Random S-boxes Research Articles

Correction to: A remote sensing image encryption and compression scheme using novel hyperchaotic system and plaintext related random S-box

Correction to: A remote sensing image encryption and compression scheme using novel hyperchaotic system and plaintext related random S-box

A remote sensing image encryption and compression scheme using novel hyperchaotic system and plaintext related random S-box

A remote sensing image encryption and compression scheme using novel hyperchaotic system and plaintext related random S-box

FRAST: TFHE-Friendly Cipher Based on Random S-Boxes

A transciphering framework, also known as hybrid homomorphic encryption, is a practical method of combining a homomorphic encryption (HE) scheme with a symmetric cipher in the client-server model to reduce computational and communication overload on the client side. As a server homomorphically evaluates a symmetric cipher in this framework, new design rationales are required for “HE-friendly” ciphers that take into account the specific properties of the HE schemes. In this paper, we propose a new TFHE-friendly cipher, dubbed FRAST, with a TFHE-friendly round function based on a random S-box to minimize the number of rounds. The round function of FRAST can be efficiently evaluated in TFHE by a new optimization technique, dubbed double blind rotation. Combined with our new WoP-PBS method, the double blind rotation allows computing multiple S-box calls in the round function of FRAST at the cost of a single S-box call. In this way, FRAST enjoys 2.768 (resp. 10.57) times higher throughput compared to Kreyvium (resp. Elisabeth) for TFHE keystream evaluation in the offline phase of the transciphering framework at the cost of slightly larger communication overload.

DNA-level action accompanied by Vigenere using strong pseudo random S-box for color image encryption

DNA-level action accompanied by Vigenere using strong pseudo random S-box for color image encryption

Strong s-box construction approach based on Josephus problem

There are two basic requirements for symmetric encryption algorithms. The first of these is diffusion. The second and most important is confusion. In these algorithms, this requirement is usually met by s-box structures. Therefore, s-box structures must be strong. So, a cryptographically good s-box will make the encryption algorithm difficult to crack. However, obtaining a strong s-box is a rather difficult problem. In this study, Josephus circle logic is used to solve this problem. Initially, with a random s-box structure, the elements are replaced according to their Josephus positions, and the s-box is made stronger. In the proposed algorithm, according to the Josephus logic, the elements that kill each other are replaced and this process continues until one element remains. The last 30 surviving elements are replaced with all elements. In this way, three different s-boxes were obtained. In two of them, the nonlinearity value was 110.5, and in one of them, the nonlinearity value was 110.75. Fixed points in the proposed s-box structures were identified and eliminated. In addition, it has been proven because of the analysis that the obtained s-box structures also meet other cryptographic requirements. In addition to leaving behind most studies in the literature, the proposed method will also provide strong s-box structures for encryption algorithms to be built in the future.

Enhancing Smart Communication Security: A Novel Cost Function for Efficient S-Box Generation in Symmetric Key Cryptography

In the realm of smart communication systems, where the ubiquity of 5G/6G networks and IoT applications demands robust data confidentiality, the cryptographic integrity of block and stream cipher mechanisms plays a pivotal role. This paper focuses on the enhancement of cryptographic strength in these systems through an innovative approach to generating substitution boxes (S-boxes), which are integral in achieving confusion and diffusion properties in substitution–permutation networks. These properties are critical in thwarting statistical, differential, linear, and other forms of cryptanalysis, and are equally vital in pseudorandom number generation and cryptographic hashing algorithms. The paper addresses the challenge of rapidly producing random S-boxes with desired cryptographic attributes, a task notably arduous given the complexity of existing generation algorithms. We delve into the hill climbing algorithm, exploring various cost functions and their impact on computational complexity for generating S-boxes with a target nonlinearity of 104. Our contribution lies in proposing a new cost function that markedly reduces the generation complexity, bringing down the iteration count to under 50,000 for achieving the desired S-box. This advancement is particularly significant in the context of smart communication environments, where the balance between security and performance is paramount.

