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The need for fast and strong image cryptosystems motivates researchers to develop new techniques to apply traditional cryptographic primitives in order to exploit the intrinsic features of digital images. One of the most popular and mature technique is the use of complex ynamic phenomena, including chaotic orbits and quantum walks, to generate the required key stream. In this paper, under the assumption of plaintext attacks we investigate the security of a classic diffusion mechanism (and of its variants) used as the core cryptographic rimitive in some image cryptosystems based on the aforementioned complex dynamic phenomena. We have theoretically found that regardless of the key schedule process, the data complexity for recovering each element of the equivalent secret key from these diffusion mechanisms is only O(1). The proposed analysis is validated by means of numerical examples. Some additional cryptographic applications of our work are also discussed., Comment: 16 pages, 7 figures

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.

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 figures

Recently, an image encryption algorithm based on scrambling and Vegin`ere cipher has been proposed. However, it was soon cryptanalyzed by Zhang et al. using a combination of chosen-plaintext attack and differential attack. This paper briefly reviews the two attack methods proposed by Zhang et al. and outlines the mathematical interpretations of them. Based on their work, we present an improved chosen-plaintext attack to further reduce the number of chosen-plaintexts required, which is proved to be optimal. Moreover, it is found that an elaborately designed known-plaintex attack can efficiently compromise the image cipher under study. This finding is verified by both mathematical analysis and numerical simulations. The cryptanalyzing techniques described in this paper may provide some insights for designing secure and efficient multimedia ciphers., Comment: 11 pages, 14 figures

Some pioneering works have investigated embedding cryptographic properties in compressive sampling (CS) in a way similar to one-time pad symmetric cipher. This paper tackles the problem of constructing a CS-based symmetric cipher under the key reuse circumstance, i.e., the cipher is resistant to common attacks even a fixed measurement matrix is used multiple times. To this end, we suggest a bi-level protected CS (BLP-CS) model which makes use of the advantage of the non-RIP measurement matrix construction. Specifically, two kinds of artificial basis mismatch techniques are investigated to construct key-related sparsifying bases. It is demonstrated that the encoding process of BLP-CS is simply a random linear projection, which is the same as the basic CS model. However, decoding the linear measurements requires knowledge of both the key-dependent sensing matrix and its sparsifying basis. The proposed model is exemplified by sampling images as a joint data acquisition and protection layer for resource-limited wireless sensors. Simulation results and numerical analyses have justified that the new model can be applied in circumstances where the measurement matrix can be re-used., Comment: 14 pages, 8 figures

The robust coding of natural images and the effective compression of encrypted images have been studied individually in recent years. However, little work has been done in the robust coding of encrypted images. The existing results in these two individual research areas cannot be combined directly for the robust coding of encrypted images. This is because the robust coding of natural images relies on the elimination of spatial correlations using sparse transforms such as discrete wavelet transform (DWT), which is ineffective to encrypted images due to the weak correlation between encrypted pixels. Moreover, the compression of encrypted images always generates code streams with different significance. If one or more such streams are lost, the quality of the reconstructed images may drop substantially or decoding error may exist, which violates the goal of robust coding of encrypted images. In this work, we intend to design a robust coder, based on compressive sensing with structurally random matrix, for encrypted images over packet transmission networks. The proposed coder can be applied in the scenario that Alice needs a semi-trusted channel provider Charlie to encode and transmit the encrypted image to Bob. In particular, Alice first encrypts an image using globally random permutation and then sends the encrypted image to Charlie who samples the encrypted image using a structural matrix. Through an imperfect channel with packet loss, Bob receives the compressive measurements and reconstructs the original image by joint decryption and decoding. Experimental results show that the proposed coder can be considered as an efficient multiple description coder with a number of descriptions against packet loss., Comment: 10 pages, 11 figures

