Baker Map Research Articles

Fusion-based encryption scheme for cancelable fingerprint recognition

This paper presents a fingerprint image encryption scheme based on fingerprint image fusion with another visible image that is rich in details. The encryption process is performed with chaotic Baker map, which has large immunity to noise. The image fusion process is performed with the Haar wavelet transform, and it can be implemented with the average or maximum fusion rule. The fusion process is performed, because fingerprint images are not rich in details, and hence the direct application of chaotic Baker map encryption will not be efficient for encrypting this type of images. To obtain an image that is rich in details, it is possible to use another encrypted image with a strong ciphering algorithm such as the RC6. Several perspectives are considered for performance evaluation of the proposed encryption scheme including visual inspection, histogram analysis, correlation coefficient, entropy analysis, processing time, and the effect of noise after decryption. The proposed fingerprint encryption scheme is appropriate for cancelable biometric applications to preserve the privacy of users by keeping their original fingerprints away from usage in the recognition system. The simulation results demonstrate that the proposed image encryption scheme gives a proficient and secure path for unique encrypted fingerprints. Both Equal Error Rate (EER) and Area under Receiver Operating Characteristic (AROC) curve are used for performance evaluation of the proposed cancelable fingerprint recognition scheme revealing high performance.

A novel chaotic image encryption algorithm based on improved baker map and logistic map

A novel image encryption algorithm based on double chaotic systems is proposed in this paper. On account of the limited chaotic range and vulnerability of a single chaotic map, we use the two-dimensional Baker chaotic map to control the system parameters and the state variable of the logistic chaotic map. After control, the parameter of the logistic map is varying, and the generated logistic sequence is non-stationary. The improved map has been proven to be random and unpredictable by complexity analysis. Furthermore, a novel image encryption algorithm, including shuffling and substituting processes, is proposed based on the improved chaotic maps. Many statistical tests and security analysis indicate that this algorithm has an excellent security performance, and it can be competitive with some other recently proposed image encryption algorithms.

A Novel Block Encryption Algorithm Based on Chaotic S-Box for Wireless Sensor Network

In order to ensure the basic security of wireless sensor networks (WSNs), a block encryption algorithm based on chaotic substitution box (S-box) is proposed. In this paper, we generated a new S-box based on the compound chaotic map, sinusoidal chaotic map, Baker map, and linear congruence generator. In addition, the limited computing power and communication capability of WSN are also considered in this paper. The method of generating round subkeys and F function is constructed based on the S-box. The extensive security and performance tests show that the proposed encryption algorithm has high security and low resource consumption which is suitable for WSN.

2020 Ian Snook Prize Problem: Three Routes to the Information Dimensions for One-Dimensional Stochastic Random Walks and Their Equivalent Two-Dimensional Baker Maps

2020 Ian Snook Prize Problem: Three Routes to the Information Dimensions for One-Dimensional Stochastic Random Walks and Their Equivalent Two-Dimensional Baker Maps

Discrete Wavelet Transform Based Cancelable Biometric System for Speaker Recognition

The biometric template characteristics and privacy conquest are challenging issues. To resolve such limitations, the cancelable biometric systems have been briefed. In this paper, the efficient cancelable biometric system based on the cryptosystem is introduced. It depends on permutation using a chaotic Baker map and substitution using masks in various transform domains. The proposed cancelable system features extraction phase is based on the Cepstral analysis from the encrypted speech signal in the time domain combined with the encrypted speech signal in the discrete wavelet transform (DWT). Then, the resultant features are applied to the artificial neural network for classification. Furthermore, wavelet denoising is used at the receiver side to enhance the proposed system. The cryptosystem provides a robust protection level of the speech template. This speech template can be replaced and recertified if it is breached. Our proposed system enables the generation of various templates from the same speech signal under the constraint of linkability between them. The simulation results confirmed that the proposed cancelable biometric system achieved higher a level of performance than traditional biometric systems, which achieved 97.5% recognition rate at low signal to noise ratio (SNR) of -25dB and 100% with -15dB and above.

