Analysis of Iterated Modular Exponentiation: The Orbits of xα mod N

Let N and α be integers larger than 1. Define an orbit to be the collection of residues in generated byiteratively applying mod N to an element which eventually maps back to itself.An orbit's length is the number of distinct residues in the orbit. When N isa large bicomposite integer, such as is commonly used in many cryptographicapplications, and when certain prime factorizations related to N are known,all orbit lengths and the number of orbits of each possible length can beefficiently computed using the results presented. If the required integerfactorizations are only partially known, the risk that a randomly selectedperiodic element might produce an orbit shorter than some (typically large)divisor of can be bounded. The information needed to producesuch a bound is fully available when the prime factors of N are generatedusing the prime generation algorithm defined in Maurer maur. Resultspresented can assist in choosing wisely a modulus N for the Blum, Blum, andShub pseudo-random bit generator. If N is a bicomposite RSA modulus, theanalysis shows how to quantify the risk posed by an iterated encryptionattack.     

Double images hiding based on optical interference

A double images hiding technology based on optical interference is proposed. The images are hiding into two computer generated phase only masks which are located at the determined positions. Two beams propagate through the masks and interfere at the preset positions. The desired images will appear at the preset positions. The positions coordinates and wavelength can also be used as encoding parameters. Computer simulations show the validity of this new method.     

Joint Lossless Image Compression and Encryption Scheme Based on CALIC and Hyperchaotic System

For efficiency and security of image transmission and storage, the joint image compression and encryption method that performs compression and encryption in a single step is a promising solution due to better security. Moreover, on some important occasions, it is necessary to save images in high quality by lossless compression. Thus, a joint lossless image compression and encryption scheme based on a context-based adaptive lossless image codec (CALIC) and hyperchaotic system is proposed to achieve lossless image encryption and compression simultaneously. Making use of the characteristics of CALIC, four encryption locations are designed to realize joint image compression and encryption: encryption for the predicted values of pixels based on gradient-adjusted prediction (GAP), encryption for the final prediction error, encryption for two lines of pixel values needed by prediction mode and encryption for the entropy coding file. Moreover, a new four-dimensional hyperchaotic system and plaintext-related encryption based on table lookup are all used to enhance the security. The security tests show information entropy, correlation and key sensitivity of the proposed methods reach 7.997, 0.01 and 0.4998, respectively. This indicates that the proposed methods have good security. Meanwhile, compared to original CALIC without security, the proposed methods increase the security and reduce the compression ratio by only 6.3%. The test results indicate that the proposed methods have high security and good lossless compression performance.     

Robust image encryption by combined use of integral imaging and pixel scrambling techniques

A robust image encryption method by using the integral imaging and pixel scrambling (PS) techniques is proposed. In this method, pixels of the cover image are scrambled with the PS technique and elemental images for this scrambled image are picked up through a lenslet array. Subsequently, an encrypted image is obtained by scrambling these picked-up elemental images. Since this encrypted image has the hologram-like property of data redundancy resulted from the integral imaging scheme, while it can as well be decoded by multiple keys such as the orders of pixel scrambling and the pickup conditions of the elemental images, its security against the various attacks could be dramatically improved. Good experimental results also confirm that the proposed method could provide more enhanced robustness against data loss and Gaussian noises compared to the conventional methods.     

An Image Encryption Approach Using a Shuffling Map

A new image encryption approach is proposed. First, a sort transformation based on nonlinear chaotic algorithm is used to shuffle the positions of image pixels. Then the states of hyper-chaos are used to change the grey values of the shuffled image according to the changed chaotic values of the same position between the above nonlinear chaotic sequence and the sorted chaotic sequence. The experimental results demonstrate that the image encryption scheme based on a shuffling map shows advantages of large key space and high-level security. Compared with some encryption algorithms, the suggested encryption scheme is more secure.     

Performance of encryption schemes in chaotic optical communication: A multifractal approach

From the estimation of the Hurst exponent and the multifractality degree we discriminate the security levels of two typical encoding schemes usually applied in chaos-based communication systems. We also analyze the effects that the sampling period and the message amplitude have on the goodness of these techniques. We compare our results with those obtained by considering an information theory approach [O.A. Rosso, R. Vicente, C.R. Mirasso, Phys. Lett. A 372 (2007) 1018]. The Hurst exponent seems to be a sensitive and powerful tool for discriminating the presence of a message embedded in a chaotic carrier.     

Optical image encryption using Hartley transform and logistic map

We propose a new method for image encryption using Hartley transform with jigsaw transform and logistic map. Logistic map has been used to generate the random intensity mask which is known as chaotic random intensity mask. The problem of bare decryption with Hartley transform has been solved by using the jigsaw transform. In the proposed technique, the image is encrypted using two methods in which the second method is the extension of the first method. In the first method, the image is encrypted using Hartley transform and jigsaw transform. In the second method, the image is encrypted using Hartley transform, jigsaw transform and logistic map. The mean square errors and the signal to noise ratio have been calculated. Robustness of the technique in terms of blind decryption and the algorithmic complexity has been evaluated. The optical implementation has been proposed. The computer simulations are presented to verify the validity of the proposed technique.     

A minimum broadcast graph on 26 vertices

Broadcasting is the process of information dissemination in a communication network in which a message, originated by one member, is transmitted to all members of the network. A broadcast graph is a graph which permits broadcasting from any originator in minimum time. The broadcast function B(n) is the minimum number of edges in any broadcast graph on n vertices. In this paper, we construct a broadcast graph on 26 vertices with 42 edges to prove B(26) = 42.     

RSA公开密钥密码体制及其安全性分析

介绍了公开密钥密码技术、RSA加密算法及密钥产生的方法.分析了公开密钥密码技术的安全性、保密性以及发展前景.     

基于2D Chebyshev-Sine映射的图像加密算法

混沌系统因对初始条件和参数具有极度的敏感性、遍历性和不可预测性,被广泛应用于图像加密领域。提出了一种二维映射——二维Chebyshev-Sine映射。通过分析轨迹图得到映射,与其他混沌映射相比,此映射拥有更宽广的混沌范围和良好的遍历性,对初始条件和系统参数具有高度敏感性,实现成本相对较低。基于此,提出了一种线性混合层图像加密算法:通过行移位和列混合有效改变图像像素空间位置和像素频域中的值,同时使用了中国剩余定理的扩散原则。实验仿真结果证明,此加密算法具有抵抗差分攻击和选择明文攻击的性能,且运行速度快,安全性较高。