When an attacker meets a cipher-image in 2018: A year in review

“– Many image encryption schemes are not designed and presented following the basic rules and general guidelines given in [35, 132], which makes essential improvement on the security level of the analyzed schemes very hard.”

“[38], Hua et al. design a sine-transform-based chaotic system (STBCS) of generating one-dimensional (1-D) chaotic maps by performing a sine transform to the combination of the outputs of two maps. In [42], Hua et al. design a two-dimensional (2-D) Logistic-Sine-couplingmap (LSCM) and use it as a source of PRNS control…”

“In [82], 2-D Hénon-Sine map (2D-HSM) is constructed as a PRNG to control the involved DNA rules, DNA operation and the position permutation.”

“In contrast to many data hiding schemes focusing on LSB, an efficient MSB predictionbased method for RDH-EI is proposed in [94], where reserving embedding room before encryption and vacating embedding room after encryption are discussed, respectively.”

“In [61], a bit-level image encryption algorithm is designed by operating multiple rounds of bitwise shift operation and XOR in two directions, where a hyperchaotic map is constructed as the source of PRNG by cascading sine map and Logistic map.”

“nearchaoticmap)[25,26], and coupled map lattice [27]. Rigorously, only the encryptionschemesusingspecialchaosmethodologiescanbe classified as chaos-based encryption schemes, e.g. chaos synchronization [28, 29]. As the opposite of image cryptography,someimpressiveimagecryptanalysisworkswere developed in 2018 [30, 31, 32…”

“As only one round of the two basic operations are used, the encryption scheme designed in [51, 37] are both vulnerable to chosen-plaintext attack.”

“ic map can demonstrate complex bifurcation dynamics in continuous domain. Actually, the real structure of the final chaotic systems obtained with any above way in digital computer should be analyzedas [47] with the perspectiveof state-mappingnetwork. 2.1.2. Design of single round PTDWOS Among the encryption schemes com…”

“Following the framework of Fridrich’s image encryption scheme cryptanalyzed in [2], many image encryption schemes adopting permutationthen-diffusion without substitution-box (PTDWOS) have been proposed since 1998 [3, 4, 5].”

“Especially, all image encryption schemes published in the journal Nonlinear Dynamics before 2018 are critically reviewed in [35].”

“In [113], security of a block-wise image encryption scheme using an ECG signal and the plain-image to determine the used PRNG is analyzed comprehensively.”

“Designing image encryption schemes (algorithms, techniques, methods) and further processing in the domain of the cipher-images received intensive attention from researchers in the field of security, signal procressing, nonlinear science, and etc [1].”

“Due to simplicity and obvious security enhancing effect of position permutation, it is widely used in image encryption scheme [89, 108].”

“In 2018, improvement (enhancement, remedy) methods were proposed to fix the reported security defects in many papers on image cryptanalysis as references [6, 13, 14, 15, 16, 17, 18, 19, 20, 30, 32, 115, 127].”

“cascading two existing chaotic maps [38]; iteratively expanding a parametric 2-D Cat matrix to any higher dimension [24]; arbitrarily combining six basic nonlinear operations [39]; anti-control [40]; constructing hyperchaotic system [41].”

“But, the correlation among blocks in cipher-images may still facilitate the advanced jigsaw puzzle solvers to optimize the attacking on the block-wise permutation schemes analyzed in [110, 111].”

“urgently. •The previous lessons drawn by tough cryptanlaysis are ignored by the designers of new image encryption schemes. For example, the sensitivity mechanisms of PRNS on the plain-image built in [79, 115, 27, 89] can be easily cancelled by constructing some special plain-images, which has been reportedin many cryp…”

“Following the framework of Fridrich’s image encryption scheme cryptanalyzed in [2], many image encryption schemes adopting permutationthen-diffusion without substitution-box (PTDWOS) have been proposed since 1998 [3, 4, 5].”

“In [54], a PRNG based on a 3-D chaotic map is designed.”

“• Quantum image encryption The developmentof quantumcryptographyand quantum chaos attracts image presentation in quantum world and study on how to utilize quantum properties for protecting image data [109, 110]. In [111], a quantum representation model is proposed to let quantum hardware encrypt any number of plainima…”

“In [96], a RDH-EI is designed using homomorphic multiplication and probabilistic properties of Paillier cryptosystem, where the embedding room is reserved before encryption.”

