A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Provably secure and efficient audio compression based on compressive sensing

The advancement of systems with the capacity to compress audio signals and simultaneously secure is a highly attractive research subject. This is because of the need to enhance storage usage and speed up the transmission of data, as well as securing the transmission of sensitive signals over limited and insecure communication channels. Thus, many researchers have studied and produced different systems, either to compress or encrypt audio data using different algorithms and methods, all of which suffer from certain issues including high time consumption or complex calculations. This paper proposes a compressing sensing-based system that compresses audio signals and simultaneously provides an encryption system. The audio signal is segmented into small matrices of samples and then multiplied by a non-square sensing matrix generated by a Gaussian random generator. The reconstruction process is carried out by solving a linear system using the pseudoinverse of Moore-Penrose. The statistical analysis results obtaining from implementing different types and sizes of audio signals prove that the proposed system succeeds in compressing the audio signals with a ratio reaching 28% of real size and reconstructing the signal with a correlation metric between 0.98 and 0.99. It also scores very good results in the normalized mean square error (MSE), peak signal-to-noise ratio metrics (PSNR), and the structural similarity index (SSIM), as well as giving the signal a high level of security

The Determinants, Inverses, Norm, and Spread of Skew Circulant Type Matrices Involving Any Continuous Lucas Numbers

We consider the skew circulant and skew left circulant matrices with any continuous Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrices and present the determinant and the inverse matrices by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the skew left circulant matrices by utilizing the relationship between skew left circulant matrices and skew circulant matrix, respectively. Finally, the four kinds of norms and bounds for the spread of these matrices are given, respectively

The Interpolating Random Spline Cryptosystem and the Chaotic-Map Public-Key Cryptosystem

The feasibility of implementing the interpolating cubic spline function as encryption and decryption transformations is presented. The encryption method can be viewed as computing a transposed polynomial. The main characteristic of the spline cryptosystem is that the domain and range of encryption are defined over real numbers, instead of the traditional integer numbers. Moreover, the spline cryptosystem can be implemented in terms of inexpensive multiplications and additions. Using spline functions, a series of discontiguous spline segments can execute the modular arithmetic of the RSA system. The similarity of the RSA and spline functions within the integer domain is demonstrated. Furthermore, we observe that such a reformulation of RSA cryptosystem can be characterized as polynomials with random offsets between ciphertext values and plaintext values. This contrasts with the spline cryptosystems, so that a random spline system has been developed. The random spline cryptosystem is an advanced structure of spline cryptosystem. Its mathematical indeterminacy on computing keys with interpolants no more than 4 and numerical sensitivity to the random offset t( increases its utility. This article also presents a chaotic public-key cryptosystem employing a one-dimensional difference equation as well as a quadratic difference equation. This system makes use of the El Gamal’s scheme to accomplish the encryption process. We note that breaking this system requires the identical work factor that is needed in solving discrete logarithm with the same size of moduli

Noise-Resistant Image Encryption Scheme for Medical Images in the Chaos and Wavelet Domain

In this paper, a noise-resistant image encryption scheme is proposed. We have used a cubic-logistic map, Discrete Wavelet Transform (DWT), and bit-plane extraction method to encrypt the medical images at the bit-level rather than pixel-level. The proposed work is divided into three sections; In the first and the last section, the image is encrypted in the spatial domain. While the middle section of the proposed algorithm is devoted to the frequency domain encryption in which DWT is incorporated. As the frequency domain encryption section is a sandwich between the two spatial domain encryption sections, we called it a ”sandwich encryption.” The proposed algorithm is lossless because it can decrypt the exact pixel values of an image. Along with this, we have also gauge the proposed scheme's performance using statistical analysis such as entropy, correlation, and contrast. The entropy values of the cipher images generated from the proposed encryption scheme are more remarkable than 7.99, while correlation values are very close to zero. Furthermore, the number of pixel change rate (NPCR) and unified average change intensity (UACI) for the proposed encryption scheme is higher than 99.4% and 33, respectively. We have also tested the proposed algorithm by performing attacks such as cropping and noise attacks on enciphered images, and we found that the proposed algorithm can decrypt the plaintext image with little loss of information, but the content of the original image is visible

