Digital Design of New Chaotic Ciphers for Ethernet Traffic

Durante los últimos años, ha habido un gran desarrollo en el campo de la criptografía, y muchos algoritmos de encriptado así como otras funciones criptográficas han sido propuestos.Sin embargo, a pesar de este desarrollo, hoy en día todavía existe un gran interés en crear nuevas primitivas criptográficas o mejorar las ya existentes. Algunas de las razones son las siguientes:• Primero, debido el desarrollo de las tecnologías de la comunicación, la cantidad de información que se transmite está constantemente incrementándose. En este contexto, existen numerosas aplicaciones que requieren encriptar una gran cantidad de datos en tiempo real o en un intervalo de tiempo muy reducido. Un ejemplo de ello puede ser el encriptado de videos de alta resolución en tiempo real. Desafortunadamente, la mayoría de los algoritmos de encriptado usados hoy en día no son capaces de encriptar una gran cantidad de datos a alta velocidad mientras mantienen altos estándares de seguridad.• Debido al gran aumento de la potencia de cálculo de los ordenadores, muchos algoritmos que tradicionalmente se consideraban seguros, actualmente pueden ser atacados por métodos de “fuerza bruta” en una cantidad de tiempo razonable. Por ejemplo, cuando el algoritmo de encriptado DES (Data Encryption Standard) fue lanzado por primera vez, el tamaño de la clave era sólo de 56 bits mientras que, hoy en día, el NIST (National Institute of Standards and Technology) recomienda que los algoritmos de encriptado simétricos tengan una clave de, al menos, 112 bits. Por otro lado, actualmente se está investigando y logrando avances significativos en el campo de la computación cuántica y se espera que, en el futuro, se desarrollen ordenadores cuánticos a gran escala. De ser así, se ha demostrado que algunos algoritmos que se usan actualmente como el RSA (Rivest Shamir Adleman) podrían ser atacados con éxito.• Junto al desarrollo en el campo de la criptografía, también ha habido un gran desarrollo en el campo del criptoanálisis. Por tanto, se están encontrando nuevas vulnerabilidades y proponiendo nuevos ataques constantemente. Por consiguiente, es necesario buscar nuevos algoritmos que sean robustos frente a todos los ataques conocidos para sustituir a los algoritmos en los que se han encontrado vulnerabilidades. En este aspecto, cabe destacar que algunos algoritmos como el RSA y ElGamal están basados en la suposición de que algunos problemas como la factorización del producto de dos números primos o el cálculo de logaritmos discretos son difíciles de resolver. Sin embargo, no se ha descartado que, en el futuro, se puedan desarrollar algoritmos que resuelvan estos problemas de manera rápida (en tiempo polinomial).• Idealmente, las claves usadas para encriptar los datos deberían ser generadas de manera aleatoria para ser completamente impredecibles. Dado que las secuencias generadas por generadores pseudoaleatorios, PRNGs (Pseudo Random Number Generators) son predecibles, son potencialmente vulnerables al criptoanálisis. Por tanto, las claves suelen ser generadas usando generadores de números aleatorios verdaderos, TRNGs (True Random Number Generators). Desafortunadamente, los TRNGs normalmente generan los bits a menor velocidad que los PRNGs y, además, las secuencias generadas suelen tener peores propiedades estadísticas, lo que hace necesario que pasen por una etapa de post-procesado. El usar un TRNG de baja calidad para generar claves, puede comprometer la seguridad de todo el sistema de encriptado, como ya ha ocurrido en algunas ocasiones. Por tanto, el diseño de nuevos TRNGs con buenas propiedades estadísticas es un tema de gran interés.En resumen, es claro que existen numerosas líneas de investigación en el ámbito de la criptografía de gran importancia. Dado que el campo de la criptografía es muy amplio, esta