A symmetric image encryption scheme based on 3D chaotic cat maps
TL;DR: The two-dimensional chaotic cat map is generalized to 3D for designing a real-time secure symmetric encryption scheme that uses the 3D cat map to shuffle the positions of image pixels and uses another chaotic map to confuse the relationship between the cipher-image and the plain-image, thereby significantly increasing the resistance to statistical and differential attacks.
Abstract: Encryption of images is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which are generally difficult to handle by traditional methods. Due to the exceptionally desirable properties of mixing and sensitivity to initial conditions and parameters of chaotic maps, chaos-based encryption has suggested a new and efficient way to deal with the intractable problem of fast and highly secure image encryption. In this paper, the two-dimensional chaotic cat map is generalized to 3D for designing a real-time secure symmetric encryption scheme. This new scheme employs the 3D cat map to shuffle the positions (and, if desired, grey values as well) of image pixels and uses another chaotic map to confuse the relationship between the cipher-image and the plain-image, thereby significantly increasing the resistance to statistical and differential attacks. Thorough experimental tests are carried out with detailed analysis, demonstrating the high security and fast encryption speed of the new scheme.
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TL;DR: The suggested guidelines address three main issues: implementation, key management and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements.
Abstract: In recent years, a large amount of work on chaos-based cryptosystems have been published. However, many of the proposed schemes fail to explain or do not possess a number of features that are fundamentally important to all kind of cryptosystems. As a result, many proposed systems are difficult to implement in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a thorough security analysis. Consequently, it is difficult for other researchers and end users to evaluate their security and performance. This work is intended to provide a common framework of basic guidelines that, if followed, could benefit every new cryptosystem. The suggested guidelines address three main issues: implementation, key management and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements. Meanwhile, several recommendations are made regarding some practical aspects of analog chaos-based secure communications, such as channel noise, limited bandwith and attenuation.
1,620 citations
Cites methods from "A symmetric image encryption scheme..."
...A variation of differential cryptanalysis applied to image encryption can be found for instance in [Chen et al., 2004; Mao et al., 2004]....
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TL;DR: The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.
1,109 citations
01 Jan 2011
TL;DR: The question of whether a given NPCR/UACI score is sufficiently high such that it is not discernible from ideally encrypted images is answered by comparing actual NPCR and UACI scores with corresponding critical values.
Abstract: The number of changing pixel rate (NPCR) and the unified averaged changed intensity (UACI) are two most common quantities used to evaluate the strength of image encryption algorithms/ciphers with respect to differential attacks. Conventionally, a high NPCR/UACI score is usually interpreted as a high resistance to differential attacks. However, it is not clear how high NPCR/UACI is such that the image cipher indeed has a high security level. In this paper, we approach this problem by establishing a mathematical model for ideally encrypted images and then derive expectations and variances of NPCR and UACI under this model. Further, these theoretical values are used to form statistical hypothesis NPCR and UACI tests. Critical values of tests are consequently derived and calculated both symbolically and numerically. As a result, the question of whether a given NPCR/UACI score is sufficiently high such that it is not discernible from ideally encrypted images is answered by comparing actual NPCR/UACI scores with corresponding critical values. Experimental results using the NPCR and UACI randomness tests show that many existing image encryption methods are actually not as good as they are purported, although some methods do pass these randomness tests.
857 citations
Cites background or methods from "A symmetric image encryption scheme..."
...However, unlike binary sequence encryption, image encryption [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] is a relatively new area with distinctive characteristics including 1) it is a type of two-dimensional data with high information redundancy [15]; and 2) it usually contains of a large number…...
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...In image encryption, the cipher resistance to differential attacks is commonly analyzed via the NPCR and UACI tests [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]....
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...For our best knowledge, NPCR and UACI are first shown in 2004 [5] [18], both of which point to Yaobin Mao and Guanrong Chen....
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TL;DR: Simulations and performance evaluations show that the proposed system is able to produce many 1D chaotic maps with larger chaotic ranges and better chaotic behaviors compared with their seed maps.
694 citations
Additional excerpts
...Encrypted images Chen's algorithm [39] 0....
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TL;DR: In this Letter, a new image encryption scheme is presented, in which shuffling the positions and changing the grey values of image pixels are combined to confuse the relationship between the cipher-image and the plain-image.
644 citations
References
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TL;DR: A theory of secrecy systems is developed on a theoretical level and is intended to complement the treatment found in standard works on cryptography.
