A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

2D Sine Logistic modulation map for image encryption

Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence

A novel image encryption algorithm in streaming mode is proposed which exhaustively employs an entire set of DNA complementary rules alongwith one dimensional chaotic maps. The proposed algorithm is highly efficient due to encrypting the subset of digital image which contains 92.125 % of information. DNA addition operation is carried out on this MSB part. The core idea of the proposed scheme is to scramble the whole image by means of piecewise linear chaotic map (PWLCM) followed by decomposition of image into most significant bits (MSB) and least significant bits (LSB). The logistic sequence is XORed with the decoded MSB and LSB parts separately and finally these two parts are combined to get the ciphered image. The parameters for PWLCM, logistic map and selection of different DNA rules for encoding and decoding of both parts of an image are derived from 128-bit MD5 hash of the plain image. Simulated experimental results in terms of quantitative and qualitative ways prove the encryption quality. Efficiency and robustness against different noises make the proposed cipher a good candidate for real time applications.

An efficient and noise resistive selective image encryption scheme for gray images based on chaotic maps and DNA complementary rules

Book review: Applied cryptography: Protocols, algorithms, and source code in C

In recent years, several methods of secure image encryption were studied and developed through chaotic processes or functions. In this paper, a new image encryption scheme based on a coupling of chaotic function and xor operator is presented. The main advantages of such a method are the abilities to produce a large key space to resist brute-force attacks, and to encrypt securely images with any entropy structure assuring indistinguishability, confusion and diffusion properties in the corresponding cipher-images. The results of several statistical analysis about randomness, sensitivity and correlation of the cipher-images show that the proposed cryptosystem is efficient and secure enough to be used for the image encryption and transmission. Moreover, the implementation of the corresponding algorithm is easy and only integers are used.

A new image encryption scheme based on a chaotic function

Pseudo-random number generator based on mixing of three chaotic maps

A new pseudo-random number generator (PRNG) is proposed The principle of the method consists in mixing chaotic maps produced from an input initial vector The algorithm uses permutations whose positions are computed and indexed by a chaotic function based on linear congruences The performance of this scheme is evaluated through statistical analysis Such a cryptosystem lets appear significant cryptographic qualities for a good security level

/pdf/a-new-pseudo-random-number-generator-based-on-two-chaotic-2vg7skf6rq.pdf

A New Pseudo-Random Number Generator Based on Two Chaotic Maps

The paper describes a symmetric encryption algorithm based on bit permutations and using an iterative process combined with a chaotic function. The main advantages of such a cryptosystem is its ability to encrypt securely bit sequences and assuring confusion, diffusion and indistinguishability properties in the cipher. The algorithm is applied on the image encryption where the plain-image is viewed as binary sequence. The results of statistical analysis about randomness, sensitivity and correlation on the cipher-images show the relevance of the proposed cryptosystem.

/pdf/image-encryption-algorithm-based-on-a-chaotic-iterative-4gf6dq0m14.pdf

Image Encryption Algorithm Based on a Chaotic Iterative Process

Chaos-based cryptography is widely investigated in recent years, especially in the field of random number generators. The paper describes a novel pseudo-random bit generator (PRBG) based on chaotic logistic maps. Three logistic maps are combined in the algorithmic process, and a block of 32 random bits is produced at each iteration. The binary64 double precision format is used according to the IEEE 754-2008 standard for floating-point arithmetic. This generator provides a considerable improvement of an existing generator in the literature. Rigorous statistical analyses are carefully conducted to evaluate the quality and the robustness of the PRBG. The obtained results showed the relevance of the proposed generator, which is suitable even for real-time applications. Povzetek: V ˇ

/pdf/a-fast-chaos-based-pseudo-random-bit-generator-using-308411ycur.pdf

Michael François

Papers

A new image encryption scheme based on a chaotic function

Pseudo-random number generator based on mixing of three chaotic maps

A New Pseudo-Random Number Generator Based on Two Chaotic Maps

Image Encryption Algorithm Based on a Chaotic Iterative Process

A Fast Chaos-Based Pseudo-Random Bit Generator Using Binary64 Floating-Point Arithmetic