With the growing exchange of digital images in the Internet of Things (IoT), securing sensitive data, particularly medical images, has become critical. These images are essential for diagnosis but vulnerable to cyberattacks due to predictable anatomical patterns. Traditional encryption methods typically ignore these patterns, making them vulnerable to statistical attacks. We propose a novel image encryption scheme that incorporates both local and global image information using isomorphic elliptic curves (ECs) for optimal security. At the local level, central pixels and their neighboring are identified and independently encrypted using points on isomorphic ECs, selected through a carefully designed random walk algorithm. This process ensures robust disruption of spatial dependencies while maintaining computational efficiency. At the global level, a plain-image-sensitive shuffling generator is designed for a second confusion layer. The proposed scheme demonstrates high security against statistical cryptanalysis when evaluated using a benchmark medical image database MedPix and standard evaluation criteria. Additionally, comparisons with state-of-the-art methods reveal up to an 8-fold reduction in pixel correlation and significant computational efficiency, with encryption speeds up to 60 times faster than existing approaches. These findings highlight the potential of our scheme for real-world applications, particularly in securing sensitive medical data while balancing security and performance.

In this paper, we propose a novel family of descriptors of chemical graphs, named cycle-configuration (CC), that can be used in the standard "two-layered (2L) model" of mol-infer, a molecular inference framework based on mixed integer linear programming (MILP) and machine learning (ML). Proposed descriptors capture the notion of ortho/meta/para patterns that appear in aromatic rings, which has been impossible in the framework so far. Computational experiments show that, when the new descriptors are supplied, we can construct prediction functions of similar or better performance for all of the 27 tested chemical properties. We also provide an MILP formulation that asks for a chemical graph with desired properties under the 2L model with CC descriptors (2L+CC model). We show that a chemical graph with up to 50 non-hydrogen vertices can be inferred in a practical time.

A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In this paper, we design a new method for inferring a polymer based on the framework. For this, we introduce a new way of representing a polymer as a form of monomer and define new descriptors that feature the structure of polymers. We also use linear regression as a building block of constructing a prediction function in the framework. The results of our computational experiments reveal a set of chemical properties on polymers to which a prediction function constructed with linear regression performs well. We also observe that the proposed method can infer polymers with up to 50 non-hydrogen atoms in a monomer form.

A novel framework for designing the molecular structure of chemical compounds with a desired chemical property has recently been proposed. The framework infers a desired chemical graph by solving a mixed integer linear program (MILP) that simulates the computation process of two functions: a feature function defined by a two-layered model on chemical graphs and a prediction function constructed by a machine learning method. To improve the learning performance of prediction functions in the framework, we design a method that splits a given data set$\mathcal {C}$into two subsets$\mathcal {C}^{(i)},i=1,2$by a hyperplane in a chemical space so that most compounds in the first (resp., second) subset have observed values lower (resp., higher) than a threshold$\theta$. We construct a prediction function$\psi$to the data set$\mathcal {C}$by combining prediction functions$\psi _{i},i=1,2$each of which is constructed on$\mathcal {C}^{(i)}$independently. The results of our computational experiments suggest that the proposed method improved the learning performance for several chemical properties to which a good prediction function has been difficult to construct.

Drug discovery is one of the major goals of computational biology and bioinformatics. A novel framework has recently been proposed for the design of chemical graphs using both artificial neural networks (ANNs) and mixed integer linear programming (MILP). This method consists of a prediction phase and an inverse prediction phase. In the first phase, an ANN is trained using data on existing chemical compounds. In the second phase, given a target chemical property, a feature vector is inferred by solving an MILP formulated from the trained ANN and then a set of chemical structures is enumerated by a graph enumeration algorithm. Although exact solutions are guaranteed by this framework, the types of chemical graphs have been restricted to such classes as trees, monocyclic graphs, and graphs with a specified polymer topology with cycle index up to 2. To overcome the limitation on the topological structure, we propose a new flexible modeling method to the framework so that we can specify a topological substructure of graphs and a partial assignment of chemical elements and bond-multiplicity to a target graph. The results of computational experiments suggest that the proposed system can infer chemical graphs with around up to 50 non-hydrogen atoms.