tesis se ha centra en tres líneas de investigación: el diseño de nuevos TRNGs, el diseño de nuevos cifradores de flujo caóticos rápidos y seguros y, finalmente, la implementación de nuevos criptosistemas para comunicaciones ópticas Gigabit Ethernet a velocidades de 1 Gbps y 10 Gbps. Dichos criptosistemas han estado basados en los algoritmos caóticos propuestos, pero se han adaptado para poder realizar el encriptado en la capa física, manteniendo el formato de la codificación. De esta forma, se ha logrado que estos sistemas sean capaces no sólo de encriptar los datos sino que, además, un atacante no pueda saber si se está produciendo una comunicación o no. Los principales aspectos cubiertos en esta tesis son los siguientes:• Estudio del estado del arte, incluyendo los algoritmos de encriptado que se usan actualmente. En esta parte se analizan los principales problemas que presentan los algoritmos de encriptado standard actuales y qué soluciones han sido propuestas. Este estudio es necesario para poder diseñar nuevos algoritmos que resuelvan estos problemas.• Propuesta de nuevos TRNGs adecuados para la generación de claves. Se exploran dos diferentes posibilidades: el uso del ruido generado por un acelerómetro MEMS (Microelectromechanical Systems) y el ruido generado por DNOs (Digital Nonlinear Oscillators). Ambos casos se analizan en detalle realizando varios análisis estadísticos a secuencias obtenidas a distintas frecuencias de muestreo. También se propone y se implementa un algoritmo de post-procesado simple para mejorar la aleatoriedad de las secuencias generadas. Finalmente, se discute la posibilidad de usar estos TRNGs como generadores de claves. • Se proponen nuevos algoritmos de encriptado que son rápidos, seguros y que pueden implementarse usando una cantidad reducida de recursos. De entre todas las posibilidades, esta tesis se centra en los sistemas caóticos ya que, gracias a sus propiedades intrínsecas como la ergodicidad o su comportamiento similar al comportamiento aleatorio, pueden ser una buena alternativa a los sistemas de encriptado clásicos. Para superar los problemas que surgen cuando estos sistemas son digitalizados, se proponen y estudian diversas estrategias: usar un sistema de multi-encriptado, cambiar los parámetros de control de los sistemas caóticos y perturbar las órbitas caóticas.• Se implementan los algoritmos propuestos. Para ello, se usa una FPGA Virtex 7. Las distintas implementaciones son analizadas y comparadas, teniendo en cuenta diversos aspectos tales como el consumo de potencia, uso de área, velocidad de encriptado y nivel de seguridad obtenido. Uno de estos diseños, se elige para ser implementado en un ASIC (Application Specific Integrate Circuit) usando una tecnología de 0,18 um. En cualquier caso, las soluciones propuestas pueden ser también implementadas en otras plataformas y otras tecnologías.• Finalmente, los algoritmos propuestos se adaptan y aplican a comunicaciones ópticas Gigabit Ethernet. En particular, se implementan criptosistemas que realizan el encriptado al nivel de la capa física para velocidades de 1 Gbps y 10 Gbps. Para realizar el encriptado en la capa física, los algoritmos propuestos en las secciones anteriores se adaptan para que preserven el formato de la codificación, 8b/10b en el caso de 1 Gb Ethernet y 64b/10b en el caso de 10 Gb Ethernet. En ambos casos, los criptosistemas se implementan en una FPGA Virtex 7 y se diseña un set experimental, que incluye dos módulos SFP (Small Form-factor Pluggable) capaces de transmitir a una velocidad de hasta 10.3125 Gbps sobre una fibra multimodo de 850 nm. Con este set experimental, se comprueba que los sistemas de encriptado funcionan correctamente y de manera síncrona. Además, se comprueba que el encriptado es bueno (pasa todos los test de seguridad) y que el patrón del tráfico de datos está oculto.<br /

