Symmetric Ciphers Based on Two-Dimensional Chaotic Maps
01 Jun 1998-International Journal of Bifurcation and Chaos (World Scientific Publishing Company)-Vol. 08, Iss: 06, pp 1259-1284
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...
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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.
1,904 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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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 background from "Symmetric Ciphers Based on Two-Dime..."
...As Fridrich pointed out in [Fridrich, 1998], amongst many other desirable properties, from a security viewpoint a good cryptosystem (based on symmetric or asymmetric encryption) should: 1....
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...…& Kocarev, 2001; Papadimitriou et al., 2001; Tang et al., 2005]; • Block ciphers based on forward/backward chaotic iterations [Habutsu et al., 1991; Fridrich, 1998; Uı́s et al., 1998; Masuda & Aihara, 2002]; 1It is also possible that some signals are sent from one system to another (A to…...
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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
Cites methods from "Symmetric Ciphers Based on Two-Dime..."
...Fridrich [ 4 ] demonstrated the construction of a symmetric block encryption technique based on two-dimensional standard baker map....
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...There are three basic steps in the method of Fridrich [ 4 ]: (a) choose a chaotic map and generalize it by introducing some parameter, (b) discretize the chaotic map to a finite square lattice of points that represent pixels, (c) extend the discretized map to three-dimensions and further compose it with a simple diffusion mechanism....
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TL;DR: In this paper, the authors provide a set of guidelines that new cryptosystems would benefit from adhering to, such as correct key management and security analysis, and some practical aspects of communications such as channel noise, limited bandwith, and attenuation.
Abstract: In recent years, a great amount of secure communications systems based on chaotic synchronization have been published. Most of the proposed schemes fail to explain a number of features of fundamental importance to all cryptosystems, such as key definition, characterization, and generation. As a consequence, the proposed ciphers are difficult to realize in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a security analysis. Thus, it is hard for the reader to have a hint about their security. In this work we provide a set of guidelines that every new cryptosystems would benefit from adhering to. The proposed guidelines address these two main gaps, i.e., correct key management and security analysis, to help new cryptosystems be presented in a more rigorous cryptographic way. Also some recommendations are offered regarding some practical aspects of communications, such as channel noise, limited bandwith, and attenuation.
863 citations
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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Book•
01 Jan 1968
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Abstract: A fuel pin hold-down and spacing apparatus for use in nuclear reactors is disclosed. Fuel pins forming a hexagonal array are spaced apart from each other and held-down at their lower end, securely attached at two places along their length to one of a plurality of vertically disposed parallel plates arranged in horizontally spaced rows. These plates are in turn spaced apart from each other and held together by a combination of spacing and fastening means. The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid. This apparatus is particularly useful in connection with liquid cooled reactors such as liquid metal cooled fast breeder reactors.
17,939 citations
11,456 citations
"Symmetric Ciphers Based on Two-Dime..." refers background in this paper
...The average number of cycles, cyc(N ), is dened as the expected value of k. It can be shown [ Feller, 1957 ], that for a random permutation,...
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TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
Abstract: Certain subsystems of nonlinear, chaotic systems can be made to synchronize by linking them with common signals. The criterion for this is the sign of the sub-Lyapunov exponents. We apply these ideas to a real set of synchronizing chaotic circuits.
9,201 citations
"Symmetric Ciphers Based on Two-Dime..." refers background in this paper
...Caroll and Pecora [1990, 1991, 1992, 1993a, 1993b, 1995a, 1995b] , Cuomo and Oppenheim [1994, 1995], Murali [1993], Kocarev [1992], Parlitz [1992], Papadimitriou [1992] describe encryption schemes based on synchronized chaotic circuits....
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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
"Symmetric Ciphers Based on Two-Dime..." refers background in this paper
...The only thing left would be the crypt-analysis of function h. Clearly, a diusion mechanism must be present in any secure cipher [ Shannon, 1949 ]....
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