“In [104], a searchable symmetric encryption over encrypted multimedia data is proposed by considering the search criteria as a high-dimensional feature vector, which are further mapped by locality sensitive hashing (LSH).”

“the XOR operation and position permutation on amedicalimage. Asonlyoneroundofthetwobasicoperations are used, the encryptionschemes designedin [52, 37] are both vulnerable to chosen-plaintextattack. In[53], Pinget al. encrypttwoadjacentpixelswithpositionpermutationcontrolledby2-DHe´nonmapandmodulo addition. In [54], Pi…”

“cascading two existing chaotic maps [38]; iteratively expanding a parametric 2-D Cat matrix to any higher dimension [24]; arbitrarily combining six basic nonlinear operations [39]; anti-control [40]; constructing hyperchaotic system [41].”

“In [56], nine special pixels in the plain-image are selected to generate initial conditions of Lorenz system with Secure Hash Algorithms (SHA-256).”

“The equivalent secret key of such diffusion mechanism can be easily recovered [116].”

“To deal with the compressed images, [95] proposes a separable RDH for encrypted JPEG bitstreams, where the original bitstream is losslessly reconstructed using an iterative recovery algorithm.”

“In [26], PWLCM is used as PRNG to control combination of two rounds of position permutation and modular addition.”

“Only a few chaotic image encryption schemes use S-box such as [6, 7, 8].”

“Reference [57] proposes an image encryption scheme based on two rounds of position permutation and XOR operation, which are controlled by PRNSs generated by 2-D”

“In [48], 1-round PTDWOS is proposed, where the algorithm on traversing a graph with the strategy of breadthfirst search is used to implement position permutation, and a hyperchaotic system is used as PRNG to realize the second permutation and diffusion with XOR (bitwise exclusive OR) and modular addition.”

“The development of quantum cryptography and quantum chaos attracts image presentation in quantum world and study on how to utilize quantum properties for protecting image data [106, 107].”

“onand XOR. Then,the intermediate image is further encrypted in the DNA domain with XOR operation. In [80], a scheme encrypting optical image is designed with the same strategy as that in [77, 79]. In [81], an image encryption scheme using pixel-level scrambling, bit-level scrambling, and DNA encoding is proposed, wher…”

“In 2018, improvement (enhancement, remedy) methods were proposed to fix the reported security defects in many papers on image cryptanalysis as references [6, 13, 14, 15, 16, 17, 18, 19, 20, 30, 32, 115, 127].”

“As only one round of the two basic operations are used, the encryption scheme designed in [51, 37] are both vulnerable to chosen-plaintext attack.”

“In [59], multiple rounds of PTDWOS are implemented in the level of bit plane, where Skew Tent map is used as source of PRNS.”

“ution-box (PTDWOS) have been proposedsince 1998 [3, 4, 5]. Only a few chaotic image encryption schemes use S-box such as [6, 7, 8]. There are some papers focusing on designing S-box with chaotic maps [9, 10, 11, 12]. In [6, 13, 14, 15, 16, 17, 18, 19, 20], the analyzedimageencryptionschemeswere fixedtowithstand the pro…”

“cascading two existing chaotic maps [38]; iteratively expanding a parametric 2-D Cat matrix to any higher dimension [24]; arbitrarily combining six basic nonlinear operations [39]; anti-control [40]; constructing hyperchaotic system [41].”

“In [63], a 2-D partitioned cellular automata is designed to generate PRNS satisfying the global Strict Avalanche Criterion, which is used to control combination of some basic operations including substituting with an S-box.”

“Due to the large size of conventional image files, compression and encryption should be combined well [89, 130].”

“Due to simplicity and obvious security enhancing effect of position permutation, it is widely used in image encryption scheme [89, 108].”

“With the development of DNA computing, designing image encryption schemes based on DNA encoding received intensive attentions in the past decade [76].”

“In 2018, improvement (enhancement, remedy) methods were proposed to fix the reported security defects in many papers on image cryptanalysis as references [6, 13, 14, 15, 16, 17, 18, 19, 20, 30, 32, 115, 127].”

“In [80], a scheme encrypting optical image is designed with the same strategy as that in [77, 79].”