Proposed enhanced hybrid framework for efficient 3D-MVC and 3D-HEVC wireless communication

The streaming of Three-Dimensional Video (3DV) over erroneous wireless channels causes Macro-Blocks (MBs) corruptions. Thus, the efficient performance of 3DV communication techniques over wireless channels has become an interesting research topic because of the restricted resources and the existence of severe communication losses. The 3DV consists of various video sequences captured via multiple cameras surrounding an object, and working simultaneously. Therefore, there is a need to achieve high encoding efficiency. Unfortunately, the highly-compressed 3DV content is subject to communication channel corruptions. Thus, in this research, we suggest the utilization of a chaotic randomization technique based on Baker map with convolution coding and equalization for high-quality 3D Multi-view Video Coding (MVC) and High Efficiency Video Coding (HEVC) transmission over an Orthogonal Frequency Division Multiplexing (OFDM) wireless system. Rayleigh fading and Additive White Gaussian Noise (AWGN) are considered in this paper in a real scenario of 3DV transmission. Firstly, the 3DV volume is compressed making use of the intra- and inter-prediction correlations between frames. Then, the compressed 3D-MVC and 3D-HEVC frames are converted into binary data format. After that, the chaotic randomization technique is employed before the modulation stage. It is utilized to minimize the channel corruptions on the streamed encoded 3DV data, and it as well introduces a degree of encryption to the transmitted 3DV frames. To evaluate the efficiency of the suggested hybrid framework; different simulations on several 3D-MVC and 3D-HEVC frames have been executed. The results prove that the delivered 3DV frames with the suggested framework have high Peak Signal-to-Noise Ratios (PSNRs).

Invariant graphs for chaotically driven maps

This paper investigates the geometrical structures of invariant graphs of skew product systems of the form driven by a hyperbolic base map (e.g. a baker map or an Anosov surface diffeomorphism) and with monotone increasing fibre maps having negative Schwarzian derivatives. We recall a classification, with respect to the number and to the Lyapunov exponents of invariant graphs, for this class of systems. Our major goal here is to describe the structure of invariant graphs and study the properties of the pinching set, the set of points where the values of all of the invariant graphs coincide. In Keller and Otani (2018 Stoch. Dyn. 18 1850009), the authors studied skew product systems driven by a generalized baker map with the restrictive assumption that depend on only through the stable coordinate x of θ. Our aim is to relax this assumption and construct a fibre-wise conjugation between the original system and a new system for which the fibre maps depend only on the stable coordinate of the drive. As an application of this construction we prove that, when S is an Anosov diffeomorphism, the pinching set is a union of global unstable fibres for S.

Efficient hybrid framework for transmission enhancement of composite 3D H.264 and H.265 compressed video frames

Three-Dimensional Multi-View Video (3D-MVV) transmission over wireless networks suffers from losses. Therefore, the robust performance of 3D-MVV transmission techniques over wireless channels has become a recent hot research issue due to the restricted resources and the presence of severe channel errors. The 3D-MVV is composed of multiple video stream shots by several cameras around a single object, simultaneously. So, it is an urgent task to achieve high compression ratios to meet future bandwidth constraints. Unfortunately, the highly-compressed 3D-MVV data becomes more sensitive and vulnerable to packet losses, especially in the case of heavy channel errors. Thus, in this paper, we propose the application of a chaotic Baker map interleaving technique with equalization for efficient transmission of composite 3D-MVV compressed frames over an Orthogonal Frequency Division Multiplexing (OFDM) wireless channel. Rayleigh fading and Additive White Gaussian Noise (AWGN) are considered in the real scenario of 3D-MVV transmission. Firstly, the 3D-MVV content is compressed exploiting the intra- and inter-prediction correlations between frames. After that, a composite frame of luminance is generated from each four consecutive frames using Discrete Cosine Transform (DCT), which represents a second level of compression. The resultant composite frame is converted to binary data format. Then, chaotic interleaving is applied on the binary information prior to the modulation process. This chaotic interleaving is used to mitigate the OFDM induced Peak-to-Average Power Ratio (PAPR) problem and to reduce the wireless channel effects on the transmitted bit streams. It also adds a degree of encryption to the transmitted 3D-MVV compressed frames. To evaluate the performance of the proposed hybrid technique, several simulation experiments on different 3D-MVV frames have been executed. The experimental results show that the received 3D-MVV frames have high average Peak Signal-to-Noise Ratio (PSNR) gains up to 4.25 dB and a reduction of the average PAPR values by about 12 dB with the proposed hybrid technique compared to the other traditional techniques.

