Abstract: This paper proposes an image encryption algorithm based on a chaotic map and information entropy. Unlike Fridrich’s structure, the proposed method contains permutation, modulation, and diffusion (PMD) operations. This method avoids the shortcoming in traditional schemes of strictly shuffling the pixel positions before diffusion encryption. Information entropy is employed to influence the generation of the keystream. The initial keys used in the permutation and diffusion stages interact with each other. As a result, the algorithm acts as an indivisible entity to enhance security. Experimental results and security analyses demonstrate the good performance of the proposed algorithm as a secure and effective communication method for images.

Abstract: We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids (e.g. images). However, point clouds are irregular and unordered, thus directly convolving kernels against features associated with the points, will result in desertion of shape information and variance to point ordering. To address these problems, we propose to learn an $\mathcal{X}$-transformation from the input points, to simultaneously promote two causes. The first is the weighting of the input features associated with the points, and the second is the permutation of the points into a latent and potentially canonical order. Element-wise product and sum operations of the typical convolution operator are subsequently applied on the $\mathcal{X}$-transformed features. The proposed method is a generalization of typical CNNs to feature learning from point clouds, thus we call it PointCNN. Experiments show that PointCNN achieves on par or better performance than state-of-the-art methods on multiple challenging benchmark datasets and tasks.

Abstract: Recently, several multimedia encryption techniques with permutation–diffusion architecture have been developed. The traditional architecture applies the diffusion and permutation functions as two separate phases. This separable design enables the attacker to launch several forms of attacks in addition to the degradation of the encryption speed. Furthermore, during the diffusion phase, the image pixels are masked in a static order, which may expose significant information about the encryption technique to the attacker. Accordingly, to remedy these problems, this paper suggests an efficient image cryptosystem based on simultaneous permutation and diffusion functions that process the image pixels in a dynamic order fashion. Specifically, the proposed method employs the Chebyshev-Chebyshev map to horizontally and vertically mix the plain-image information. Then, it utilizes the modified Logistic map to mask the image pixels and shuffle the masked values simultaneously. Meanwhile, the control parameters of the employed chaos systems are directly correlated to the plain-image to assure that different key-streams are created for distinct plain-images. Simulation results and security scrutiny confirm that the suggested cipher has several brilliant characteristics, including the robustness against various types of attacks.

Abstract: Utterance level permutation invariant training (uPIT) technique is a state-of-the-art deep learning architecture for speaker independent multi-talker separation. uPIT solves the label ambiguity problem by minimizing the mean square error (MSE) over all permutations between outputs and targets. However, uPIT may be sub-optimal at segmental level because the optimization is not calculated over the individual frames. In this paper, we propose a constrained uPIT (cuPIT) to solve this problem by computing a weighted MSE loss using dynamic information (i.e., delta and acceleration). The weighted loss ensures the temporal continuity of output frames with the same speaker. Inspired by the heuristics (i.e., vocal tract continuity) in computational auditory scene analysis, we then extend the model by adding a Grid LSTM layer, that we name it as cuPIT-Grid LSTM, to automatically learn both temporal and spectral patterns over the input magnitude spectrum simultaneously. The experimental results show 9.6% and 8.5% relative improvements on WSJ0-2mix dataset under both closed and open conditions comparing with the uPIT baseline.

Abstract: We consider the problem of learning a Bayesian network or directed acyclic graph (DAG) model from observational data. A number of constraint-based, score-based and hybrid algorithms have been developed for this purpose. For constraint-based methods, statistical consistency guarantees typically rely on the faithfulness assumption, which has been show to be restrictive especially for graphs with cycles in the skeleton. However, there is only limited work on consistency guarantees for score-based and hybrid algorithms and it has been unclear whether consistency guarantees can be proven under weaker conditions than the faithfulness assumption. In this paper, we propose the sparsest permutation (SP) algorithm. This algorithm is based on finding the causal ordering of the variables that yields the sparsest DAG. We prove that this new score-based method is consistent under strictly weaker conditions than the faithfulness assumption. We also demonstrate through simulations on small DAGs that the SP algorithm compares favorably to the constraintbased PC and SGS algorithms as well as the score-based Greedy Equivalence Search and hybrid MaxMin Hill-Climbing method. In the Gaussian setting, we prove that our algorithm boils down to finding the permutation of the variables with sparsest Cholesky decomposition for the inverse covariance matrix. Using this connection, we show that in the oracle setting, where the true covariance matrix is known, the SP algorithm is in fact equivalent to `0-penalized maximum likelihood estimation.

