This paper performs the cryptanalysis of a newly proposed chaotic image cipher using latin squarebased confusion and diffusion. There is a standardization process for cryptosystems based on theoretical research in mathematics and complexity theory. In recent years, a variety of chaos based image cryptosystems have been proposed. Theory and practice of cryptography and network security protocols and technologies edited by jaydip sen. The unpredictable nature of a deterministic system would seem to lend itself well to be a basis of a cryptosystem. Cryptography refers almost exclusively to encryption, the process of converting ordinary information plaintext into unintelligible gibberish i. In 1996, baptista published his paper entitled cryptography with chaos. Speech cryptography literature has recently shown an increased utilization of chaos theory as well. Theory and practice of chaotic cryptography sciencedirect. This pdf ebook is one of digital edition of cryptography.
Request pdf theory and practice of chaotic cryptography in this letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. Chaos theory aims to understand the asymptotic behavior of iterative process whereas cryptography focuses on the properties of a number of first few iterations chaos and cryptology. In the substitution stage, a two or higherdimensional chaotic map is employed to shuffle the image pixels for confusion purpose. The last fifth chapter is assigned to the summary of findings and possibilities to solve some problems of the so called chaotic cryptography. The application of the chaos theory in cryptography.
Authentication, chaos theory, cryptography, cryptanalysis. Theory and practice garnered enormous praise and popularity, and soon became the standard textbook for cryptography courses around the world. Chaos theory is a branch of mathematics that involves deterministic systems whose behavior are very dependent on initial conditions. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. Chaotic electronic circuits in cryptography matej alamon university of maribor, faculty of electrical engineering and compute r science slovenia 1. A system is simply a set of interacting components that form a larger whole. A chaotic henon map is used to generate a random sequence for the aes algorithm, and the shuffledimage is encrypted using the aes algorithm. Chaos based cryptography, attracting many researchers in the past decade, is a research field across two fields, i. In this paper, a novel image encryption scheme is proposed based on combination of. Pdf modern cryptography theory and practice isromi. Theory and practice provides a comprehensive treatment of publickey cryptosystems and the associated cryptanalytic techniques. In this paper, chaos based cryptography is discussed from a point of view which the author believes is closer to the spirit of both cryptography and chaos theory than the way the subject has been.
In this paper, chaos based cryptography is discussed from a point of view which the author believes is closer to the spirit of both cryptography and chaos theory than the way the subject has. Chaos theory becomes popular cryptography becomes more important 30 publications in 1990s various ciphers suggested focus on analog circuits. It stands to reason that this sensitive could be bene. Since 1990s, many researchers have noticed that there exists an interesting relationship between chaos and cryptography. A new image encryption scheme based on hybrid chaotic maps. The entropy production theory of chaotic maps was developed later by. Introduction chaotic electronic circuits represent deterministic systems which can be used as random number generators in cryptography. Most chaotic crypto papers appear in the general physicsengineering literature, and. Nonlinear means that due to feedback or multiplicative effects between the components, the whole becomes something greater than the mere sum of its individual parts. The guide to secrecy from ancient to modern times richard a. Some basic cryptographic requirements for chaosbased. Applications of cryptography include military information transmission, computer passwords, electronic commerce, and others. Pdf implementation and practical problems of chaosbased. This dependence on initial conditions makes predicting the behavior of the system very difficult.
Discrete mathematics and its applications series by douglas r. The second edition was equally embraced, and enjoys status as a perennial bestseller. In a nutshell, depend able and trustworthy security solutions based on strong cryptography are needed. Jun 25, 2007 chaos based cryptography sometimes called chaotic cryptography has been around for more than a decade by now. Chaotic cryptography pronounces the use of chaos theory in specific physical. Also, most chaotic systems are continuous, need infinite precision real numbers to represent, so since samplingquantization will be needed, some of the properties of chaos may be lost. Cryptographic hashing using chaotic hydrodynamics pnas. Some business managers underestimate the possibility for large unexpected changes, and should reconsider their mindset on this matter. Chaotic cryptology is the application of the mathematical chaos theory to the practice of the cryptography, the study or techniques used to privately and securely transmit information with the presence of a thirdparty or adversary. Almost a century later, despite its proven absolute security, the otp is still not adopted for lack of a practical and secure way for users to. There is the security of the structure itself, based on mathematics.