A Proposed Fingerprint Image Encryption Scheme Based on Wavelet Fusion

This paper presents two chaotic image encryption plans combined with Discrete Wavelet Transform (DWT) to encrypt unique fingerprint. In the first proposal, the fingerprint which has few details (low entropy) is fused with another image which is rich in details (high entropy) using the Discrete Wavelet Transform (DWT) prior to encryption. The fusion process is a pre-processing step to alter the homogeneity of flat areas in the few-details fingerprint image. Then, the technique of the Chaotic Baker map randomization is applied on the output fused image. In the second proposal, the fingerprint is fused with an image encrypted with RC6 block cipher algorithm prior to encryption. Several metrics are used in this paper for performance evaluation of the proposed encryption scheme including, visual inspection, histogram analysis, encryption quality analysis, and diffusion analysis. The outcomes demonstrate that the proposed image encryption schemes give a proficient and secure path for unique fingerprint encryption.

Persistent two-dimensional strange attractors for a two-parameter family of Expanding Baker Maps

<p style='text-indent:20px;'>We characterize the attractors for a two-parameter class of two-dimensional piecewise affine maps. These attractors are strange attractors, probably having finitely many pieces, and coincide with the support of an ergodic absolutely invariant probability measure. Moreover, we demonstrate that every compact invariant set with non-empty interior contains one of these attractors. We also prove the existence, for each natural number <inline-formula><tex-math id="M1">\begin{document}$ n, $\end{document}</tex-math></inline-formula> of an open set of parameters in which the respective transformation exhibits at least <inline-formula><tex-math id="M2">\begin{document}$ 2^n $\end{document}</tex-math></inline-formula> non connected two-dimensional strange attractors each one of them formed by <inline-formula><tex-math id="M3">\begin{document}$ 4^n $\end{document}</tex-math></inline-formula> pieces.

Chaotic encryption with different modes of operation based on Rubik’s cube for efficient wireless communication

A novel image encryption algorithm based on the Rubik’s cube scrambling is proposed in this paper to achieve simultaneous encryption of a group of images. This proposed encryption algorithm begins with chaotic Baker map permutation with a selected mode of operation or RC6 algorithm as a first step for encrypting the images, separately. After that, the obtained encrypted images are further encrypted in a second stage with Rubik’s cube. Chaotic or RC6 encrypted images are used as the faces of the Rubik’s cube. From the concepts of image encryption, the RC6 algorithm adds a degree of diffusion, while chaotic Baker map adds a degree of permutation. The Rubik’s cube algorithm adds more permutation to the encrypted images, simultaneously. The simulation results demonstrate that the proposed encryption algorithm is efficient, and it exhibits strong robustness and security. The encrypted images are further transmitted over a wireless channel with Orthogonal Frequency Division Multiplexing (OFDM) system, and decrypted at the receiver side. Evaluation of the quality of the decrypted images at the receiver side reveals good performance.

