Using GPU to exploit parallelism on cryptography

In this article we explore the NVIDIA graphical processing units (GPU) computational power in cryptography using CUDA (Compute Unified Device Architecture) technology. CUDA makes the general purpose computing easy using the parallel processing presents in GPUs. To do this, the NVIDIA GPUs architectures and CUDA are presented, besides cryptography concepts. Furthermore, we do the comparison between the versions executed in CPU with the parallel version of the cryptography algorithms Advanced Encryption Standard (AES) and Message-digest Algorithm 5 (MD5) wrote in CUDA. © 2011 AISTI.

ANALYSIS AND VISUALIZATION OF FLOW FIELDS USING INFORMATION-THEORETIC TECHNIQUES AND GRAPH-BASED REPRESENTATIONS

Three-dimensional flow visualization plays an essential role in many areas of science and engineering, such as aero- and hydro-dynamical systems which dominate various physical and natural phenomena. For popular methods such as the streamline visualization to be effective, they should capture the underlying flow features while facilitating user observation and understanding of the flow field in a clear manner. My research mainly focuses on the analysis and visualization of flow fields using various techniques, e.g. information-theoretic techniques and graph-based representations. Since the streamline visualization is a popular technique in flow field visualization, how to select good streamlines to capture flow patterns and how to pick good viewpoints to observe flow fields become critical. We treat streamline selection and viewpoint selection as symmetric problems and solve them simultaneously using the dual information channel [81]. To the best of my knowledge, this is the first attempt in flow visualization to combine these two selection problems in a unified approach. This work selects streamline in a view-independent manner and the selected streamlines will not change for all viewpoints. My another work [56] uses an information-theoretic approach to evaluate the importance of each streamline under various sample viewpoints and presents a solution for view-dependent streamline selection that guarantees coherent streamline update when the view changes gradually. When projecting 3D streamlines to 2D images for viewing, occlusion and clutter become inevitable. To address this challenge, we design FlowGraph [57, 58], a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. We enable observation and exploration of the relationships among field line clusters, spatiotemporal regions and their interconnection in the transformed space. Most viewpoint selection methods only consider the external viewpoints outside of the flow field. This will not convey a clear observation when the flow field is clutter on the boundary side. Therefore, we propose a new way to explore flow fields by selecting several internal viewpoints around the flow features inside of the flow field and then generating a B-Spline curve path traversing these viewpoints to provide users with closeup views of the flow field for detailed observation of hidden or occluded internal flow features [54]. This work is also extended to deal with unsteady flow fields. Besides flow field visualization, some other topics relevant to visualization also attract my attention. In iGraph [31], we leverage a distributed system along with a tiled display wall to provide users with high-resolution visual analytics of big image and text collections in real time. Developing pedagogical visualization tools forms my other research focus. Since most cryptography algorithms use sophisticated mathematics, it is difficult for beginners to understand both what the algorithm does and how the algorithm does that. Therefore, we develop a set of visualization tools to provide users with an intuitive way to learn and understand these algorithms.

Secure architectures for pairing based public key cryptography

Along with the growing demand for cryptosystems in systems ranging from large servers to mobile devices, suitable cryptogrophic protocols for use under certain constraints are becoming more and more important. Constraints such as calculation time, area, efficiency and security, must be considered by the designer. Elliptic curves, since their introduction to public key cryptography in 1985 have challenged established public key and signature generation schemes such as RSA, offering more security per bit. Amongst Elliptic curve based systems, pairing based cryptographies are thoroughly researched and can be used in many public key protocols such as identity based schemes. For hardware implementions of pairing based protocols, all components which calculate operations over Elliptic curves can be considered. Designers of the pairing algorithms must choose calculation blocks and arrange the basic operations carefully so that the implementation can meet the constraints of time and hardware resource area. This thesis deals with different hardware architectures to accelerate the pairing based cryptosystems in the field of characteristic two. Using different top-level architectures the hardware efficiency of operations that run at different times is first considered in this thesis. Security is another important aspect of pairing based cryptography to be considered in practically Side Channel Analysis (SCA) attacks. The naively implemented hardware accelerators for pairing based cryptographies can be vulnerable when taking the physical analysis attacks into consideration. This thesis considered the weaknesses in pairing based public key cryptography and addresses the particular calculations in the systems that are insecure. In this case, countermeasures should be applied to protect the weak link of the implementation to improve and perfect the pairing based algorithms. Some important rules that the designers must obey to improve the security of the cryptosystems are proposed. According to these rules, three countermeasures that protect the pairing based cryptosystems against SCA attacks are applied. The implementations of the countermeasures are presented and their performances are investigated.

Secret Sharing Schemes Using Visual Cryptography

Secret sharing schemes allow a secret to be shared among a group of participants so that only qualified subsets of participants can recover the secret. A visual cryptography scheme (VCS) is a special kind of secret sharing scheme in which the secret to share consists of an image and the shares consist of xeroxed transparencies which are stacked to recover the shared image. In this thesis we have given the theoretical background of Secret Sharing Schemes and the historical development of the subject. We have included a few examples to improve the readability of the thesis. We have tried to maintain the rigor of the treatment of the subject. The limitations and disadvantages of the various forms secret sharing schemes are brought out. Several new schemes for both dealing and combining are included in the thesis. We have introduced a new number system, called, POB number system. Representation using POB number system has been presented. Algorithms for finding the POB number and POB value are given.We have also proved that the representation using POB number system is unique and is more efficient. Being a new system, there is much scope for further development in this area.