Small deviations in the initial conditions due to approximations or numerical calculations lead to large deviations of the corresponding orbits, rendering the longterm forecast for the chaotic systems intractable lighthill 1986. Image encryption and decryption based on chaotic algorithm. Since first being investigated by robert matthews in 1989, the use of chaos in cryptography has attracted much interest. Chaos theory and cryptography cryptography ii term paper. This dissertation only focuses on digital chaotic ciphers, i. Bountis chaotic dynamics theory and practice world of. Meet cryptography a branch of both mathematics and computer science, cryptography is the study and practice of obscuring information.
Here, we show that this process bears strong similarity to the chaotic behavior of certain types of flows observed when ordinary fluids mix, such as the. Shannon explicitly mentions that the basic stretchandfold mechanism of chaos can be used in cryptology. During this time of foundation and development, it came to mean different things, mostly depending on the implementation. Mollin, fundamental number theory with applications richard a. Truly chaotic signals can only be generated by analog. Chaos theory is a branch of mathematics focusing on the study of chaos dynamical systems whose apparently random states of disorder and irregularities are actually governed by underlying patterns and deterministic laws that are highly sensitive to initial conditions. However, longstanding concerns about its security and implementation speed continue to limit its implementation. This public document was automatically mirrored from pdfy. A new image encryption algorithm based on the proposed chaotic maps is introduced. The security and performance is acceptable to deal with high resolution and multispectral satellite imagery. Modern cryptography theory and practice wenbo mao pdf al. Modern cryptography is heavily based on mathematical theory and computer science practice. Chaotic cryptography is the blending of mathematical chaos theory and cryptography.
Chaotic maps in cryptography chaotic maps are simple unstable dynamical systems with high sensitivity to initial conditions devaney 1992. Our proposed cryptosystem works well, although encryption is slower than. This paper will examine the theory behind chaotic cryptosystems, some implemented cryptosystems, and the factors preventing chaos based cryptography from becoming common practice. Oct 22, 2020 in this paper, chaos based cryptography is discussed from a point of view which the author believes is closer to the spirit of both cryptography and chaos theory than the way the subject has been. In this letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems.
Basic concepts in cryptography fiveminute university. Although vernams cipher provides total security, from a practical point of view. Cryptography is the practice of hiding information, converting some secret information to not readable texts. We elaborate also on possible limits of chaotic cryptography. The evaluation consisted of theoretical derivations and prac. Chaos theory has been used for many years in cryptography. Many conferences, meetings, workshops, summer schools and symposia on nonlinear dynamical systems are being organized these days, dealing with a great variety of topics and themes classical and quantum, theoretical and experimental. Cryptanalysis of a chaotic image cipher using latin square. Many cryptographic schemes and protocols, especially those based on publickeycryptography, have basic or socalled textbook crypto versions, as these versionsare usually the subjects for many textbooks on cryptography. Now in its third edition, this authoritative text continues to provide a solid.
In the past few decades, chaos and nonlinear dynamics have been used in the design of hundreds of cryptographic primitives. Cryptography is fascinating because of the close ties it forges between theory and practice, and because todays practical applications of cryptography are pervasive and critical components of our informationbased society. Search the worlds most comprehensive index of fulltext books. Chaos based cryptography sometimes called chaotic cryptography has been around for more than a decade by now. Chaotic cryptography is a new field of academic interest, and is only starting to be rigorously studied. In this paper, chaos based cryptography is discussed from a point of view which the author believes is closer to the spirit of both cryptography and chaos theory than the way the subject has been treated. Solutions of cryptography theory and practice author december 20, 2010 1 classical cryptography 1. Discrete lyapunov exponent and differential cryptanalysis. This course is your invitation to this fascinating. For each operation, the tcc is calculated according to the published manual. Perfect secrecy cryptography via mixing of chaotic waves in. Subsequently, the theory of cryptosystems based on the integer factoring problem and on.