Efficient multi-level security for robust 3D color-plus-depth HEVC

This paper presents two robust hybrid watermarking techniques for securing the Three-Dimensional High Efficiency Video Coding (3D-HEVC). The first watermarking technique is the homomorphic-transform-based Singular Value Decomposition (SVD) in Discrete Wavelet Transform (DWT) domain. The second watermarking technique is the three-level Discrete Stationary Wavelet Transform (DSWT) in Discrete Cosine Transform (DCT) domain. The objective of the two proposed hybrid watermarking techniques is to increase the immunity of the watermarked 3D-HEVC streams to attacks. Also, we propose a wavelet-based fusion technique to combine two depth watermark frames into one fused depth watermark frame. Then, the resultant fused depth watermark is encrypted using chaotic Baker map to increase the level of security. After that, the resultant chaotic encrypted fused depth watermark is embedded in the 3D-HEVC color frames using the proposed hybrid watermarking techniques to produce the watermarked 3D-HEVC streams. In addition to achieving multi-level security in the transmitted 3D-HEVC streams, the proposed hybrid techniques reduce the required bit rate for transmitting the color-plus-depth 3D-HEVC data over limited-bandwidth networks. The performance of the proposed hybrid techniques is compared with those of the state-of-the-art techniques. Extensive simulation results on standard 3D video sequences have been conducted in the presence of attacks. The obtained results confirm that the proposed hybrid fusion-encryption-watermarking techniques achieve not only a good perceptual quality with high Peak Signal-to-Noise Ratio (PSNR) values and less bit rate, but also high correlation coefficient values between the original and extracted watermarks in the presence of attacks. Furthermore, the proposed hybrid techniques improve the capacity of information embedding and the robustness without affecting the perceptual quality of the original 3D-HEVC frames. Indeed, the extraction of the encrypted, fused, primary, and secondary depth watermark frames is possible in the presence of attacks.

Dolgopyat’s method and the fractal uncertainty principle

We show a fractal uncertainty principle with exponent $1/2-\delta+\epsilon$, $\epsilon>0$, for Ahflors-David regular subsets of $\mathbb R$ of dimension $\delta\in (0,1)$. This improves over the volume bound $1/2-\delta$, and $\epsilon$ is estimated explicitly in terms of the regularity constant of the set. The proof uses a version of techniques originating in the works of Dolgopyat, Naud, and Stoyanov on spectral radii of transfer operators. Here the group invariance of the set is replaced by its fractal structure. As an application, we quantify the result of Naud on spectral gaps for convex co-compact hyperbolic surfaces and obtain a new spectral gap for open quantum baker maps.

Reducing the Dynamical Degradation by Bi-Coupling Digital Chaotic Maps

A chaotic map which is realized on a computer will suffer dynamical degradation. Here, a coupled chaotic model is proposed to reduce the dynamical degradation. In this model, the state variable of one digital chaotic map is used to control the parameter of the other digital map. This coupled model is universal and can be used for all chaotic maps. In this paper, two coupled models (one is coupled by two logistic maps, the other is coupled by Chebyshev map and Baker map) are performed, and the numerical experiments show that the performances of these two coupled chaotic maps are greatly improved. Furthermore, a simple pseudorandom bit generator (PRBG) based on coupled digital logistic maps is proposed as an application for our method.

Chaos Baker-based Image Encryption in Operation Modes

This research paper study the application of chaos baker map for digital image encryption in different operation modes. The employed modes include the electronic code book (ECB), cipher block chaining (CBC), output feedback chaining (OFB), and cipher feedback chaining (CFB). The proposed method works by applying the chaos baker map in different operation modes for encrypting digital images. A group of tests were carried out to examine the impact of operation modes on chaos baker-based encryption. This is done using several encryption metrics like visual inspection, statistical measures, entropy measure, encryption quality measures, and noise resistance measures. Simulation results demonstrated the effectively of baker-based encryption in CBC mode.