The influence of S-boxes on the arrival of the cipher to the state of random substitution

The subject of this study is the process of developing block symmetric ciphers with improved cryptographic stability indicators for solving the problems of information protection in information and communication systems. The goal of this study is to develop a mathematical model of the optimal s-box design (non-linear substitution block) for modern block symmetric ciphers. Task: to show that the stability of block symmetric ciphers does not significantly depend on the indicators of the s-boxes included in these ciphers; to justify their use without reducing the stability of random substitutions as s-box constructions of modern block symmetric ciphers; and to prove the futility of searching for s-boxes with special properties. The methods used are: methods of probability theory; mathematical statistics; combinatorics and system analysis; methods of statistical tests; and methods of Boolean algebra. The following results were obtained. In modern ciphers, nonlinear substitution transformations are used as S-boxes (in most ciphers, byte substitutions are used). S-boxes perform the main function of encryption transformation - mixing of text bits. Dynamic indicators of the arrival of the cipher in the state of random substitution depend on their effectiveness. The presented results confirm that the indicators of cipher stability do not significantly depend on the indicators of the S-boxes included in the ciphers. It is not the individual properties of substitutions, but the results of their sequential interactions decisive for achieving stability indicators. It is shown that the fee for encryption is chosen to be three to four times greater than the depth of the avalanche effect - the minimum number of cycles of the cipher’s arrival to the state of random substitution) is hardly noticeable. Conclusions. The scientific novelty of the obtained results is as follows. This work represents a generalization of the transition to the use of random permutations as S-boxes is an increase of only one cycle in the number of cycles of the arrival of the cipher to the state of random permutations, and this is hardly noticeable against the background of the stability margin used in modern ciphers. The result of this generalization is a scientific statement that can be described as follows: random S-boxes can be used in all known modern ciphers without reducing stability. That is, the task of finding S-boxes with special properties loses any meaning, which means that the scientific direction related to the search for S-boxes with special properties becomes redundant.

Optimizing Hill Climbing Algorithm for S-Boxes Generation

Nonlinear substitutions or S-boxes are important cryptographic primitives of modern symmetric ciphers. They are designed to complicate the plaintext-ciphertext dependency. According to modern ideas, the S-box should be bijective, have high nonlinearity and algebraic immunity, low delta uniformity, and linear redundancy. These criteria directly affect the cryptographic strength of ciphers, providing resistance to statistical, linear, algebraic, differential, and other cryptanalysis techniques. Many researchers have used various heuristic search algorithms to generate random S-boxes with high nonlinearity; however, the complexity of this task is still high. For example, the best-known algorithm to generate a random 8-bit bijective S-box with nonlinearity 104 requires high computational effort—more than 65,000 intermediate estimates or search iterations. In this article, we explore a hill-climbing algorithm and optimize the heuristic search parameters. We show that the complexity of generating S-boxes can be significantly reduced. To search for a random bijective S-box with nonlinearity 104, only about 50,000 intermediate search iterations are required. In addition, we generate cryptographically strong S-Boxes for which additional criteria are provided. We present estimates of the complexity of the search and estimates of the probabilities of generating substitutions with various cryptographic indicators. The extracted results demonstrate a significant improvement in our approach compared to the state of the art in terms of providing linear non-redundancy, nonlinearity, algebraic immunity, and delta uniformity.

Advanced approach for encryption using advanced encryption standard with chaotic map

At present, security is significant for individuals and organizations. All information need security to prevent theft, leakage, alteration. Security must be guaranteed by applying some or combining cryptography algorithms to the information. Encipherment is the method that changes plaintext to a secure form called cipherment. Encipherment includes diverse types, such as symmetric and asymmetric encipherment. This study proposes an improved version of the advanced encryption standard (AES) algorithm called optimized advanced encryption standard (OAES). The OAES algorithm utilizes sine map and random number to generate a new key to enhance the complexity of the generated key. Thereafter, multiplication operation was performed on the original text, thereby creating a random matrix (4×4) before the five stages of the coding cycles. A random substitution-box (S-Box) was utilized instead of a fixed S-Box. Finally, we utilized the eXclusive OR (XOR) operation with digit 255, also with the key that was generated last. This research compared the features of the AES and OAES algorithms, particularly the extent of complexity, key size, and number of rounds. The OAES algorithm can enhance complexity of encryption and decryption by using random values, random S-Box, and chaotic maps, thereby resulting in difficulty guessing the original text.