These algorithms include image encryption algorithms, hash functions, secure pseudorandom number generators, stream ciphers, watermarking and steganography. Chaos theory is a branch of mathematics that deals with nonlinear dynamical systems. The collection of chapters in this book focuses on theory and the practice of cryptographic security solutions for deployment in information systems is. Theory and practice of chaotic cryptography request pdf.
It chaos properties, such as randomness and ergodicity, have been proved to be suitable for designing the means for data protection. This paper aims to introduce the reader to applications of number theory in cryptography. This book takes adifferent approach to introducing cryptography. Table 1 contains a partial list of these properties. Recently, an interesting variant of chaotic image cipher using latin square has been studied extensively, but the lack of the corresponding cryptanalysis hampers its further development. An architecture of such kind of cryptosystems is composed of multiple rounds of substitution and diffusion. Chaos theory involves the study of dynamical systems that are highly sensitive to initial conditions. Chaotic systems are defined on realcomplex numbers spaces bounded continuous space whereas cryptography uses binary sequences finite discrete space. Cryptography overview john mitchell cryptography uis a tremendous tool the basis for many security mechanisms uis not the solution to all security problems reliable unless implemented properly reliable unless used improperly uencryption scheme. But the most basic problem remains the classical one of ensuring security of communication across an insecure medium. Most chaotic crypto papers appear in the general physicsengineering literature, and are not even seen by most crypto researchers. Introduction to cryptography cryptography is the study of secret crypto writing graphy concerned with developing algorithms which may be used to. Existing research shows that the chaotic sequence generated by the chaos system is a nonlinear sequence, its structure is complex and difficult to analysis and forecast, it also has good randomness, correlation and complexity, so it can be as a chaotic encryption key sequence.
Pdf theory and practice of cryptography solutions for. Mollin, an introduction to cryptography, second edition richard a. This special edition completed with other document such as. Analyses and new designs of digital chaotic ciphers. Laws of quantum mechanics quantum cryptography quantum cryptanalysis quantum bits and registers operations on a system measurement of a system quantum bit qubit a classical bit cbit can take two values. Review on different chaotic based image encryption techniques. Standard, ecc elliptic curve cryptography, and many more. Theory and practice of cryptography and network security protocols and. Informationprotection protocols designed on theoretical foundations one year appear in products and standards. Applications of chaos theory to cryptography author. Chaotic cryptography describes the use of chaos theory in particular physical. Chaotic electronic circuits in cryptography, applied cryptography and network security, jaydip sen, intechopen, doi.
This problem is very evident by an encryp tion with very similar secret keys. Paterson discrete mathematics with ducks, second edition sarahmarie belcastro business process modeling, simulation and design, third edition manual laguna and johan marklund graph theory and its applications, third edition jonathan l. Chaotic and aes cryptosystem for satellite imagery. Small deviations in the initial conditions due to approximations or numerical calculations lead to large deviations of the corresponding orbits, rendering the longterm forecast for the chaotic. Chaosbased crypto and joint cryptocompression systems for. Comparison between chaos and cryptography properties. Tesis doctoral framework for the analysis and design of. Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of chaotic complex systems, there. The books starts with a huge collection of mathematical tools necessary for understanding this area. The possibility for selfsynchronization of chaotic oscillations has sparked an avalanche of works on application of chaos in cryptography.
May 08, 2018 an essential component of digital communication is hashing, in which a complex piece of information a document, video, etc. Despite the claim that the cryptosystem is of high security, we demonstrate that. Image encryption using chaos and block cipher citeseerx. Chaotic system orbit structure image cipher image encryption algorithm.
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