Torus Automorphism Research Articles

Thermodynamical u-formalism I: measures of maximal u-entropy for maps that factor over Anosov

AbstractWe construct measures of maximal u-entropy for any partially hyperbolic diffeomorphism that factors over an Anosov torus automorphism and has mostly contracting center direction. The space of such measures has finite dimension, and its extreme points are ergodic measures with pairwise disjoint supports.

Cancelable Multimodal Biometrics Based on Chaotic Maps

Biometric authentication systems raise certain concerns with regard to security, violation of privacy, and storage issues of biometric templates. This paper proposes a protection approach of biometric templates storage in a multimodal biometric system while ensuring both the cancelability of biometric templates and the efficiency of the authentication process. We propose applying a chaotic maps-based transform on the biometric features to address the cancelability issue. We used Logistic map and Torus Automorphism to generate cancelable biometric features of the face and fingerprint minutia points, respectively. Both transformed features would be concatenated and saved in the database of the system instead of the original features. In the authentication stage, the similarity scores of both transformed face and fingerprint templates are computed and fused using the weighted sum rule. The results of the experimentation, conducted using images from the ORL face and FVC2002 DB1 fingerprint databases, demonstrated the higher performance of the proposed approach achieving a genuine accept rate equal to 100%. Moreover, the obtained results confirmed the soundness of the proposed cancelable technique to satisfy the biometric systems’ requirements (i.e., security, revocability, and diversity).

A Bayer pattern-based fragile watermarking scheme for color image tamper detection and restoration

The security of multimedia documents becomes an urgent need, especially with the increasing image falsifications provided by the easy access and use of image manipulation tools. Hence, usage of image authentication techniques fulfills this need. In this paper, we propose an effective self-embedding fragile watermarking scheme for color images tamper detection and restoration. To decrease the capacity of insertion, a Bayer pattern is used to reduce the color host image into a gray-level watermark, to further improve the security Torus Automorphism permutation is used to scramble the gray-level watermark. In our algorithm, three copies of the watermark are inserted over three components (R, G, and B channels) of the color host image, providing a high probability of detection accuracy and recovery if one copy is destroyed. In the tamper detection process, a majority voting technique is used to determine the legitimacy of the image and recover the tampered regions after interpolating the extracted gray-level watermark. Using our proposed method, tampering rate can achieve 25% with a high visual quality of recovered image and PSNR values greater than 34 (dB). Experimental results demonstrate that the proposed method affords three major properties: the high quality of watermarked image, the sensitive tamper detection and high localization accuracy besides the high-quality of recovered image.

ADAPTIVE IMAGE WATERMARKING USING DISCRETE WAVELET TRANSFORM, SINGULAR VALUE DECOMPOSITION AND AUTOMORPHISM

Watermarking is a method to hide the image efficiently into any covering object (image in our case) so no intruder can interpret it by any means. Proposed work is a new design of image watermarking which include pre-processing of cover image with Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD). Proposed work using an alphanumeric key which initially modifies the watermark using simple ‘XOR’ operation, and at the receiver end this key must be there so that receiver can extract the watermark. Proposed work is also using torus Automorphism which initially changes the watermark into a scramble format which cannot be recognised as original watermark.

A Genetic Algorithm for the Generation of Packetization Masks for Robust Image Communication.

Image interleaving has proven to be an effective solution to provide the robustness of image communication systems when resource limitations make reliable protocols unsuitable (e.g., in wireless camera sensor networks); however, the search for optimal interleaving patterns is scarcely tackled in the literature. In 2008, Rombaut et al. presented an interesting approach introducing a packetization mask generator based in Simulated Annealing (SA), including a cost function, which allows assessing the suitability of a packetization pattern, avoiding extensive simulations. In this work, we present a complementary study about the non-trivial problem of generating optimal packetization patterns. We propose a genetic algorithm, as an alternative to the cited work, adopting the mentioned cost function, then comparing it to the SA approach and a torus automorphism interleaver. In addition, we engage the validation of the cost function and provide results attempting to conclude about its implication in the quality of reconstructed images. Several scenarios based on visual sensor networks applications were tested in a computer application. Results in terms of the selected cost function and image quality metric PSNR show that our algorithm presents similar results to the other approaches. Finally, we discuss the obtained results and comment about open research challenges.