“In[49], an encryption scheme of image blocks with variable size is proposed, which is composed of position permutation and modulo addition.”

“In [78], a robust color image encryption system using Lorenz-Rossler chaotic map and DNA encoding is proposed, where Lorenz-Rossler chaotic map is used as the source for producing PRNS.”

“In [103], a privacy preserving biometrics-based authentication solution is proposed”

“In [121], usability of a 4-round DTPWOS (diffusion-then-permutation without substitution-box) is questioned, which can be considered as a special form of 5-round PTDWOS.”

“In [71], GA is used to perform parallel permutation and substitution on multiple bit-planes of the plain-image.”

“In 2018, improvement (enhancement, remedy) methods were proposed to fix the reported security defects in many papers on image cryptanalysis as references [6, 13, 14, 15, 16, 17, 18, 19, 20, 30, 32, 115, 127].”

“As the insecurity of sole permutation analyzed in [114], position permutation is still a simple but efficient measure to improve the security level of the whole encryption scheme.”

“In [25], a self-adapting colour image encryption scheme based on chaotic maps and the interactions among three channels is proposed.”

“The framework of the image encryption scheme is the same as that of [53].”

“In [50], the proposed image encryption scheme performs only one round of position permutation and XOR operation, which are both controlled by PRNS generated by iterating 2-D Baker’s map.”

“In [56], Ping et al.”

“In [69], an image encryption scheme using beta chaotic map, NSCT (Nonsubsampled Contourlet Transform), and GA (genetic algorithm) is proposed.”

“Using strong correlation among neighboring bits in every bit-plane in a natural image, a cipher-text only attack is proposed in [34] to recover”

“s scheme suggested in [16] is found still vulnerable against chosenplaintextattack[17]. Assumingaparameterseedis known, the parameter determining the shift permutation of Pak’s scheme is disclosed in [18] by its internalproperties. Then, Pak’s scheme is degenerated into the version analyzed in [16]. Based on the preli…”

“e parts: position permutation; nonlinear substitution; XOR operation. In [122], M. Li et al. recover the permutation relation of image encryption scheme using PTDWOS with some chosen plain-images. In [123], M. Li et al. recover the equivalent secret key of an encryptionalgorithmusingone-roundPTDWOSwith512pairsof chose…”

“cascading two existing chaotic maps [38]; iteratively expanding a parametric 2-D Cat matrix to any higher dimension [24]; arbitrarily combining six basic nonlinear operations [39]; anti-control [40]; constructing hyperchaotic system [41].”

“In [70], teaching learning based optimization algorithm and gravitational search algorithm are used to optimize selection of the parameters.”

“ansform [88]. Detailed experimental results demonstrate that MPFrQFT is superior to other eight existing algorithms on multiplemetrics: keyspace,keysensitivity,statistical analysis and robustness. In [89], an optical hyperspectral image cryptosystem is proposed using improved Chirikov mapping in the gyrator transform…”

“Following the framework of Fridrich’s image encryption scheme cryptanalyzed in [2], many image encryption schemes adopting permutationthen-diffusion without substitution-box (PTDWOS) have been proposed since 1998 [3, 4, 5].”

“In [122], M.”

“In [84], the saliency detection of a plainimage is detected with a given model and encrypted with a chaos-based encryption function.”

“Only a few image encryption schemes are designed for solving security challenge in specific application scenario: surveillance [37], IIoT (industrial Internet of Things) [29], social media [88].”

“In [80], a scheme encrypting optical image is designed with the same strategy as that in [77, 79].”

“In [65], the four LSB (least significant bit) planes of two images are encrypted by position permutation and value confusion, which are controlled by Logistic map and CA, respectively.”

“In [86], a holographic encryption scheme based on interleaving operation of CGHs (computer-generated holograms) is proposed.”

“pace complexity for storing the intermediate data. In 2018, improvement (enhancement,remedy) methods were proposedto fix the reportedsecurity defects in manypapers on image cryptanalysis as references [6, 13, 14, 15, 16, 17, 18, 19, 20, 30, 32, 115, 127]. In fact, the proposed improvement methods fail to obtain the exp…”

“In [72], an image encryption scheme based on compressive sensing and chaotic map were proposed.”