Abstract: This paper presents Xoodoo, a 48-byte cryptographic permutation with excellent propagation properties. Its design approach is inspired by Keccak-p, while it is dimensioned like Gimli for efficiency on low-end processors. The structure consists of three planes of 128 bits each, which interact per 3-bit columns through mixing and nonlinear operations, and which otherwise move as three independent rigid objects. We analyze its differential and linear propagation properties and, in particular, prove lower bounds on the weight of trails using the tree search-based technique of Mella et al. (ToSC 2017). Xoodoo’s primary target application is in the Farfalle construction that we instantiate for the doubly-extendable cryptographic keyed (or deck) function Xoofff. Combining a relatively narrow permutation with the parallelism of Farfalle results in very efficient schemes on a wide range of platforms, from low-end devices to high-end processors with vector instructions.

Abstract: In recent years, a number of chaos-based image encryption schemes have been proposed. In digital images, pixel is considered as the smallest element. So, most of the image encryption schemes implement diffusion and permutation operation at the pixel level. The substitution process creates diffusion. It can be done by using the substitution box (S-box). Although the S-box plays a vital role in any cryptosystem, the S-box substitution takes too much time to substitute the pixels of an image of size $ 256 \times 256$ or more than $ 256 \times 256$ . So, in this paper, for the low time complexity, bit level permutation is performed by extracting the binary bit planes from the plaintext image. Bit level permutation has an ability to create confusion and diffusion at the same time. A new random image is introduced to create more diffusion. The chaotic cubic-logistic and logistic map are also used in the proposed cryptosystem. Experimental results are carried out to show the efficiency of the proposed cryptosystem.

Abstract: Polar codes are a channel coding scheme for the next generation of wireless communications standard (5G). The belief propagation (BP) decoder allows for parallel decoding of polar codes, making it suitable for high throughput applications. However, the error-correction performance of polar codes under BP decoding is far from the requirements of 5G. It has been shown that the error-correction performance of BP can be improved if the decoding is performed on multiple permuted factor graphs of polar codes. However, a different BP decoding scheduling is required for each factor graph permutation which results in the design of a different decoder for each permutation. Moreover, the selection of the different factor graph permutations is at random, which prevents the decoder to achieve a desirable error correction performance with a small number of permutations. In this paper, we first show that the permutations on the factor graph can be mapped into suitable permutations on the codeword positions. As a result, we can make use of a single decoder for all the permutations. In addition, we introduce a method to construct a set of predetermined permutations which can provide the correct codeword if the decoding fails on the original permutation. We show that for the 5G polar code of length 1024, the error-correction performance of the proposed decoder is more than 0.25 dB better than that of the BP decoder with the same number of random permutations at the frame error rate of 0.0001.

Abstract: Motivated by communication channels in which the transmitted sequences are subjected to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted in the form of multisets of symbols from a given finite alphabet. A general channel model is assumed in which the transmitted multisets are potentially impaired by insertions, deletions, substitutions, and erasures of symbols. Several constructions of error-correcting codes for this channel are described, and bounds on the size of optimal codes correcting any given number of errors are derived. The construction based on the notion of Sidon sets in finite Abelian groups is shown to be optimal, in the sense of the asymptotic scaling of code redundancy, for any error radius and alphabet size. It is also shown to be optimal in the stronger sense of maximal code cardinality in various cases.

Abstract: When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole permutation group is used, and methods based on random permutations tend to be seen as approximate. There exists a very limited amount of literature on exact testing with random permutations, and only recently a thorough proof of exactness was given. In this paper, we provide an alternative proof, viewing the test as a “conditional Monte Carlo test” as it has been called in the literature. We also provide extensions of the result. Importantly, our results can be used to prove properties of various multiple testing procedures based on random permutations.

Abstract: G-quadruplexes are unusual DNA and RNA secondary structures ubiquitous in a variety of organisms including vertebrates, plants, viruses and bacteria. The folding topology and stability of intramolecular G-quadruplexes are determined to a large extent by their loops. Loop permutation is defined as swapping two or three of these regions so that intramolecular G-quadruplexes only differ in the sequential order of their loops. Over the past two decades, both length and base composition of loops have been studied extensively, but a systematic study on the effect of loop permutation has been missing. In the present work, 99 sequences from 21 groups with different loop permutations were tested. To our surprise, both conformation and thermal stability are greatly dependent on loop permutation. Loop permutation actually matters as much as loop length and base composition on G-quadruplex folding, with effects on Tm as high as 17°C. Sequences containing a longer central loop have a high propensity to adopt a stable non-parallel topology. Conversely, sequences containing a short central loop tend to form a parallel topology of lower stability. In addition, over half of interrogated sequences were found in the genomes of diverse organisms, implicating their potential regulatory roles in the genome or as therapeutic targets. This study illustrates the structural roles of loops in G-quadruplex folding and should help to establish rules to predict the folding pattern and stability of G-quadruplexes.