A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In the framework, a chemical graph with a target chemical value is inferred as a feasible solution of a mixed integer linear program that represents a prediction function and other requirements on the structure of graphs. In this paper, we propose a procedure for generating other feasible solutions of the mixed integer linear program by searching the neighbor of output chemical graph in a search space. The procedure is combined in the framework as a new building block. The results of our computational experiments suggest that the proposed method can generate an additional number of new chemical graphs with up to 50 non-hydrogen atoms.

Elliptic curve cryptography has been used in many security systems due to its small key size and high security compared with other cryptosystems. In many well-known security systems, a substitution box (S-box) is the only non-linear component. Recently, it has been shown that the security of a cryptosystem can be improved using dynamic S-boxes instead of a static S-box. This necessitates the construction of new secure S-boxes. We propose an efficient method to generate S-boxes that are based on a class of Mordell elliptic curves over prime fields and achieved by defining different total orders. The proposed scheme is developed in such a way that for each input it outputs an S-box in linear time and constant space. Due to this property, our method takes less time and space than the existing S-box construction methods over elliptic curves. Computational results show that the proposed method is capable of generating cryptographically strong S-boxes with security comparable to some of the existing S-boxes constructed via different mathematical structures.

Elliptic curves (ECs) are considered as one of the highly secure structures against modern computational attacks. In this paper, we present an efficient method based on an ordered isomorphic EC for the generation of a large number of distinct, mutually uncorrelated, and cryptographically strong injective S-boxes. The proposed scheme is characterized in terms of time complexity and the number of the distinct S-boxes. Furthermore, rigorous analysis and comparison of the newly developed method with some of the existing methods are conducted. Experimental results reveal that the newly developed scheme can efficiently generate a large number of distinct, uncorrelated, and secure S-boxes when compared with some of the well-known existing schemes.

This paper presents a novel image encryption technique based on multiple right translated AES Gray S-boxes (RTSs) and phase embedding technique. First of all, a secret image is diffused with a fuzzily selected RTS. The fuzzy selection of RTS is variable and depends upon pixels of the secret image. Then two random masks are used to enhance confusion in the spatial and frequency domains of the diffused secret image. These random masks are generated by applying two different RTSs on a host image. The decryption process of the proposed cryptosystem needs the host image for generation of masks. It is therefore, necessary, to secure the host image from unauthorized users. This task is achieved by diffusing the host image with another RTS and embedding the diffused secret image into the phase terms of the diffused host image. The cryptographic strength of the proposed security system is measured by implementing it on several images and applying rigorous analyses. Performance comparison of the proposed security technique with some of the state-of-the-art security systems, including S-box cryptosystem and steganocryptosystems, is also performed. Results and comparison show that the newly developed cryptosystem is more secure.

Abstract This article deals with an algorithm for the generation of impregnable substitution boxes (S‐box). The proposed scheme involves the application of right translation and Gray codes over the original Advanced Encryption Standard (AES) S‐box. Regular representation of Galois field GF(28) is used to produce the translational effect in the AES S‐box. The translated AES S‐box is then subjected to Gray codes for the enhancement in their algebraic complexity. The proposed scheme results 256 different cryptographically strong S‐boxes. Several tests such as non‐linearity, bit independence, strict avalanche, linear approximation and differential approximation, algebraic complexity, correlation and histogram are implemented on every newly generated S‐box to analyze their resistance against computational attacks. Furthermore, the newly generated S‐boxes are compared with the existing well‐known S‐boxes. The simulation results indicate that the resistance of proposed S‐boxes against computational attacks including linear, interpolation, differential and algebraic attacks approaches to the optimal values. Copyright © 2014 John Wiley & Sons, Ltd.