Compressive sensing (CS) has been widely studied and applied in many fields. Recently, the way to perform secure compressive sensing (SCS) has become a topic of growing interest. The existing works on SCS usually take the sensing matrix as a key and the resultant security level is not evaluated in depth. They can only be considered as a preliminary exploration on SCS, but a concrete and operable encipher model is not given yet. In this paper, we are going to investigate SCS in a systematic way. The relationship between CS and symmetric-key cipher indicates some possible encryption models. To this end, we propose the two-level protection models (TLPM) for SCS which are developed from measurements taking and something else, respectively. It is believed that these models will provide a new point of view and stimulate further research in both CS and cryptography. Specifically, an efficient and secure encryption scheme for parallel compressive sensing (PCS) is designed by embedding a two-layer protection in PCS using chaos. The first layer is undertaken by random permutation on a two-dimensional signal, which is proved to be an acceptable permutation with overwhelming probability. The other layer is to sample the permuted signal column by column with the same chaotic measurement matrix, which satisfies the restricted isometry property of PCS with overwhelming probability. Both the random permutation and the measurement matrix are constructed under the control of a chaotic system. Simulation results show that unlike the general joint compression and encryption schemes in which encryption always leads to the same or a lower compression ratio, the proposed approach of embedding encryption in PCS actually improves the compression performance. Besides, the proposed approach possesses high transmission robustness against additive Gaussian white noise and cropping attack., Comment: 10 pages, 6 figures

As a fundamental theorem in number theory, the Chinese Reminder Theorem (CRT) is widely used to construct cryptographic primitives. This paper investigates the security of a class of image encryption schemes based on CRT, referred to as CECRT. Making use of some properties of CRT, the equivalent secret key of CECRT can be recovered efficiently. The required number of pairs of chosen plaintext and the corresponding ciphertext is only $(1+\lceil (\log_2L)/l \rceil)$. The attack complexity is only $O(L)$, where $L$ is the plaintext length and $l$ is the number of bits representing a plaintext symbol. In addition, other defects of CECRT such as invalid compression function and low sensitivity to plaintext, are reported. The work in this paper will help clarify positive role of CRT in cryptology., Comment: 7 pages

This paper presents a novel efficient chaotic image encryption scheme, in which the temp-value feedback mechanism is introduced to the permutation and diffusion procedures. Firstly, a simple trick is played to map the plain-image pixels to the initial condition of the Logistic map. Then, a pseudorandom number sequence (PRNS) is obtained from iterating the map. The permutation procedure is carried out by a permutation sequence which is generated by comparing the PRNS and its sorted version. The diffusion procedure is composed of two reversely executed rounds. During each round, the current plain-image pixel and the last cipher-image pixel are used to produce the current cipher-image pixel with the help of the Logistic map and a pseudorandom number generated by the Chen system. To enhance the efficiency, only expanded XOR operation and modulo 256 addition are employed during diffusion. Experimental results show that the new scheme owns a large key space and can resist the differential attack. It is also efficient., Comment: 10 pages, 4 figures

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 figure

Recently, a chaos-based image encryption algorithm using alternate structure (IEAS) was proposed. This paper focuses on differential cryptanalysis of the algorithm and finds that some properties of IEAS can support a differential attack to recover equivalent secret key with a little small number of known plain-images. Detailed approaches of the cryptanalysis for cryptanalyzing IEAS of the lower round number are presented and the breaking method can be extended to the case of higher round number. Both theoretical analysis and experiment results are provided to support vulnerability of IEAS against differential attack. In addition, some other security defects of IEAS, including insensitivity with respect to changes of plain-images and insufficient size of key space, are also reported., Comment: 19 pages

In recent years, a variety of effective chaos-based image encryption schemes have been proposed. The typical structure of these schemes has the permutation and the diffusion stages performed alternatively. The confusion and diffusion effect is solely contributed by the permutation and the diffusion stage, respectively. As a result, more overall rounds than necessary are required to achieve a certain level of security. In this paper, we suggest to introduce certain diffusion effect in the confusion stage by simple sequential add-and-shift operations. The purpose is to reduce the workload of the time-consuming diffusion part so that fewer overall rounds and hence a shorter encryption time is needed. Simulation results show that at a similar performance level, the proposed cryptosystem needs less than one-third the encryption time of an existing cryptosystem. The effective acceleration of the encryption speed is thus achieved., Comment: 16 pages, 7 figures

In 1998, M. S. Baptista proposed a chaotic cryptosystem, which has attracted much attention from the chaotic cryptography community: some of its modifications and also attacks have been reported in recent years. In [Phys. Lett. A 307 (2003) 22], we suggested a method to enhance the security of Baptista-type cryptosystem, which can successfully resist all proposed attacks. However, the enhanced Baptista-type cryptosystem has a nontrivial defect, which produces errors in the decrypted data with a generally small but nonzero probability, and the consequent error propagation exists. In this Letter, we analyze this defect and discuss how to rectify it. In addition, we point out some newly-found problems existing in all Baptista-type cryptosystems and consequently propose corresponding countermeasures., Comment: 13 pages, 2 figures