“In 2018, improvement (enhancement, remedy) methods were proposed to fix the reported security defects in many papers on image cryptanalysis as references [6, 13, 14, 15, 16, 17, 18, 19, 20, 30, 32, 115, 127].”

“In [31], another encryption scheme using PTDWOS is cryptanalyzed.”

“In [90], the fast methods on implementing real and complex Walsh-Hadamard Transform in the cipher-images are proposed.”

“In [101], an image secret sharing with three decoding options, lossless recovery, grayscale stacking recovery and visual previewing, is designed based on random grid-based VSS and Chinese remainder theorem.”

“n invisible watermark. 2.3. Encrypting image in transform domain A series of encryption schemes protecting optical images are proposed in 2018. But, most of them are simulated with digital images. In [84], a monospectral SAII (synthetic aperture integral imaging) system is designed to capture 2-D optical elemental ima…”

“In [46], a 6-D discrete chaotic systems (SDDCS) is constructed with some sine and cosine functions, which is then used as a source of PRNS used in a stream cipher.”

“In [121], M.”

“In [73], a plain-image is first decomposed by wavelet packet transform (WPT).”

“at more than k shares can also reveal the secret image. As for progressive (k,n) secret image sharing (PSIS) scheme, it is requiredthat k to n shares can reconstructthe secret image progressively. In [103], three PSIS schemesare constructed using XOR operation, a variant of Hamming code and modified version of shorten…”

“In [67], a sequence of images are simultaneously encrypted and compressed using Tensor Compressive Sensing, which is controlled by PRNS generated by a 3-D discrete Lorenz system.”

“In [62], an image encryption algorithm based on 1-D PWLCM and least squares approximation (LSA) is proposed, where PWLCM is used to determine the permutation relationship among the rows and columns of the plain-image and intermediate matrixes.”

“In 2018, improvement (enhancement, remedy) methods were proposed to fix the reported security defects in many papers on image cryptanalysis as references [6, 13, 14, 15, 16, 17, 18, 19, 20, 30, 32, 115, 127].”

“Based on comprehensive analysis of ranomness of the PRNS generated by iterating a map, one variant of Logistic map is selected in [45] as a PRNG.”

“Only a few image encryption schemes are designed for solving security challenge in specific application scenario: surveillance [37], IIoT (industrial Internet of Things) [29], social media [88].”

“In [75], compressive sensing technique is combined with a stream cipher to simultaneously compress and encrypt image and video files, where the measurement matrix is generated using a stream cipher.”

“In [123], a ciphertext-only attack on a double-image optical encryption technique based on an asymmetric (publickey encryption) algorithm is proposed using phase retrieval algorithm with median filtering and normalization operation.”

“Similar to the strategy introduced in [2], the permutation relation of a multiple-round PTDWOS is recovered by checking how the changes of the cipher-pixels influence that of the plain-pixels in the scenario of chosen-ciphertext attack [122].”

“As analyzed in [21], coupled logistic map can demonstrate complex bifurcation dynamics in continuous domain.”

“The same strategy is used in [43], where a spatio-temporal chaotic system is coupled with Tent-Sine system to generate PRNS.”

“In [99], three efficient and flexible XOR-based (k, n)VSS schemes is constructed, such that more than k shares can also reveal the secret image.”

“Reference [58] adopts the same encryption structure as [57] with hardware implementation, where Lorenz chaotic system, Lü’s chaotic system and cellular automata are used as the source of PRNS instead.”

“In [22], 2-D Logistic map is used to generate PRNG to control combination of position permutation and diffusion with XOR.”

“wireless communication [36], surveillance [37].”

“ptions, lossless recovery, grayscale stacking recovery and visual previewing, is designed based on random grid-based VSS and Chinese remaindertheorem. • Privacy-preservingapplication of image data In [105], Yuan et al. use similarity degree among encrypted higher-dimensional profile vectors of users images as a metric…”

“ransform domain, the original hyperspectral image is converted into binary format and then extended into a 1- D array, then the scrambled and exchanged image is transformedusingthegyratortransform. In[90],quickresponse (QR) code-based non-linear technique for image encryption using shearlet transform and spiral phase…”

“In [133], Lin et al.”

“same research group presented a specific attack based on phase retrieval algorithm with normalization and a bilateral filter in [124].”