A Chaos-Based Authenticated Cipher with Associated Data

In recent years, there has been a rising interest in authenticated encryptionwith associated data (AEAD)which combines encryption and authentication into a unified scheme. AEAD schemes provide authentication for a message that is divided into two parts: associated data which is not encrypted and the plaintext which is encrypted. However, there is a lack of chaos-based AEAD schemes in recent literature. This paper introduces a new128-bit chaos-based AEAD scheme based on the single-key Even-Mansour and Type-II generalized Feistel structure. The proposed scheme provides both privacy and authentication in a single-pass using only one 128-bit secret key. The chaotic tent map is used to generate whitening keys for the Even-Mansour construction, round keys, and random s-boxes for the Feistel round function. In addition, the proposed AEAD scheme can be implemented with true randomnumber generators to map a message tomultiple possible ciphertexts in a nondeterministic manner. Security and statistical evaluation indicate that the proposed scheme is highly secure for both the ciphertext and the authentication tag. Furthermore, it has multiple advantages over AES-GCM which is the current standard for authenticated encryption

A new simple technique for improving the random properties of chaos-based cryptosystems

A new technique for improving the security of chaos-based stream ciphers has been proposed and tested experimentally. This technique manages to improve the randomness properties of the generated keystream by preventing the system to fall into short period cycles due to digitation. In order to test this technique, a stream cipher based on a Skew Tent Map algorithm has been implemented on a Virtex 7 FPGA. The randomness of the keystream generated by this system has been compared to the randomness of the keystream generated by the same system with the proposed randomness-enhancement technique. By subjecting both keystreams to the National Institute of Standards and Technology (NIST) tests, we have proved that our method can considerably improve the randomness of the generated keystreams. In order to incorporate our randomness-enhancement technique, only 41 extra slices have been needed, proving that, apart from effective, this method is also efficient in terms of area and hardware resources

Some Words on Cryptanalysis of Stream Ciphers

In the world of cryptography, stream ciphers are known as primitives used to ensure privacy over a communication channel. One common way to build a stream cipher is to use a keystream generator to produce a pseudo-random sequence of symbols. In such algorithms, the ciphertext is the sum of the keystream and the plaintext, resembling the one-time pad principal. Although the idea behind stream ciphers is simple, serious investigation of these primitives has started only in the late 20th century. Therefore, cryptanalysis and design of stream ciphers are important. In recent years, many designs of stream ciphers have been proposed in an effort to find a proper candidate to be chosen as a world standard for data encryption. That potential candidate should be proven good by time and by the results of cryptanalysis. Different methods of analysis, in fact, explain how a stream cipher should be constructed. Thus, techniques for cryptanalysis are also important. This thesis starts with an overview of cryptography in general, and introduces the reader to modern cryptography. Later, we focus on basic principles of design and analysis of stream ciphers. Since statistical methods are the most important cryptanalysis techniques, they will be described in detail. The practice of statistical methods reveals several bottlenecks when implementing various analysis algorithms. For example, a common property of a cipher to produce n-bit words instead of just bits makes it more natural to perform a multidimensional analysis of such a design. However, in practice, one often has to truncate the words simply because the tools needed for analysis are missing. We propose a set of algorithms and data structures for multidimensional cryptanalysis when distributions over a large probability space have to be constructed. This thesis also includes results of cryptanalysis for various cryptographic primitives, such as A5/1, Grain, SNOW 2.0, Scream, Dragon, VMPC, RC4, and RC4A. Most of these results were achieved with the help of intensive use of the proposed tools for cryptanalysis

Analysis and Design Security Primitives Based on Chaotic Systems for eCommerce

Security is considered the most important requirement for the success of electronic commerce, which is built based on the security of hash functions, encryption algorithms and pseudorandom number generators. Chaotic systems and security algorithms have similar properties including sensitivity to any change or changes in the initial parameters, unpredictability, deterministic nature and random-like behaviour. Several security algorithms based on chaotic systems have been proposed; unfortunately some of them were found to be insecure and/or slow. In view of this, designing new secure and fast security algorithms based on chaotic systems which guarantee integrity, authentication and confidentiality is essential for electronic commerce development. In this thesis, we comprehensively explore the analysis and design of security primitives based on chaotic systems for electronic commerce: hash functions, encryption algorithms and pseudorandom number generators. Novel hash functions, encryption algorithms and pseudorandom number generators based on chaotic systems for electronic commerce are proposed. The securities of the proposed algorithms are analyzed based on some well-know statistical tests in this filed. In addition, a new one-dimensional triangle-chaotic map (TCM) with perfect chaotic behaviour is presented. We have compared the proposed chaos-based hash functions, block cipher and pseudorandom number generator with well-know algorithms. The comparison results show that the proposed algorithms are better than some other existing algorithms. Several analyses and computer simulations are performed on the proposed algorithms to verify their characteristics, confirming that these proposed algorithms satisfy the characteristics and conditions of security algorithms. The proposed algorithms in this thesis are high-potential for adoption in e-commerce applications and protocols

Security of Ubiquitous Computing Systems

The chapters in this open access book arise out of the EU Cost Action project Cryptacus, the objective of which was to improve and adapt existent cryptanalysis methodologies and tools to the ubiquitous computing framework. The cryptanalysis implemented lies along four axes: cryptographic models, cryptanalysis of building blocks, hardware and software security engineering, and security assessment of real-world systems. The authors are top-class researchers in security and cryptography, and the contributions are of value to researchers and practitioners in these domains. This book is open access under a CC BY license