Cryptanalysis of DRPE using complex S-Box based on linear canonical transform

During recent decades, double random phase encoding grasped more attention for researchers. To achieve nonlinearity, it had been done with random S-Box. We exhibit this involvement that DRPE system is much vulnerable in the above methodology. Concatenating anything with DRPE needs an imaginary value, wherein S-Box unsuccessful in it. Used S-Box has been reformed into various sizes. Due to this scenario, S-Box values are replicating. So, complex S-Box has been employed and proposed size of the S-Box is similar to an input image. Numerical simulations such as performance analysis, histogram analysis and 3D plot analysis have been performed out to validate the practicability and trustworthiness of traditional DRPE system with complex S-Box. Moreover, in order to check the cryptanalysis, much other analysis done such as occlusion attack, noise attack, chosen plaintext analysis and sensitivity analysis also accomplished.

Optimization of a Simulated Annealing Algorithm for S-Boxes Generating.

Cryptographic algorithms are used to ensure confidentiality, integrity and authenticity of data in information systems. One of the important areas of modern cryptography is that of symmetric key ciphers. They convert the input plaintext into ciphertext, representing it as a random sequence of characters. S-boxes are designed to complicate the input–output relationship of the cipher. In other words, S-boxes introduce nonlinearity into the encryption process, complicating the use of different methods of cryptanalysis (linear, differential, statistical, correlation, etc.). In addition, S-boxes must be random. This property means that nonlinear substitution cannot be represented as simple algebraic constructions. Random S-boxes are designed to protect against algebraic methods of cryptanalysis. Thus, generation of random S-boxes is an important area of research directly related to the design of modern cryptographically strong symmetric ciphers. This problem has been solved in many related works, including some using the simulated annealing (SA) algorithm. Some works managed to generate 8-bit bijective S-boxes with a nonlinearity index of 104. However, this required enormous computational resources. This paper presents the results of our optimization of SA via various parameters. We were able to significantly reduce the computational complexity of substitution generation with SA. In addition, we also significantly increased the probability of generating the target S-boxes with a nonlinearity score of 104.

Study of a new cost function for generating random substitutions of symmetric ciphers

Cryptographic transformations with a secret key play an essential role in providing information and cyber security. Block and stream symmetric ciphers are used in various applications both as a separate cryptographic protection mechanism and as part of other applications (pseudo-random sequence generators, hashing algorithms, electronic signature protocols, etc.). Therefore, the design and study of individual components of symmetric ciphers is a relevant and important scientific task. In this paper we consider and investigates iterative algorithms for generating non-linear substitutions (substitutions, S-boxes), which are used in modern block and stream encryption algorithms with a symmetric key. Cryptographic resistance of symmetric ciphers to statistical, differential, linear and other methods of cryptanalysis is provided by the properties of substitutions. In addition, S-boxes must be random from the point of view of the possibility to use algebraic cryptanalysis. Therefore, the task of quickly generating random S-boxes with the desired cryptographic properties is an urgent, but extremely difficult task. For example, the best known generation algorithm requires more than 65 thousand iterations to find a random bijective 8-bit substitution with a non-linearity of 104. In this paper, we study an iterative algorithm for generating substitutions for hill climbing with different cost functions and propose a new cost function, the use of which can significantly reduce the number of search iterations. In particular, the search for a bijective S-box with nonlinearity 104 requires less than 50 thousand iterations.