“Logistic map [21, 22], Tent map [12, 23], Cat map [24], PWLCM (piecewise linear chaotic map) [25, 26], and coupled map lattice [27].”

“In [93], an enhanced RDH-EI embedding two bits in each cipher-pixel with minimum distortion of stego-pixel is achieved through homomorphic encryption.”

“In [128], a chosen-ciphertext attack on a chaotic stream cipher using self-synchronization and closed-loop feedback were proposed.”

“As the opposite of image cryptography, some impressive image cryptanalysis works were developed in 2018 [30, 31, 32, 33, 34, 35].”

“But, how to perform the attack on the PTDWOS with multiple rounds are not theoretically proved in [13].”

“In [120], some special plain-images are selected to narrow the scope of some subkeys of a PTDWOS with less than or equal to 3 rounds.”

“As [131], only ROI (region of interest) of DICOM (Digital Imaging and Communications in Medicine) medical images are encrypted with one round of permutation and substitution to satisfy real-time processing requirement.”

“In [85], the original image is first scrambled, and then multiplied by the random-phase mask function.”

“Logistic map [21, 22], Tent map [12, 23], Cat map [24], PWLCM (piecewise linear chaotic map) [25, 26], and coupled map lattice [27].”

“In [68], an encryption scheme encrypting multiple optical colour images is proposed based on phase retrieval in quaternion gyrator domain, nonlinear quaternion correlation is developed to perform authentication.”

“But, the correlation among blocks in cipher-images may still facilitate the advanced jigsaw puzzle solvers to optimize the attacking on the block-wise permutation schemes analyzed in [110, 111].”

“In [64], another DCIE using Gyrator transform and Hénon map is proposed.”

“In [101], C.”

“cascading two existing chaotic maps [38]; iteratively expanding a parametric 2-D Cat matrix to any higher dimension [24]; arbitrarily combining six basic nonlinear operations [39]; anti-control [40]; constructing hyperchaotic system [41].”

“In [92], two RDH-EI schemes are proposed with private-key homomorphism and publickey homomorphism, respectively.”

“ve recovery algorithm. In [96], a RDH-EI is designed using homomorphic multiplication and probabilistic properties of Paillier cryptosystem, where the embedding room is reserved before encryption. In [97], C. Wang et al. formulate lossy compression on low-frequency wavelet coefficients as a problem of weighted rate-dist…”

“In 2018, improvement (enhancement, remedy) methods were proposed to fix the reported security defects in many papers on image cryptanalysis as references [6, 13, 14, 15, 16, 17, 18, 19, 20, 30, 32, 115, 127].”

“Following the basic structure of AES, a robust image symmetric cryptosystem (RISC) is proposed in [61], where Arnold’s cat map is used to generate permutation matrix permuting the entire plain-image.”

“In [130], a large number of plaintexts and the corresponding ciphertexts encrypted by any optical encryption technique based on random phase encoding are used as training samples for optimizing the parameters of a deep neural network, which can reconstruct any plain-image from its corresponding cipher-image.”

“Chosen-plaintext attack (CPA) is the strongest one of the four classical cipher attack methods [35].”

“Therefore, communication security in a digital world becomes a serious problem and gains more and more attention [1] .”

“The representative image encryption schemes published in year 2018 are reviewed in [50].”

“Certainly, implementing the 2-D sine map-based PRNG and cryptosystem for secure communications [34] and image encryptions [35] deserves further”

“In [24], the attack can also build the equivalent keys for the diffusion process by selecting plain images to encrypt.”

“As CS has the potentials of significantly improving the sampling speed and sensor energy efficiency, it has been applied in many practical applications, including single pixel imaging [2], fast magnetic resonance imaging [3], high-speed video cameras [4] and image encryption [5].”

“Consequently, in many application scenarios, traditional The associate editor coordinating the review of this manuscript and approving it for publication was Lefei Zhang . encryption schemes such as Data Encryption Standard (DES) cannot well meet the requirements of protecting image data [3], [4].”

“As mentioned in [64,65], to withstand dynamical degradation, several approaches have been put forward, for example, adoption of higher precision [66], perturbing chaotic states [67], perturbing control parameters [68], cascading multiple chaotic maps [69], switching multiple chaotic maps [70] and…”

“Furthermore, the representation of the secret key should also use a more canonical binary sequence form, otherwise it easily leads to the key sensitivity problem pointed out by Li et al [3,44].”