Iterative decoding of Gold sequences

International audienceGold sequences are widely used in communications and positioning systems for synchronization purposes or spread spectrum transmissions. This paper addresses the decoding of the initial state of a Gold sequence. This can be used to detect a harmful interferer closed to a 3G femtocell base station and implement interference mitigation techniques. The decoder implements an iterative message-passing algorithm which is built upon a parity check matrix. Thus, it depends on the coding properties of Gold codes. In this paper, we synthesize the coding properties of Gold codes and use them to compute the number of parity check equations of weight t = 3, 4 or 5. Eventually, the impact of the parity check equations used for decoding is highlighted

On Some Symmetric Lightweight Cryptographic Designs

This dissertation presents cryptanalysis of several symmetric lightweight primitives, both stream ciphers and block ciphers. Further, some aspects of authentication in combination with a keystream generator is investigated, and a new member of the Grain family of stream ciphers, Grain-128a, with built-in support for authentication is presented. The first contribution is an investigation of how authentication can be provided at a low additional cost, assuming a synchronous stream cipher is already implemented and used for encryption. These findings are then used when presenting the latest addition to the Grain family of stream ciphers, Grain-128a. It uses a 128-bit key and a 96-bit initialization vector to generate keystream, and to possibly also authenticate the plaintext. Next, the stream cipher BEAN, superficially similar to Grain, but notably using a weak output function and two feedback with carry shift registers (FCSRs) rather than linear and (non-FCSR) nonlinear feedback shift registers, is cryptanalyzed. An efficient distinguisher and a state-recovery attack is given. It is shown how knowledge of the state can be used to recover the key in a straightforward way. The remainder of this dissertation then focuses on block ciphers. First, a related-key attack on KTANTAN is presented. The attack notably uses only a few related keys, runs in less than half a minute on a current computer, and directly contradicts the designers' claims. It is discussed why this is, and what can be learned from this. Next, PRINTcipher is subjected to linear cryptanalysis. Several weak key classes are identified and it is shown how several observations of the same statistical property can be made for each plaintext--ciphertext pair. Finally, the invariant subspace property, first observed for certain key classes in PRINTcipher, is investigated. In particular, its connection to large linear biases is studied through an eigenvector which arises inside the cipher and leads to trail clustering in the linear hull which, under reasonable assumptions, causes a significant number of large linear biases. Simulations on several versions of PRINTcipher are compared to the theoretical findings

Contributions to Confidentiality and Integrity Algorithms for 5G

The confidentiality and integrity algorithms in cellular networks protect the transmission of user and signaling data over the air between users and the network, e.g., the base stations. There are three standardised cryptographic suites for confidentiality and integrity protection in 4G, which are based on the AES, SNOW 3G, and ZUC primitives, respectively. These primitives are used for providing a 128-bit security level and are usually implemented in hardware, e.g., using IP (intellectual property) cores, thus can be quite efficient. When we come to 5G, the innovative network architecture and high-performance demands pose new challenges to security. For the confidentiality and integrity protection, there are some new requirements on the underlying cryptographic algorithms. Specifically, these algorithms should: 1) provide 256 bits of security to protect against attackers equipped with quantum computing capabilities; and 2) provide at least 20 Gbps (Gigabits per second) speed in pure software environments, which is the downlink peak data rate in 5G. The reason for considering software environments is that the encryption in 5G will likely be moved to the cloud and implemented in software. Therefore, it is crucial to investigate existing algorithms in 4G, checking if they can satisfy the 5G requirements in terms of security and speed, and possibly propose new dedicated algorithms targeting these goals. This is the motivation of this thesis, which focuses on the confidentiality and integrity algorithms for 5G. The results can be summarised as follows.1. We investigate the security of SNOW 3G under 256-bit keys and propose two linear attacks against it with complexities 2172 and 2177, respectively. These cryptanalysis results indicate that SNOW 3G cannot provide the full 256-bit security level. 2. We design some spectral tools for linear cryptanalysis and apply these tools to investigate the security of ZUC-256, the 256-bit version of ZUC. We propose a distinguishing attack against ZUC-256 with complexity 2236, which is 220 faster than exhaustive key search. 3. We design a new stream cipher called SNOW-V in response to the new requirements for 5G confidentiality and integrity protection, in terms of security and speed. SNOW-V can provide a 256-bit security level and achieve a speed as high as 58 Gbps in software based on our extensive evaluation. The cipher is currently under evaluation in ETSI SAGE (Security Algorithms Group of Experts) as a promising candidate for 5G confidentiality and integrity algorithms. 4. We perform deeper cryptanalysis of SNOW-V to ensure that two common cryptanalysis techniques, guess-and-determine attacks and linear cryptanalysis, do not apply to SNOW-V faster than exhaustive key search. 5. We introduce two minor modifications in SNOW-V and propose an extreme performance variant, called SNOW-Vi, in response to the feedback about SNOW-V that some use cases are not fully covered. SNOW-Vi covers more use cases, especially some platforms with less capabilities. The speeds in software are increased by 50% in average over SNOW-V and can be up to 92 Gbps.Besides these works on 5G confidentiality and integrity algorithms, the thesis is also devoted to local pseudorandom generators (PRGs). 6. We investigate the security of local PRGs and propose two attacks against some constructions instantiated on the P5 predicate. The attacks improve existing results with a large gap and narrow down the secure parameter regime. We also extend the attacks to other local PRGs instantiated on general XOR-AND and XOR-MAJ predicates and provide some insight in the choice of safe parameters