Abstract: In recent days, there is a high demand of encryption of multiple digital images for secure transmission of multiple images. This paper proposes a multi-level permutation operation based secure multiple colour image encryption technique which is totally different than the currently used multiple image encryption techniques. The proposed encryption technique uses three levels of permutation operation: the first level of permutation operation performs pixel-shuffling operations in R, G, and B components, itself; the second level of permutation operation performs row-shuffling operations in between the pixel-shuffled R, G, and B components; the third level of permutation operation performs column-shuffling operations in between the row-shuffled components. At last, the proposed encryption algorithm performs block-diffusion operations to get the final encrypted images. Multi-level permutation operations and diffusion operation only use PWLCM systems multiple times to make the algorithm more secure and stronger. Multiple PWLCM systems in multi-level permutation operations not only produces larger key space and higher key sensitivity but also generates greater randomness of pixels and weaker correlation of adjacent pixels in images as compared to the currently used multiple image encryption techniques. In addition the secret keys which are used in this proposed algorithm not only depends on the original key values but also depends on the original colour images. This protects the algorithm against known-plaintext attack and chosen-plaintext attack. The simulation results and the security analysis indicate that the proposed algorithm has good encryption results, large secret-key space, higher sensitivity towards secret keys and the plaintext, weaker correlation of adjacent pixels, greater randomness of pixels, and enough resistance against various common attacks.

Abstract: Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme is presented. Through a nearest neighbor approach, the test efficiently adapts also to non-smooth distributions due to strongly nonlinear dependencies. Numerical experiments demonstrate that the test reliably simulates the null distribution even for small sample sizes and with high-dimensional conditioning sets. The test is better calibrated than kernel-based tests utilizing an analytical approximation of the null distribution, especially for non-smooth densities, and reaches the same or higher power levels. Combining the local permutation scheme with the kernel tests leads to better calibration, but suffers in power. For smaller sample sizes and lower dimensions, the test is faster than random fourier feature-based kernel tests if the permutation scheme is (embarrassingly) parallelized, but the runtime increases more sharply with sample size and dimensionality. Thus, more theoretical research to analytically approximate the null distribution and speed up the estimation for larger sample sizes is desirable.

Abstract: Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and polar codes. Using the symmetric group of RM and polar codes, the specific decoding algorithm can be carried out on multiple permutations of the factor graph to boost the error-correction performance. However, this approach results in high decoding complexity. In this paper, we first derive the total number of factor graph permutations on which the decoding can be performed. We further propose a successive permutation (SP) scheme which finds the permutations on the fly, thus the decoding always progresses on a single factor graph permutation. We show that SP can be used to improve the error-correction performance of RM and polar codes under successive-cancellation (SC) and SC list (SCL) decoding, while keeping the memory requirements of the decoders unaltered. Our results for RM and polar codes of length 128 and rate 0.5 show that when SP is used and at a target frame error rate of 10−4, up to 0.5 dB and 0.1 dB improvement can be achieved for RM and polar codes respectively.

Abstract: We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with $k$-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.

Abstract: Polar codes are a channel coding scheme for the next generation of wireless communications standard (5G). The belief propagation (BP) decoder allows for parallel decoding of polar codes, making it suitable for high throughput applications. However, the error-correction performance of polar codes under BP decoding is far from the requirements of 5G. It has been shown that the error-correction performance of BP can be improved if the decoding is performed on multiple permuted factor graphs of polar codes. However, a different BP decoding scheduling is required for each factor graph permutation which results in the design of a different decoder for each permutation. Moreover, the selection of the different factor graph permutations is at random, which prevents the decoder to achieve a desirable error-correction performance with a small number of permutations. In this paper, we first show that the permutations on the factor graph can be mapped into suitable permutations on the codeword positions. As a result, we can make use of a single decoder for all the permutations. In addition, we introduce a method to construct a set of predetermined permutations which can provide the correct codeword if the decoding fails on the original permutation. We show that for the 5G polar code of length $1024$, the error-correction performance of the proposed decoder is more than $0.25$ dB better than that of the BP decoder with the same number of random permutations at the frame error rate of $10^{-4}$.

