Joint Quantization and Diffusion for Compressed Sensing Measurements of Natural Images

Recent research advances have revealed the computational secrecy of the compressed sensing (CS) paradigm. Perfect secrecy can also be achieved by normalizing the CS measurement vector. However, these findings are established on real measurements while digital devices can only store measurements at a finite precision. Based on the distribution of measurements of natural images sensed by structurally random ensemble, a joint quantization and diffusion approach is proposed for these real-valued measurements. In this way, a nonlinear cryptographic diffusion is intrinsically imposed on the CS process and the overall security level is thus enhanced. Security analyses show that the proposed scheme is able to resist known-plaintext attack while the original CS scheme without quantization cannot. Experimental results demonstrate that the reconstruction quality of our scheme is comparable to that of the original one.Comment: 4 pages, 4 figure

Chosen-plaintext attack of an image encryption scheme based on modified permutation-diffusion structure

Since the first appearance in Fridrich's design, the usage of permutation-diffusion structure for designing digital image cryptosystem has been receiving increasing research attention in the field of chaos-based cryptography. Recently, a novel chaotic Image Cipher using one round Modified Permutation-Diffusion pattern (ICMPD) was proposed. Unlike traditional permutation-diffusion structure, the permutation is operated on bit level instead of pixel level and the diffusion is operated on masked pixels, which are obtained by carrying out the classical affine cipher, instead of plain pixels in ICMPD. Following a \textit{divide-and-conquer strategy}, this paper reports that ICMPD can be compromised by a chosen-plaintext attack efficiently and the involved data complexity is linear to the size of the plain-image. Moreover, the relationship between the cryptographic kernel at the diffusion stage of ICMPD and modulo addition then XORing is explored thoroughly

Breaking a novel colour image encryption algorithm based on chaos

Recently, a colour image encryption algorithm based on chaos was proposed by cascading two position permutation operations and one substitution operation, which are all determined by some pseudo-random number sequences generated by iterating the Logistic map. This paper evaluates the security level of the encryption algorithm and finds that the position permutation-only part and the substitution part can be separately broken with only $\lceil (\log_2(3MN))/8 \rceil$ and 2 chosen plain-images, respectively, where $MN$ is the size of the plain-image. Concise theoretical analyses are provided to support the chosen-plaintext attack, which are verified by experimental results also.Comment: 5 pages, 1 figur

Gibbs Sampling using Anti-correlation Gaussian Data Augmentation, with Applications to L1-ball-type Models

L1-ball-type priors are a recent generalization of the spike-and-slab priors. By transforming a continuous precursor distribution to the L1-ball boundary, it induces exact zeros with positive prior and posterior probabilities. With great flexibility in choosing the precursor and threshold distributions, we can easily specify models under structured sparsity, such as those with dependent probability for zeros and smoothness among the non-zeros. Motivated to significantly accelerate the posterior computation, we propose a new data augmentation that leads to a fast block Gibbs sampling algorithm. The latent variable, named ``anti-correlation Gaussian'', cancels out the quadratic exponent term in the latent Gaussian distribution, making the parameters of interest conditionally independent so that they can be updated in a block. Compared to existing algorithms such as the No-U-Turn sampler, the new blocked Gibbs sampler has a very low computing cost per iteration and shows rapid mixing of Markov chains. We establish the geometric ergodicity guarantee of the algorithm in linear models. Further, we show useful extensions of our algorithm for posterior estimation of general latent Gaussian models, such as those involving multivariate truncated Gaussian or latent Gaussian process. Keywords: Blocked Gibbs sampler; Fast Mixing of Markov Chains; Latent Gaussian Models; Soft-thresholding