Algebraic Geometric Codes and their relation to Cryptography using Elliptic Curves

Communication is the process of transmitting data across channel. Whenever data is transmitted across a channel, errors are likely to occur. Coding theory is a stream of science that deals with finding efficient ways to encode and decode data, so that any likely errors can be detected and corrected. There are many methods to achieve coding and decoding. One among them is Algebraic Geometric Codes that can be constructed from curves. Cryptography is the science ol‘ security of transmitting messages from a sender to a receiver. The objective is to encrypt message in such a way that an eavesdropper would not be able to read it. A eryptosystem is a set of algorithms for encrypting and decrypting for the purpose of the process of encryption and decryption. Public key eryptosystem such as RSA and DSS are traditionally being prel‘en‘ec| for the purpose of secure communication through the channel. llowever Elliptic Curve eryptosystem have become a viable altemative since they provide greater security and also because of their usage of key of smaller length compared to other existing crypto systems. Elliptic curve cryptography is based on group of points on an elliptic curve over a finite field. This thesis deals with Algebraic Geometric codes and their relation to Cryptography using elliptic curves. Here Goppa codes are used and the curves used are elliptic curve over a finite field. We are relating Algebraic Geometric code to Cryptography by developing a cryptographic algorithm, which includes the process of encryption and decryption of messages. We are making use of fundamental properties of Elliptic curve cryptography for generating the algorithm and is used here to relate both.

FAST, PARALLEL AND SECURE CRYPTOGRAPHY ALGORITHM USING LORENZ`S ATTRACTOR

A novel cryptography method based on the Lorenz`s attractor chaotic system is presented. The proposed algorithm is secure and fast, making it practical for general use. We introduce the chaotic operation mode, which provides an interaction among the password, message and a chaotic system. It ensures that the algorithm yields a secure codification, even if the nature of the chaotic system is known. The algorithm has been implemented in two versions: one sequential and slow and the other, parallel and fast. Our algorithm assures the integrity of the ciphertext (we know if it has been altered, which is not assured by traditional algorithms) and consequently its authenticity. Numerical experiments are presented, discussed and show the behavior of the method in terms of security and performance. The fast version of the algorithm has a performance comparable to AES, a popular cryptography program used commercially nowadays, but it is more secure, which makes it immediately suitable for general purpose cryptography applications. An internet page has been set up, which enables the readers to test the algorithm and also to try to break into the cipher.

Vector Boolean Functions: Applications in Symmetric Cryptography

Esta tesis establece los fundamentos teóricos y diseña una colección abierta de clases C++ denominada VBF (Vector Boolean Functions) para analizar funciones booleanas vectoriales (funciones que asocian un vector booleano a otro vector booleano) desde una perspectiva criptográfica. Esta nueva implementación emplea la librería NTL de Victor Shoup, incorporando nuevos módulos que complementan a las funciones de NTL, adecuándolas para el análisis criptográfico. La clase fundamental que representa una función booleana vectorial se puede inicializar de manera muy flexible mediante diferentes estructuras de datas tales como la Tabla de verdad, la Representación de traza y la Forma algebraica normal entre otras. De esta manera VBF permite evaluar los criterios criptográficos más relevantes de los algoritmos de cifra en bloque y de stream, así como funciones hash: por ejemplo, proporciona la no-linealidad, la distancia lineal, el grado algebraico, las estructuras lineales, la distribución de frecuencias de los valores absolutos del espectro Walsh o del espectro de autocorrelación, entre otros criterios. Adicionalmente, VBF puede llevar a cabo operaciones entre funciones booleanas vectoriales tales como la comprobación de igualdad, la composición, la inversión, la suma, la suma directa, el bricklayering (aplicación paralela de funciones booleanas vectoriales como la empleada en el algoritmo de cifra Rijndael), y la adición de funciones coordenada. La tesis también muestra el empleo de la librería VBF en dos aplicaciones prácticas. Por un lado, se han analizado las características más relevantes de los sistemas de cifra en bloque. Por otro lado, combinando VBF con algoritmos de optimización, se han diseñado funciones booleanas cuyas propiedades criptográficas son las mejores conocidas hasta la fecha. ABSTRACT This thesis develops the theoretical foundations and designs an open collection of C++ classes, called VBF, designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This new implementation uses the NTL library from Victor Shoup, adding new modules which complement the existing ones making VBF better suited for cryptography. The fundamental class representing a vector Boolean function can be initialized in a flexible way via several alternative types of data structures such as Truth Table, Trace Representation, Algebraic Normal Form (ANF) among others. This way, VBF allows the evaluation of the most relevant cryptographic criteria for block and stream ciphers as well as for hash functions: for instance, it provides the nonlinearity, the linearity distance, the algebraic degree, the linear structures, the frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, VBF can perform operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions. This thesis also illustrates the use of VBF in two practical applications. On the one hand, the most relevant properties of the existing block ciphers have been analysed. On the other hand, by combining VBF with optimization algorithms, new Boolean functions have been designed which have the best known cryptographic properties up-to-date.

On Graph-Based Cryptography and Symbolic Computations

We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed graphs of large girth and their cryptographical applications. It contains new explicit algebraic constructions of in finite families of such graphs. We show that they can be used for the implementation of secure and very fast symmetric encryption algorithms. The symbolic computations technique allow us to create a public key mode for the encryption scheme based on algebraic graphs.