On the security of a chaotic encryption scheme: problems with computerized chaos in finite computing precision

Li, Shujun; Mou, Xuanqin; Cai, Yuanlong; Ji, Zhen; Zhang, Jihong

doi:10.1016/s0010-4655(02)00875-5

Cited by 147 publications

(58 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…When using chaos in digital ciphers, many researchers have found dynamical degradation of digital chaotic systems and such degradation reduces the security of the designed chaotic ciphers [Erdmann & Murphy, 1992;Li et al, 2001aLi et al, , 2003aMasuda & Aihara, 2002b;Sang et al, 1998a,b;Wheeler & Matthews, 1991;. Actually, motivated by various "strange" phenomena of chaos observed on digital computers and in numerical simulations, pathologies of digital chaotic systems have been observed and extensively studied in the field of chaos theory [Arrowsmith & Vivaldi, 1994;Beck & Roepstorff, 1987;Benettin et al, 1978;Binder, 1992;Binder & Jensen, 1986;Blank, 1994Blank, , 1997Borcherds & McCauley, 1993;Bosioand & Vivaldi, 2000;Chambers, 1999;Chirkikov & Vivaldi, 1999;Diamond et al, 1994Diamond et al, , 1995Earn & Tremaine, 1992;Fryska & Zohdy, 1992;Góra & Boyarsku, 1988;Grebogi et al, 1988;Hogg & Huberman, 1985;Huberman, 1986;Kaneko, 1988;Karney, 1983;Keating, 1991;Levy, 1982;Li et al, 2001a;Lowenstein & Vivaldi, 1998;Masuda & Aihara, 2002b;McCauley & Palmore, 1986;Palmore & Herring, 1990;Palmore & McCauley, 1987;…”

Section: Theoretical Work: Dynamical Degradation Of Digital Chaotic Smentioning

confidence: 99%

On the Dynamical Degradation of Digital Piecewise Linear Chaotic Maps

Chen

Mou

2005

Int. J. Bifurcation Chaos

Self Cite

354

189

View full text Add to dashboard Cite

When chaotic systems are realized with finite precisions in digital computers, their dynamical properties are often found to be entirely different from the original versions in the continuous setting. In the literature, there does not seem to be much work on quantitative analysis of such degradation of digitized chaos and how to reduce its negative influence on chaos-based digital systems. Focusing on 1D piecewise linear chaotic maps (PWLCM), this paper reports some findings on a new series of dynamical indicators, which can quantitatively reflect the degradation effects on a digital PWLCM realized with a fixed-point finite precision. On top of that, the paper introduces a new method for studying digital chaos from an algorithmic point of view. In addition, the theoretical results obtained in this paper should be very helpful for the consideration of reducing negative influence of dynamical degradation in real design of various digital chaotic systems. As typical examples, the proposed dynamical indicators are applied to the performance comparison of different remedies for improving dynamical degradation, cryptanalysis of digital chaotic ciphers based on 1D PWLCM, and the design of chaotic pseudo-random number generators with desired characteristics.

show abstract

Section: Theoretical Work: Dynamical Degradation Of Digital Chaotic Smentioning

confidence: 99%

On the Dynamical Degradation of Digital Piecewise Linear Chaotic Maps

Chen

Mou

2005

Int. J. Bifurcation Chaos

Self Cite

354

189

View full text Add to dashboard Cite

show abstract

“…This is very useful because we do not need to change the public key to have a new crypto dynamic, representing a good option to protect from the attack described in this section. The chaos degradation is a well-known problem for chaos-based cryptosystems [17]. In DDE, this problem is addressed by two means: (i) as the chaotic process is involved only in the simulation part, which happens off communication, algorithms of quality verification can be performed before using the data for the encryption; and (ii) also, as we are proposing when coupled maps from nature are used, there is information from the characterization of the phenomena that can indicate the degradation of the chaos, i.e., when the data is taken from an analog circuit.…”

Section: Cryptanalysismentioning

confidence: 99%

Using the Logistic Coupled Map for Public Key Cryptography under a Distributed Dynamics Encryption Scheme

Solís-Sánchez

Barrantes

2018

Information

View full text Add to dashboard Cite

Abstract:Nowadays, there is a high necessity to create new and robust cryptosystems. Dynamical systems have promised to develop crypto-systems due to the close relationship between them and the cryptographic requirements. Distributed dynamic encryption (DDE) represents the first mathematical method to generate a public-key cryptosystem based on chaotic dynamics. However, it has been described that the DDE proposal has a weak point in the decryption process related to efficiency and practicality. In this work, we adapted the DDE to a low-dimensional chaotic system to evaluate the weakness and security of the adaption in a realistic example. Specifically, we used a non-symmetric logistic coupled map, which is known to have multiple chaotic attractors improving the shortcomings related to the simple logistic map that manifests its inadequacy for cryptographic applications. We found a full implementation with acceptable computational cost and speed for DDE, which it is essential because it provides a key cryptographic requirement for chaos-based cryptosystems.

show abstract

“…The first defect implies the difficulties of software and hardware implementation for a chaos-based image encryption method because round-off errors in real number quantizations may lead nonreversible functions for encryption and thus make the decryption process impossible [18]. The second defect implies a chaotic image encryption method could be completely nonchaotic and thus vulnerable to attacks [19]. The third defect shows these chaotic image encryption method may be broken using existing tools and methods after a long-term observation [20], [21].…”

Section: Introductionmentioning

confidence: 99%

Design of image cipher using latin squares

Zhou²,

Noonan

et al. 2014

Information Sciences

166

View full text Add to dashboard Cite

In this paper, we introduce a symmetric-key Latin square image cipher (LSIC) for grayscale and color images. Our contributions to the image encryption community include 1) we develop new Latin square image encryption primitives including Latin Square Whitening, Latin Square S-box and Latin Square P-box ; 2) we provide a new way of integrating probabilistic encryption in image encryption by embedding random noise in the least significant image bit-plane; and 3) we construct LSIC with these Latin square image encryption primitives all on one keyed Latin square in a new loom-like substitution-permutation network. Consequently, the proposed LSIC achieve many desired properties of a secure cipher including a large key space, high key sensitivities, uniformly distributed ciphertext, excellent confusion and diffusion properties, semantically secure, and robustness against channel noise. Theoretical analysis show that the LSIC has good resistance to many attack models including brute-force attacks, ciphertext-only attacks, known-plaintext attacks and chosen-plaintext attacks. Experimental analysis under extensive simulation results using the complete USC-SIPI Miscellaneous image dataset demonstrate that LSIC outperforms or reach state of the art suggested by many peer algorithms. All these analysis and results demonstrate that the LSIC is very suitable for digital image encryption. Finally, we open source the LSIC MATLAB code under webpage https://sites.google.com/site/tuftsyuewu/source-code.

show abstract

On the security of a chaotic encryption scheme: problems with computerized chaos in finite computing precision

Cited by 147 publications

References 34 publications

On the Dynamical Degradation of Digital Piecewise Linear Chaotic Maps

On the Dynamical Degradation of Digital Piecewise Linear Chaotic Maps

Using the Logistic Coupled Map for Public Key Cryptography under a Distributed Dynamics Encryption Scheme

Design of image cipher using latin squares

Contact Info

Product

Resources

About