DRPE Encryption with Chaotic Interleaving for Video Communication

Due to the need to transmit encrypted data and video securely through wireless channels, we suggest the application of the double random phase encryption (DRPE) algorithm for efficient video communication over orthogonal frequency division multiplexing (OFDM) system. Moreover, we use an efficient interleaving mechanism on the communicated data depending on chaotic Baker map to control the error level of the channel. In this paper, DRPE and chaotic Baker interleaving are used for efficient video frame transmission over OFDM. Channel equalization is implemented in the proposed scheme. Simulation results illustrate the good performance of the suggested scheme for secure video communication.

Permutation-substitution image encryption scheme based on a modified chaotic map in transform domain

A new chaotic image encryption scheme based on permutation and substitution in the Fourier domain is presented. Fractional Fourier Transform (FRFT) is used before the encryption scheme to get a large degree of randomization. The permutation is achieved by Baker map and the substitution by a key-related-to-plain-image algorithm based on the modified Logistic map. Modification of the Logistic map is developed to increase the space of the encryption key, and hence increase the security. The key of the encryption algorithm dependents on the plain image, and thus, the cipher image is sensitive to both the initial key and the plain image to resist known-plaintext and chosen plaintext attacks. The key space is large and hence the algorithm can effectively resist brute-force attacks. The proposed scheme is examined using different performance evaluation metrics and the results prove that the proposed scheme is highly secure, and it can effectively resist different attacks.

Design of a High Secure Authentication System Based on Fuzzy Fusion of Iris and Face and Incorporating 2D Baker and Henon Maps

The emergent concerns of identity theft problems and terrorism make the design of applicable accurate verification systems more crucial. No single biometric identifier could perfectly own all desired security properties. Moreover, the transmitted or stored biometric templates raise the opportunity of compromising user's privacy and identity breaching. This paper offers new scheme based on score level fuzzy fusion at decision level fusion to effectively combine face and iris identifiers. The proposed system allows an efficient identification procedure and introduces a new template locking approach based on chaos cryptography to protect the biometric data. In this study, CASIA and Faces94 databases are used to examine and appraise the robustness of the proposed schemes. The proposed template protection scheme offers new different uncorrelated secure forms of the base original templates in imperative and much speedy ciphering methodology. Furthermore, it could be rescinded at different points of probable attacks from sensed level to the final code and the matcher. It presents remarkably good key sensitivity and more robustness against different malicious attacks compared to classical encryption techniques. Furthermore, being noninvasive to the recognition process, simulation results on authentication rates introduces FAR and FRR of 0.0345%, and 0.001% respectively which illustrated a significant enhancement of the proposed fuzzy fusion over each unimodal system and existing multimodal fusion methods.

Chaotic Interleaving for the Transmission of Compressed Video Frames with Self-Embedded Digital Signatures

This paper presents an efficient video compression and transmission scheme based on the Set Partitioning In Hierarchical Trees (SPIHT) algorithm and chaotic Baker map interleaving. The compressed video frames have self-embedded digital signatures, and the transmission is performed over Orthogonal Frequency Division Multiplexing wireless systems with equalization. The video frames compressed with SPIHT algorithm are primarily converted to the luminance and chrominance scheme for self-watermark embedding, and then the binary format is reconstructed again. Prior to the modulation step, the chaotic randomization is performed on the binary data to encrypt the data to be transmitted and reduce the noise impact of the multipath channel. For performance evaluation, both Rayleigh and additive noise channels are considered for various video frames with chaotic interleaving. The simulation results reveal that the received watermarked video frames with chaotic interleaving applied achieve higher Peak Signal-to-Noise Ratios and correlation coefficients compared to other approaches.

A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) will suffer from dynamical degradation, which refers to short cycle lengths, low complexity and strong correlations. In this paper, a novel double perturbation method is proposed for reducing the dynamical degradation of the digital Baker map. Both state variables and system parameters are perturbed by the digital logistic map. Numerical experiments show that the perturbed Baker map can achieve good statistical and cryptographic properties. Furthermore, a new image encryption algorithm is provided as a simple application. With a rather simple algorithm, the encrypted image can achieve high security, which is competitive to the recently proposed image encryption algorithms.