Quantum nonlocality, cryptography and complexity

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

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.

Independent Domain of Symmetric Encryption using Least SignificantBit : Computer Vision, Steganography and Cryptography Techniques

The rapid development of data transfer through internet made it easier to send the data accurate and faster to the destination. There are many transmission media to transfer the data to destination like e-mails; at the same time it is may be easier to modify and misuse the valuable information through hacking. So, in order to transfer the data securely to the destination without any modifications, there are many approaches like cryptography and steganography. This paper deals with the image steganography as well as with the different security issues, general overview of cryptography, steganography and digital watermarking approaches.  The problem of copyright violation of multimedia data has increased due to the enormous growth of computer networks that provides fast and error free transmission of any unauthorized duplicate and possibly manipulated copy of multimedia information. In order to be effective for copyright protection, digital watermark must be robust which are difficult to remove from the object in which they are embedded despite a variety of possible attacks. The message to be send safe and secure, we use watermarking. We use invisible watermarking to embed the message using LSB (Least Significant Bit) steganographic technique. The standard LSB technique embed the message in every pixel, but my contribution for this proposed watermarking, works with the hint for embedding the message only on the image edges alone. If the hacker knows that the system uses LSB technique also, it cannot decrypt correct message. To make my system robust and secure, we added cryptography algorithm as Vigenere square. Whereas the message is transmitted in cipher text and its added advantage to the proposed system. The standard Vigenere square algorithm works with either lower case or upper case. The proposed cryptography algorithm is Vigenere square with extension of numbers also. We can keep the crypto key with combination of characters and numbers. So by using these modifications and updating in this existing algorithm and combination of cryptography and steganography method we develop a secure and strong watermarking method. Performance of this watermarking scheme has been analyzed by evaluating the robustness of the algorithm with PSNR (Peak Signal to Noise Ratio) and MSE (Mean Square Error) against the quality of the image for large amount of data. While coming to see results of the proposed encryption, higher value of 89dB of PSNR with small value of MSE is 0.0017. Then it seems the proposed watermarking system is secure and robust for hiding secure information in any digital system, because this system collect the properties of both steganography and cryptography sciences.

Who is the cowboy in Washington?: beating google at their own game with neuroscience and cryptography

Who was the cowboy in Washington? What is the land of sushi? Most people would have answers to these questions readily available,yet, modern search engines, arguably the epitome of technology in finding answers to most questions, are completely unable to do so. It seems that people capture few information items to rapidly converge to a seemingly 'obvious' solution. We will study approaches for this problem, with two additional hard demands that constrain the space of possible theories: the sought model must be both psychologically and neuroscienti cally plausible. Building on top of the mathematical model of memory called Sparse Distributed Memory, we will see how some well-known methods in cryptography can point toward a promising, comprehensive, solution that preserves four crucial properties of human psychology.

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.

Optical digital chaos cryptography

In this work we present a new way to mask the data in a one-user communication system when direct sequence - code division multiple access (DS-CDMA) techniques are used. The code is generated by a digital chaotic generator, originally proposed by us and previously reported for a chaos cryptographic system. It is demonstrated that if the user's data signal is encoded with a bipolar phase-shift keying (BPSK) technique, usual in DS-CDMA, it can be easily recovered from a time-frequency domain representation. To avoid this situation, a new system is presented in which a previous dispersive stage is applied to the data signal. A time-frequency domain analysis is performed, and the devices required at the transmitter and receiver end, both user-independent, are presented for the optical domain.

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.

Quantum cryptography without switching

We propose a new coherent state quantum key distribution protocol that eliminates the need to randomly switch between measurement bases. This protocol provides significantly higher secret key rates with increased bandwidths than previous schemes that only make single quadrature measurements. It also offers the further advantage of simplicity compared to all previous protocols which, to date, have relied on switching.

Public key cryptography and error correcting codes as Ising models

We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two randomly-constructed sparse matrices. We show that a broad range of these codes potentially saturate Shannon's bound but are limited due to the decoding dynamics used. Other codes show sub-optimal performance but are not restricted by the decoding dynamics. We show how these codes may also be employed as a practical public-key cryptosystem and are of competitive performance to modern cyptographical methods.