Selected Topics in Cryptanalysis of Symmetric Ciphers

It is well established that a symmetric cipher may be described as a system of Boolean polynomials, and that the security of the cipher cannot be better than the difficulty of solving said system. Compressed Right-Hand Side (CRHS) Equations is but one way of describing a symmetric cipher in terms of Boolean polynomials. The first paper of this thesis provides a comprehensive treatment firstly of the relationship between Boolean functions in algebraic normal form, Binary Decision Diagrams and CRHS equations. Secondly, of how CRHS equations may be used to describe certain kinds of symmetric ciphers and how this model may be used to attempt a key-recovery attack. This technique is not left as a theoretical exercise, as the process have been implemented as an open-source project named CryptaPath. To ensure accessibility for researchers unfamiliar with algebraic cryptanalysis, CryptaPath can convert a reference implementation of the target cipher, as specified by a Rust trait, into the CRHS equations model automatically. CRHS equations are not limited to key-recovery attacks, and Paper II explores one such avenue of CRHS equations flexibility. Linear and differential cryptanalysis have long since established their position as two of the most important cryptanalytical attacks, and every new design since must show resistance to both. For some ciphers, like the AES, this resistance can be mathematically proven, but many others are left to heuristic arguments and computer aided proofs. This work is tedious, and most of the tools require good background knowledge of a tool/technique to transform a design to the right input format, with a notable exception in CryptaGraph. CryptaGraph is written in Rust and transforms a reference implementation into CryptaGraphs underlying data structure automatically. Paper II introduces a new way to use CRHS equations to model a symmetric cipher, this time in such a way that linear and differential trail searches are possible. In addition, a new set of operations allowing us to count the number of active S-boxes in a path is presented. Due to CRHS equations effective initial data compression, all possible trails are captured in the initial system description. As is the case with CRHS equations, the crux is the memory consumption. However, this approach also enables the graph of a CRHS equation to be pruned, allowing the memory consumption to be kept at manageable levels. Unfortunately, pruning nodes also means that we will lose valid, incomplete paths, meaning that the hulls found are probably incomplete. On the flip side, all paths, and their corresponding probabilities, found by the tool are guaranteed to be valid trails for the cipher. This theory is also implemented in an extension of CryptaPath, and the name is PathFinder. PathFinder is also able to automatically turn a reference implementation of a cipher into its CRHS equations-based model. As an additional bonus, PathFinder supports the reference implementation specifications specified by CryptaGraph, meaning that the same reference implementation can be used for both CryptaGraph and PathFinder. Paper III shifts focus onto symmetric ciphers designed to be used in conjunction with FHE schemes. Symmetric ciphers designed for this purpose are relatively new and have naturally had a strong focus on reducing the number of multiplications performed. A multiplication is considered expensive on the noise budget of the FHE scheme, while linear operations are viewed as cheap. These ciphers are all assuming that it is possible to find parameters in the various FHE schemes which allow these ciphers to work well in symbiosis with the FHE scheme. Unfortunately, this is not always possible, with the consequence that the decryption process becomes more costly than necessary. Paper III therefore proposes Fasta, a stream cipher which has its parameters and linear layer especially chosen to allow efficient implementation over the BGV scheme, particularly as implemented in the HElib library. The linear layers are drawn from a family of rotation-based linear transformations, as cyclic rotations are cheap to do in FHE schemes that allow packing of multiple plaintext elements in one FHE ciphertext. Fasta follows the same design philosophy as Rasta, and will never use the same linear layer twice under the same key. The result is a stream cipher tailor-made for fast evaluation in HElib. Fasta shows an improvement in throughput of a factor more than 7 when compared to the most efficient implementation of Rasta.Doktorgradsavhandlin