Warbler-I can be used to generate 16-bit random numbers in the tag identification protocol of the EPC Class 1 Generation 2 standard, and Warbler-II can be employed as a random number generator in the tag identification as well as an authentication protocol for RFID systems.1 yea