“Similar to digitized Logistic map and Tent map analyzed in [24], the degradation patterns of CLS map and CLT map are similar (regardless of the implementation precision and quantization schemes).”

“Although necessary, these statistical tests are not sufficient and further analysis must be performed to show the resistance of the proposed framework to specific cryptanalysis scenarios [45], [46].”

“Acomprehensive review of recent image encryption schemes can be found in [44].”

“chaotic cryptography [21], image encryption [22], image privacy protection [23], [24], hashing scheme [25], PRNG [11], [26], random perturbation [27], designing unpredictable path flying robot [28].”

“Motivated by image encryption schemes and cryptanalysis [19], we contribute by designing and proposing a symmet-”

“Since the first quantum key distribution 66 (QKD) protocol was proposed in 1984 [19], various quantum 67 cryptographic protocols have emerged one after another, such 68 as quantum homomorphic encryption protocols [20], [21], 69 quantum voting methods [22], [23], quantum image encryp- 70 tion [24], [25], and quantum di…”

“It can be clearly seen that without the key, the content of the original image cannot be obtained by unauthorized users only from the encrypted image Ie or the marked encrypted image Iew, and both of images have security from the analysis in [33].”

“A comprehensive review of the application of nonlinear dynamics for image encryption can be found in [37], [46], [47].”

“CHAOS played a critical role in applications of chaosbased secure communication systems [1], [2].”

“The algorithm utilizes a standard diffusion and confusion configuration [23].”

“[4] Review of image cryptanalysis published in 2018 Features the challenges on design and analysis of image encryption schemes 6.”

“New methods and countermeasures should be constantly researched as new attack techniques are developed [1,2].”

“Many previous studies have dealt with Security images in general [11], and medical images in particular [12].”

“Software applications involve Bitcoin digital signature scheme [4], OpenSSL protocols [5], image encryption [6,7], and others.”

“In recent years, more and more image encryption algorithms have been proposed to withstand the challenge [3, 4, 5].”

“Current review papers [2–4] often analyse encryption techniques operated on various image types, a comprehensive review on JPEG related encryption schemes and the guideline for designing scenario-oriented JPEG encryption method are missing.”

“Various template attacks, evaluation guides, design criteria are prepared [4]–[6], [20]–[22], [28], [29], [32], [34], [35].”

“In the past two decades, chaotic image encryption technology has been widely discussed and has become a research hotspot [6].”

“The use of dynamic key-dependent S-boxes adds another layer of confusion, which increases key space and improves security of image encryption schemes [42].”

“Due to the above shortcomings, when classic simple chaotic maps are directly applied in applications, they may not necessarily achieve the desired benefits and their inherent short-comings may turn into potential (security) vulnerabilities [15].”

“Compared with traditional schemes, chaotic information encryption technology is suggested to have higher security and rapidity [3], [4].”

“– Collision Resistance - it should be computationally infeasible to find two (or more) different messages that hash to the same value [33].”

“Among them, chaotic systems are being favored bymore andmore researchers [2], [4], [5], [9].”

“update speed of the algorithm is faster than ever before [6], [7], [8], [9], [10].”

“And in order to continuously improve the efficiency and security of chaotic image encryption, many new chaotic image encryption algorithms are proposed every year [5], [14]–[16].”

“Similar to the need to protect some important private information in our lives (such as [36,37]), we need to protect some important data information from being leaked.”

“One of the most striking subjects among these alternative researches is design studies based on nonlinear dynamics [2], [3].”

“According to essential structure and used methodologies, the encryption schemes using chaotic system are roughly divided into the following five parts: randomness-oriented chaos enhancement, single round of encryption, multiple rounds of encryption, encrypting multiple images simultaneously, and compression image encr…”

“Many chaos-based image encryption schemes have been proposed by the researchers working in the field of nonlinear dynamic and information security [2, 3].”

“To address this problem, symmetric key algorithms such as the Advanced Encryption Standard (AES), Secure Hash Algorithm (SHA), and Lightweight Encryption Algorithm (LEA) with a block encryption structure have been applied to increase security [3,4].”