Abstract: Detecting abrupt correlation changes in multivariate time series is crucial in many application fields such as signal processing, functional neuroimaging, climate studies, and financial analysis. To detect such changes, several promising correlation change tests exist, but they may suffer from severe loss of power when there is actually more than one change point underlying the data. To deal with this drawback, we propose a permutation based significance test for Kernel Change Point (KCP) detection on the running correlations. Given a requested number of change points K, KCP divides the time series into K + 1 phases by minimizing the within-phase variance. The new permutation test looks at how the average within-phase variance decreases when K increases and compares this to the results for permuted data. The results of an extensive simulation study and applications to several real data sets show that, depending on the setting, the new test performs either at par or better than the state-of-the art significance tests for detecting the presence of correlation changes, implying that its use can be generally recommended.

Abstract: A new image encryption and decryption algorithm based on chaotic map and dynatomic modular curve is proposed in this paper. Firstly, the definition of dynatomic modular curve and its periodic points are introduced, and a property of the dynatomic modular curve is proved. Secondly, the relationship between the Logistic map and the dynatomic modular curve is discussed. Finally, the encryption algorithm which is composed of permutation of pixels and substitution is given. In order to eliminate sufficiently the relation between adjacent pixels in the image, pixel values of the original image are sorted as index function, which derives from Logistic map and dynatomic modular curve. And XOR operation is performed between the scrambled pixel sequence and projective transformation sequence. Simulation experiments and nonparametric hypothesis test demonstrate that the proposed algorithm is secure to resist different types of attacks and it can be applied to real-time encryption.

Abstract: Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. Particularly, permutation polynomials with few terms are more popular for their simple algebraic form and additional extraordinary properties. Very recently, G. Kyureghyan and M.E. Zieve (2016) studied permutation polynomials over Fqn$\mathbb {F}_{q^{n}}$ of the form x+?Trqn/q(xk)$x+\gamma \text {Tr}_{q^{n}/q}(x^{k})$, where q is odd, and nine classes of permutation polynomials were constructed. In this paper, we present fifteen new classes of permutation polynomials of the form cx+Trql/q(xa)$cx+\text {Tr}_{q^{l}/ q}(x^{a})$ over finite fields with even characteristic, which explain most of the examples with q = 2k, k > 1, kl < 14 and c?Fql?$c\in \mathbb {F}_{q^{l}}^{*}$. Furthermore, we also construct four classes of permutation trinomials.

Abstract: Permutation trinomials over finite fields consititute an active research due to their simple algebraic form, additional extraordinary properties and their wide applications in many areas of science and engineering. In the present paper, six new classes of permutation trinomials over finite fields of even characteristic are constructed from six fractional polynomials. Further, three classes of permutation trinomials over finite fields of characteristic three are raised. Distinct from most of the known permutation trinomials which are with fixed exponents, our results are some general classes of permutation trinomials with one parameter in the exponents. Finally, we propose a few conjectures.

Abstract: We extend conformal inference to general settings that allow for time series data. Our proposal is developed as a randomization method and accounts for potential serial dependence by including block structures in the permutation scheme. As a result, the proposed method retains the exact, model-free validity when the data are i.i.d. or more generally exchangeable, similar to usual conformal inference methods. When exchangeability fails, as is the case for common time series data, the proposed approach is approximately valid under weak assumptions on the conformity score.

Abstract: Many matching, tracking, sorting, and ranking problems require probabilistic reasoning about possible permutations, a set that grows factorially with dimension. Combinatorial optimization algorithms may enable efficient point estimation, but fully Bayesian inference poses a severe challenge in this high-dimensional, discrete space. To surmount this challenge, we start with the usual step of relaxing a discrete set (here, of permutation matrices) to its convex hull, which here is the Birkhoff polytope: the set of all doubly-stochastic matrices. We then introduce two novel transformations: first, an invertible and differentiable stick-breaking procedure that maps unconstrained space to the Birkhoff polytope; second, a map that rounds points toward the vertices of the polytope. Both transformations include a temperature parameter that, in the limit, concentrates the densities on permutation matrices. We then exploit these transformations and reparameterization gradients to introduce variational inference over permutation matrices, and we demonstrate its utility in a series of experiments.