Asymmetric Image Encryption based on Cipher Matrices

In most of the cryptological methods, the encrypted data or the cipher texts maintain same statistics of the plain texts, whereas matrix encryption method does not keep the statistics of individual cipher texts. However, it maintains the statistics of block of characters of size m where m is the size of the key matrix. One of the important features of the cipher matrix in Residue Number System (RNS) is that it is highly dicult and time consuming to obtain its inverse by standard inverse algorithms. Matrix in RNS does not have all the eigen values as dened in complex eld. The eigen factors of a matrix is dened as the irreducible factors of the characteristic equation(eigen function). All the above properties are valid for cipher matrix in Galois Field. The public key is generated by using two types of matrices. One of these matrices is a self-invertible matrix or an orthonormal matrix in Galois eld whereas the other matrix is a diagonally dominant matrix. Matrix inversion is very dicult and time consuming when size of matrix and modulo number are large. The computational overhead in generalized Hill cipher can be reduced substantially by using self-invertible matrices. Self-invertible ma- trices uses less space compared to invertible matrices. In order to overcome this problem, p(modulo) is made very large so that there would be at least pn=2 possible matrices making it extremely dicult for the intruder to nd the key matrix. In this thesis several methods of generating self-invertible matrix are proposed. Orthogonal Transform is used in signal processing. Modular Orthogonal Trans- form such as Walsh, Hadamard, Discrete Cosine Transform, Discrete Sine Trans- form, Discrete Fourier Transform have been used for encryption of image. The orthogonal matrices can be used as asymmetric key for encryption. In this work various methods of generating orthogonal matrices have been proposed. Matrix having primitive polynomial as eigen factors is used resulting in robust encryp- tion. A novel operation called exponentiation and its inverse has been dened in this thesis. All the properties of this new operation have been analyzed in Zp. This operation is used for encryption of image. The original image can be obtained by using the same exponentiation operation. Chaotic sequence and chaotic signal generation is widely used in communica- tion. Two stages of image encryption scheme using chaotic sequence is proposed in this work. First stage of encryption by chaotic sequence generated in GF(p) and the second stge of encryption is carried out by one of the encryption methods discussed in the previous chapters. Standard images have been used for encryption during simulation. Keywords: Encryption, Decryption, Cipher matrix, Public key, Private key, Residue number system, Eigen function, self-invertible matrix, Orthogonal, Ga- lois Field, Exponentiation, Chaotic sequence

Measurements, Models, Systems and Design

531 s.

On the Development of Novel Encryption Methods for Conventional and Biometric Images

Information security refers to the technique of protecting information from unauthorized access, use, disclosure, disruption and modification. Governments, military, corporations, financial institutions, hospitals, and private businesses amass a great deal of confidential information about their employees, customers, products, research, and financial status. Most of this information is now collected, processed and stored on electronic media and transmitted across networks to other computers. Encryption clearly addresses the need for confidentiality of information, in process of storage and transmission. Popular application of multimedia technology and increasingly transmission ability of network gradually leads us to acquire information directly and clearly through images and hence the security of image data has become inevitable. Moreover in the recent years, biometrics is gaining popularity for security purposes in many applications. However, during communication and transmission over insecure network channels it has some risks of being hacked, modified and reused. Hence, there is a strong need to protect biometric images during communication and transmission. In this thesis, attempts have been made to encrypt image efficiently and to enhance the security of biometrics images during transmission. In the first contribution, three different key matrix generation methods invertible, involuntary, and permutation key matrix generation have been proposed. Invertible and involuntary key matrix generation methods solves the key matrix inversion problem in Hill cipher. Permutation key matrix generation method increases the Hill system’s security. The conventional Hill cipher technique fails to encrypt images properly if the image consists of large area covered with same colour or gray level. Thus, it does not hide all features of the image which reveals patterns in the plaintext. Moreover, it can be easily broken with a known plaintext attack revealing weak security. To address these issues two different techniques are proposed, those are advanced Hill cipher algorithm and H-S-X cryptosystem to encrypt the images properly. Security analysis of both the techniques reveals superiority of encryption and decryption of images. On the other hand, H-S-X cryptosystem has been used to instil more diffusion and confusion on the cryptanalysis. FPGA implementation of both the proposed techniques has been modeled to show the effectiveness of both the techniques. An extended Hill cipher algorithm based on XOR and zigzag operation is designed to reduce both encryption and decryption time. This technique not only reduces the encryption and decryption time but also ensures no loss of data during encryption and decryption process as compared to other techniques and possesses more resistance to intruder attack. The hybrid cryptosystem which is the combination of extended Hill cipher technique and RSA algorithm has been implemented to solve the key distribution problem and to enhance the security with reduced encryption and decryption time. Two distinct approaches for image encryption are proposed using chaos based DNA coding along with shifting and scrambling or poker shuffle to create grand disorder between the pixels of the images. In the first approach, results obtained from chaos based DNA coding scheme is shifted and scrambled to provide encryption. On the other hand in the second approach the results obtained from chaos based DNA coding encryption is followed by poker shuffle operation to generate the final result. Simulated results suggest performance superiority for encryption and decryption of image and the results obtained have been compared and discussed. Later on FPGA implementation of proposed cryptosystem has been performed. In another contribution, a modified Hill cipher is proposed which is the combination of three techniques. This proposed modified Hill cipher takes advantage of all the three techniques. To acquire the demands of authenticity, integrity, and non-repudiation along with confidentiality, a novel hybrid method has been implemented. This method has employed proposed modified Hill cipher to provide confidentiality. Produced message digest encrypted by private key of RSA algorithm to achieve other features such as authenticity, integrity, and non-repudiation To enhance the security of images, a biometric cryptosystem approach that combines cryptography and biometrics has been proposed. Under this approach, the image is encrypted with the help of fingerprint and password. A key generated with the combination of fingerprint and password and is used for image encryption. This mechanism is seen to enhance the security of biometrics images during transmission. Each proposed algorithm is studied separately, and simulation experiments are conducted to evaluate their performance. The security analyses are performed and performance compared with other competent schemes