Secured Image Compression using Wavelet Transform

Objective: Image Compression is to shrink insignificance and redundancy of the image data and it is obligatory for efficient transmission and storage of images. Image data are self -descriptive and contains sensitive information, yet partial data will convey more information. Hence robust security mechanisms are required for defending and privacy protection of image data. A robust secured image compression scheme has been proposed in this paper. Methods: In this work two levels of security have been accomplished to improve the robustness of the encryption system. Torus Automorphism and Rubik’s cube principle are used for pixel scrambling and shuffling along with adaptive DWT based image compression. Findings: Extracting greatest image quality at a given bit-rate or compression ratio is the main goal of Image Compression. Experimental results have shown that the proposed system of secured image compression offers compression ratio of 97% and a bit rate of 0.25bpp and the scheme is highly robust with respect to the security parameters such as UACI (Unified Average Changing Intensity) and NPCR (Number of pixels Change Rate). Application: The proposed scheme is highly suitable for small hand held wireless communication gadgets such as mobile phones to upload/download on/from Internet, where fast and efficient on the fly image encryption and transmission are required.

A Friendly Image Sharing Method

This image sharing method is a secure way of protecting the security of the secret images. In 2011, Wang et al. proposed an image sharing method with verification. The idea of the method is to embed the secret and the watermark images into two shares by two equations to achieve the goal of the secret sharing. However, the constructed shares are meaningless images which are difficult to manage. Authors utilize the algorithm of the torus automorphism to increase the security of the shares. However, the algorithm of the torus automorphism must take much time to encrypt and decrypt an image. This paper proposes a friendly image sharing method to improve the above problem. Experimental results show the significant efficiency of the proposed method.

An Image Encryption Scheme Based on Concatenated Torus Automorphisms

A novel, chaotic map that is based on concatenated torus automorphisms is proposed in this paper. As we know, cat map, which is based on torus automorphism, is highly chaotic and is often used to encrypt information. But cat map is periodic, which decreases the security of the cryptosystem. In this paper, we propose a novel chaotic map that concatenates several torus automorphisms. The concatenated mechanism provides stronger chaos and larger key space for the cryptosystem. It is proven that the period of the concatenated torus automorphisms is the total sum of each one’s period. By this means, the period of the novel automorphism is increased extremely. Based on the novel, concatenated torus automorphisms, two application schemes in image encryption are proposed, i.e., 2D and 3D concatenated chaotic maps. In these schemes, both the scrambling matrices and the iteration numbers act as secret keys. Security analysis shows that the proposed, concatenated, chaotic maps have strong chaos and they are very sensitive to the secret keys. By means of concatenating several torus automorphisms, the key space of the proposed cryptosystem can be expanded to 2 135 . The diffusion function in the proposed scheme changes the gray values of the transferred pixels, which makes the periodicity of the concatenated torus automorphisms disappeared. Therefore, the proposed cryptosystem has high security and they can resist the brute-force attacks and the differential attacks efficiently. The diffusing speed of the proposed scheme is higher, and the computational complexity is lower, compared with the existing methods.

An efficient image authentication method based on Hamming code

Image authentication has come through a history of several years. However, up to the present time, most mainstream image authentication schemes are still unable to detect burst bit errors. Moreover, the capability of recovering tampered pixels in detail (complex) areas has not been very satisfactory either. In this paper, we offer to combine the Hamming code technique, Torus automorphism and bit rotation technique to do tamper proofing. According to our experimental results, our new hybrid method can effectively eliminate burst bit errors, and our recovered pixels in detail areas can actually gain very high clarity. The results show that our scheme is quite a practical method, which is quite able to detect and recover tampered areas.

On the torus automorphisms: analytic solution, computability and quantization

The exact solution of the classical torus automorphism, which partial case is Arnold Cat map is obtained and compared with the numerical solution. The torus, considered as the classical phase space admits the quantization in terms of the Weyl pair. The remarkable fact is that quantum map, as the evolution with respect to the discrete time, preserves the Weyl commutation relation. We have obtained also the operator solution of this quantum torus automorphism.