Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems

Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This paper aims at developing a novel methodology to design the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy the Devaney's definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via FPGA platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.Comment: 12 page

Constructing multiwing attractors from a robust chaotic system with non-hyperbolic equilibrium points

We investigate a three-dimensional (3D) robust chaotic system which only holds two nonhyperbolic equilibrium points, and finds the complex dynamical behaviour of position modulation beyond amplitude modulation. To extend the application of this chaotic system, we initiate a novel methodology to construct multiwing chaotic attractors by modifying the position and amplitude parameters. Moreover, the signal amplitude, range and distance of the generated multiwings can be easily adjusted by using the control parameters, which enable us to enhance the potential application in chaotic cryptography and secure communication. The effectiveness of the theoretical analyses is confirmed by numerical simulations. Particularly, the multiwing attractor is physically realized by using DSP (digital signal processor) chip

DNA and Plaintext Dependent Chaotic Visual Selective Image Encryption

Visual selective image encryption can both improve the efficiency of the image encryption algorithm and reduce the frequency and severity of attacks against data. In this article, a new form of encryption is proposed based on keys derived from Deoxyribonucleic Acid (DNA) and plaintext image. The proposed scheme results in chaotic visual selective encryption of image data. In order to make and ensure that this new scheme is robust and secure against various kinds of attacks, the initial conditions of the chaotic maps utilized are generated from a random DNA sequence as well as plaintext image via an SHA-512 hash function. To increase the key space, three different single dimension chaotic maps are used. In the proposed scheme, these maps introduce diffusion in a plain image by selecting a block that have greater correlation and then it is bitwise XORed with the random matrix. The other two chaotic maps break the correlation among adjacent pixels via confusion (row and column shuffling). Once the ciphertext image has been divided into the respective units of Most Significant Bits (MSBs) and Least Significant Bit (LSBs), the host image is passed through lifting wavelet transformation, which replaces the low-frequency blocks of the host image (i.e., HL and HH) with the aforementioned MSBs and LSBs of ciphertext. This produces a final visual selective encrypted image and all security measures proves the robustness of the proposed scheme

A Primer on Cryptographic Multilinear Maps and Code Obfuscation

The construction of cryptographic multilinear maps and a general-purpose code obfuscator were two long-standing open problems in cryptography. It has been clear for a number of years that constructions of these two primitives would yield many interesting applications. This thesis describes the Coron-Lepoint-Tibouchi candidate construction for multilinear maps, as well as new candidates for code obfuscation. We give an overview of current multilinear and obfuscation research, and present some relevant applications. We also provide some examples and warnings regarding the inefficiency of the new constructions. The presentation is self-contained and should be accessible to the novice reader

Entropy in Image Analysis II

Image analysis is a fundamental task for any application where extracting information from images is required. The analysis requires highly sophisticated numerical and analytical methods, particularly for those applications in medicine, security, and other fields where the results of the processing consist of data of vital importance. This fact is evident from all the articles composing the Special Issue "Entropy in Image Analysis II", in which the authors used widely tested methods to verify their results. In the process of reading the present volume, the reader will appreciate the richness of their methods and applications, in particular for medical imaging and image security, and a remarkable cross-fertilization among the proposed research areas

Security, Scalability and Privacy in Applied Cryptography

In the modern digital world, cryptography finds its place in countless applications. However, as we increasingly use technology to perform potentially sensitive tasks, our actions and private data attract, more than ever, the interest of ill-intentioned actors. Due to the possible privacy implications of cryptographic flaws, new primitives’ designs need to undergo rigorous security analysis and extensive cryptanalysis to foster confidence in their adoption. At the same time, implementations of cryptographic protocols should scale on a global level and be efficiently deployable on users’ most common devices to widen the range of their applications. This dissertation will address the security, scalability and privacy of cryptosystems by presenting new designs and cryptanalytic results regarding blockchain cryptographic primitives and public-key schemes based on elliptic curves. In Part I, I will present the works I have done in regards to accumulator schemes. More precisely, in Chapter 2, I cryptanalyze Au et al. Dynamic Universal Accumulator, by showing some attacks which can completely take over the authority who manages the accumulator. In Chapter 3, I propose a design for an efficient and secure accumulator-based authentication mechanism, which is scalable, privacy-friendly, lightweight on the users’ side, and suitable to be implemented on the blockchain. In Part II, I will report some cryptanalytical results on primitives employed or considered for adoption in top blockchain-based cryptocurrencies. In particular, in Chapter 4, I describe how the zero-knowledge proof system and the commitment scheme adopted by the privacy-friendly cryptocurrency Zcash, contain multiple subliminal channels which can be exploited to embed several bytes of tagging information in users’ private transactions. In Chapter 5, instead, I report the cryptanalysis of the Legendre PRF, employed in a new consensus mechanism considered for adoption by the blockchain-based platform Ethereum, and attacks for further generalizations of this pseudo-random function, such as the Higher-Degree Legendre PRF, the Jacobi Symbol PRF, and the Power-Residue PRF. Lastly, in Part III, I present my line of research on public-key primitives based on elliptic curves. In Chapter 6, I will describe a backdooring procedure for primes so that whenever they appear as divisors of a large integer, the latter can be efficiently factored. This technique, based on elliptic curves Complex Multiplication theory, enables to eventually generate non-vulnerable certifiable semiprimes with unknown factorization in a multi-party computation setting, with no need to run a statistical semiprimality test common to other protocols. In Chapter 7, instead, I will report some attack optimizations and specific implementation design choices that allow breaking a reduced-parameters instance, proposed by Microsoft, of SIKE, a post-quantum key-encapsulation mechanism based on isogenies between supersingular elliptic curves