Abstract: THE problems of cryptography and secrecy systems furnish an interesting application of communication theory.1 In this paper a theory of secrecy systems is developed. The approach is on a theoretical level and is intended to complement the treatment found in standard works on cryptography.2 There, a detailed study is made of the many standard types of codes and ciphers, and of the ways of breaking them. We will be more concerned with the general mathematical structure and properties of secrecy systems.
8,777 citations
Book•
10 Nov 1993
TL;DR: This document describes the construction of protocols and their use in the real world, as well as some examples of protocols used in the virtual world.
Abstract: CRYPTOGRAPHIC PROTOCOLS. Protocol Building Blocks. Basic Protocols. Intermediate Protocols. Advanced Protocols. Esoteric Protocols. CRYPTOGRAPHIC TECHNIQUES. Key Length. Key Management. Algorithm Types and Modes. Using Algorithms. CRYPTOGRAPHIC ALGORITHMS. Data Encryption Standard (DES). Other Block Ciphers. Other Stream Ciphers and Real Random-Sequence Generators. Public-Key Algorithms. Special Algorithms for Protocols. THE REAL WORLD. Example Implementations. Politics. SOURCE CODE.source Code. References.
3,432 citations
TL;DR: In this paper, the authors reported the finding of a chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.
Abstract: This Letter reports the finding of a new chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.
2,443 citations
Additional excerpts
...Taking advantage of the exceptionally good properties of mixing and sensitivity to initial conditions and parameters of the chaotic 3D cat map, the proposed scheme incorporates Chen’s chaotic system [ 4 ,21] in key scheming and alternatively uses permutation and diffusion to render the image totally unrecognizable....
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...In the proposed scheme, Chen’s chaotic system is employed in key scheming, which is modelled by [ 4 ,21]...
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TL;DR: Methods are shown how to adapt invertible two-dimensional chaotic maps on a torus or on a square to create new symmetric block encryption schemes to encrypt an N×N image.
Abstract: In this paper, methods are shown how to adapt invertible two-dimensional chaotic maps on a torus or on a square to create new symmetric block encryption schemes. A chaotic map is first generalized by introducing parameters and then discretized to a finite square lattice of points which represent pixels or some other data items. Although the discretized map is a permutation and thus cannot be chaotic, it shares certain properties with its continuous counterpart as long as the number of iterations remains small. The discretized map is further extended to three dimensions and composed with a simple diffusion mechanism. As a result, a symmetric block product encryption scheme is obtained. To encrypt an N×N image, the ciphering map is iteratively applied to the image. The construction of the cipher and its security is explained with the two-dimensional Baker map. It is shown that the permutations induced by the Baker map behave as typical random permutations. Computer simulations indicate that the cipher has g...
1,654 citations
Additional excerpts
...Then the above discretization satisfies the following asymptotic property [ 7 ]:...
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...In [ 7 ], a systematical method was suggested for adapting an invertible two-dimensional chaotic map on a torus or on a square, so as to create a symmetric block encryption scheme....
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Book•
09 Jun 1998
TL;DR: This work focuses on chaos and order ordering chaos organization of the monograph and some applications of controlling chaos, and some approaches to controlling chaos.
Abstract: Part 1 Prologue - chaos and order ordering chaos organization of the monograph. Part 2 Parametric variation approaches: parametric variation for control of chaos an earlier attempt the OGY method and its variants new development. Part 3 Conventional engineering control approaches: engineering perspectives on control of chaos controlling chaos via external forces open-loop control methods feedback mechanism - a control engineer's perspective controlling discrete-time chaotic systems controlling continuous-time chaotic systems a closer look at Lyapunov-type approach adaptive control of chaotic systems optimal control of chaotic systems robust control of chaotic systems a stochastic control technique new development. Part 4 Other approaches to controlling chaos: intelligent control approaches controlling chaos in DAI systems synchronization and control of chaos unification of synchronization and control new development. Part 5 Some applications of controlling chaos: chaotic synchronization for secure communication chaos and biomedical systems chaos and biochemical systems controlling chaos of laser systems controlling chaos in fluid dynamics new development. Part 6 Controlling chaos - further discussions: general perspectives to probe further toward an integrated and unified framework.
1,227 citations
Additional excerpts
...It is found that Arnold’s cat map [ 3 ] is a good candidate for permutation, thus it is extended to a threedimensional version, called 3D cat map, and then used for this purpose....
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...The classical Arnold cat map is a two-dimensional invertible chaotic map [ 3 ,14] described by...
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