Designing a random S-box with the mixed spatiotemporal chaos

A random S-box is designed by using the mixed linear-nonlinear spatiotemporal chaotic system. Firstly, a chaotic sequence produced by the mixed chaotic system is used to generate the elements of the S-box randomly. Then the elements of the S-box are permuted by using the mixed chaotic system. Owing to the high dimensional feature of the mixed chaotic system, the generated S-box has a strong randomness property. Finally, we analyse six properties of the designed S-box, such as bijective property, nonlinearity, strict avalanche criterion, outputs bit independence criterion, input/output XOR distribution and linear approximation probability. The experimental results indicate that the designed S-box by using the mixed chaotic system has better performance.

Power Measurement-Based Vulnerability Assessment of IoT Medical Devices at Varying Countermeasures for Cybersecurity

A method for the vulnerability assessment of Internet-of-Things (IoT) medical transducers cybersecurity at varying the power countermeasures is proposed. The implemented countermeasures reinforce the most popular cryptographic algorithm, advanced encryption standard (AES), running on a low-cost, low-energy, and low-performance smart transducer for IoT medical devices. The proposed method is based on attacks standardized in the smart-card industry: differential power analysis (DPA) and correlation power analysis (CPA). Adopting a methodically rigorous framework, a boost for the study of power countermeasures was offered for IoT medical transducers. An experimental comparison of security performance among different power countermeasures was realized. Each countermeasure increases the number of power traces needed to discover the AES secret key. Random delay, random SBox, and masking strengthen the AES of 1.3, 208, and 318 factors, respectively. The masking countermeasure was by far the most effective.

2D mixed pseudo-random coupling PS map lattice and its application in S-box generation

In this paper, firstly, we investigate a new 1D PWLCM-Sin (PS) map which derived from PWLCM and Sin map by modulo operation. Due to the stronger parameter space, bigger Lyapunov exponents and better ergodicity than simple 1D map, the PS map is more suitable for local map of spatiotemporal dynamics. Secondly, with the novel 2D pseudo-random mixed coupling method we present a spatiotemporal chaos which used PS map as local map f(x). This spatiotemporal chaos named 2D Mixed pseudo-random Coupling PS Map Lattice (2DMCPML). The experimental results of bifurcation diagrams, Kolmogorov–Sinai entropy density and spatiotemporal chaotic diagrams showed that 2DMCPML has advantages of larger parameter space, more complex chaotic behavior and more ergodic output sequence than CML. Therefore, 2DMCPML is more suitable in cryptography than CML. Subsequently, we proposed a chaos-based random S-box design algorithm employed the spatial chaotic character of 2DMCPML to generate a large number of S-boxes. The cryptographic performance indicated that generated S-boxes can resist cryptanalysis attack well. Finally, four criteria bounds are set. The numbers of S-boxes satisfying these bounds generated by 2DMCPML and several 1D chaotic maps is calculated, respectively. The result showed that spatiotemporal chaos can generate more S-boxes with high cryptographic quality than low-dimensional chaos. This new discovery is significant to the development of some cryptographic researches such as dynamic S-box algorithm.

Chaos-Based Confusion and Diffusion of Image Pixels Using Dynamic Substitution

The evolution of wireless and mobile communication from 0G to the upcoming 5G gives rise to data sharing through the Internet. This data transfer via open public networks are susceptible to several types of attacks. Encryption is a method that can protect information from hackers and hence confidential data can be secured through a cryptosystem. Due to the increased number of cyber attacks, encryption has become an important component of modern-day communication. In this article, a new image encryption algorithm is presented using chaos theory and dynamic substitution. The proposed scheme is based on two-dimensional Henon, Ikeda chaotic maps, and substitution box (S-box) transformation. Through Henon, a random S-Box is selected and the image pixel is substituted randomly. To analyze security and robustness of the proposed algorithm, several security tests such as information entropy, histogram investigation, correlation analysis, energy, homogeneity, and mean square error are performed. The entropy values of the test images are greater than 7.99 and the key space of the proposed algorithm is 2 798 . Furthermore, the correlation values of the encrypted images using the proposed scheme are close to zero when compared with other conventional schemes. The number of pixel change rate (NPCR) and unified average change intensity (UACI) for the proposed scheme are higher than 99.50% and 33, respectively. The simulation results and comparison with the state-of-the-art algorithms prove the efficiency and security of the proposed scheme.

Reconstructing an S-box from its Difference Distribution Table

In this paper we study the problem of recovering a secret S-box from its difference distribution table (DDT). While being an interesting theoretical problem on its own, the ability to recover the S-box from the DDT of a secret S-box can be used in cryptanalytic attacks where the attacker can obtain the DDT (e.g., in Bar-On et al.’s attack on GOST), in supporting theoretical analysis of the properties of difference distribution tables (e.g., in Boura et al.’s work), or in some analysis of S-boxes with unknown design criteria (e.g., in Biryukov and Perrin’s analysis).We show that using the well established relation between the DDT and the linear approximation table (LAT), one can devise an algorithm different from the straightforward guess-and-determine (GD) algorithm proposed by Boura et al. Moreover, we show how to exploit this relation, and embed the knowledge obtained from it in the GD algorithm. We tested our new algorithm on random S-boxes of different sizes, and for random 14-bit bijective S-boxes, our results outperform the GD attack by several orders of magnitude.

Reconstructing an S-box from its Difference Distribution Table

In this paper we study the problem of recovering a secret S-box from its difference distribution table (DDT). While being an interesting theoretical problem on its own, the ability to recover the S-box from the DDT of a secret S-box can be used in cryptanalytic attacks where the attacker can obtain the DDT (e.g., in Bar-On et al.’s attack on GOST), in supporting theoretical analysis of the properties of difference distribution tables (e.g., in Boura et al.’s work), or in some analysis of S-boxes with unknown design criteria (e.g., in Biryukov and Perrin’s analysis).We show that using the well established relation between the DDT and the linear approximation table (LAT), one can devise an algorithm different from the straightforward guess-and-determine (GD) algorithm proposed by Boura et al. Moreover, we show how to exploit this relation, and embed the knowledge obtained from it in the GD algorithm. We tested our new algorithm on random S-boxes of different sizes, and for random 14-bit bijective S-boxes, our results outperform the GD attack by several orders of magnitude.

A Novel Method for Constructing the S-Box Based on Spatiotemporal Chaotic Dynamics

A novel construction method for a random S-box by using the spatiotemporal nonlinear chaotic system is proposed. The chaotic sequences of the spatiotemporal chaotic system are applied to construct an initial S-box. Then, the permutation operation between independent chaotic sequences is performed to shuffle the elements of the S-box randomly. In comparisons with the former schemes, the results of the performance analysis indicate that the obtained S-box has a better output bit independence criterion and a stronger ability to resist linear password attacks. It also has a high dimensional feature due to the spatiotemporal chaotic dynamical behaviors. The proposed scheme holds superior cryptographic features.

Enhancing Security of Double Random Phase Encoding Based on Random S-Box

In this paper, we propose a novel asymmetric cryptosystem for double random phase encoding (DRPE) using random S-Box. While utilising S-Box separately is not reliable and DRPE does not support non-linearity, so, our system unites the effectiveness of S-Box with an asymmetric system of DRPE (through Fourier transform). The uniqueness of proposed cryptosystem lies on employing high sensitivity dynamic S-Box for our DRPE system. The randomness and scalability achieved due to applied technique is an additional feature of the proposed solution. The firmness of random S-Box is investigated in terms of performance parameters such as non-linearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities etc. S-Boxes convey nonlinearity to cryptosystems which is a significant parameter and very essential for DRPE. The strength of proposed cryptosystem has been analysed using various parameters such as MSE, PSNR, correlation coefficient analysis, noise analysis, SVD analysis, etc. Experimental results are conferred in detail to exhibit proposed cryptosystem is highly secure.