Differential Approximation Probability Research Articles

To Study the Effect of the Generating Polynomial on the Quality of Nonlinear Components in Block Ciphers

Substitution box (S-box), being the only nonlinear component, contributes to the confusion creating capability of a cryptosystem. Keeping in view the predominant role of S-box, many design algorithms to synthesize cryptographically stronger S-boxes have gained pivotal attention. A quick review of these algorithms shows that all these ideas mainly concentrate on the choice of bijective Boolean functions, with nonobservance to the irreducible polynomial that generates the Galois field. In this paper, we propose that the selection of irreducible polynomial has a deep influence on the highly desirable features of an S-box such as nonlinearity, strict avalanche, bit independence, linear approximation probability, and differential approximation probability. We underpin our claim by investigating a detailed model, which deploys the same algorithm but different polynomials and produces unusual changes in the results regarding the performance parameters of S-box.

Fabrication of Substitution-Box Initiated Implementing Invertible Mapping and Improving its Competency of Confusion by Compliment’s Mechanism

In this research article, an innovative strategy is exploited to design a nonlinear component Substitution Box (S-box). To achieve an objective, initially we pick out a one specific sort of primitive irreducible polynomial of degree 8 to generate elements of Galois field . Furthermore, we established a precise category of invertible mapping through an employment of left action of invertible matrix having order of on to generate elements of S-box. Moreover, to improve the confusion aptitude of erected S-box we exerted 1’s and 2’s compliment’s technique for shuffling of an elements of S-box. Eventually, to inspect the capacity of designed S-box we bring into effective action of different procedures from literature such as strict avalanche criterion, nonlinearity, linear approximation probability, bit independence criterion and differential approximation probability.

A Novel Algebraic Technique for the Construction of Strong Substitution Box

The ability of substitution box (S-box) to create confusion in the cipher attracted different authors to design strong cryptographic S-box. The S-box can further be used in different cryptosystems to create confusion. In this article, a novel scheme is introduced to develop S-box with strong arithmetic background. The construction depends on group action of projective general linear group on units of finite local ring and its features are equated with other promising S-boxes. This S-box is evaluated with the help of bit independent criterion, strict avalanche criterion, non-linearity test, linear approximation probability test and differential approximation probability test. The results of majority logic criterion suggest the strength and implementation of our S-box.

A Novel Image Encryption Based on Algebraic S-box and Arnold Transform

Recent study shows that substitution box (S-box) only cannot be reliably used in image encryption techniques. We, in this paper, propose a novel and secure image encryption scheme that utilizes the combined effect of an algebraic substitution box along with the scrambling effect of the Arnold transform. The underlying algorithm involves the application of S-box, which is the most imperative source to create confusion and diffusion in the data. The speciality of the proposed algorithm lies, firstly, in the high sensitivity of our S-box to the choice of the initial conditions which makes this S-box stronger than the chaos-based S-boxes as it saves computational labour by deploying a comparatively simple and direct approach based on the algebraic structure of the multiplicative cyclic group of the Galois field. Secondly the proposed method becomes more secure by considering a combination of S-box with certain number of iterations of the Arnold transform. The strength of the S-box is examined in terms of various performance indices such as nonlinearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities etc. We prove through the most significant techniques used for the statistical analyses of the encrypted image that our image encryption algorithm satisfies all the necessary criteria to be usefully and reliably implemented in image encryption applications.

Dynamic colour table: A novel S‐box for cryptographic applications

SummaryIn cryptography, S‐boxes play an important role in symmetric ciphers. S‐boxes are used for substitution process to enable diffusion in encryption and decryption of the messages. In most of the conventional and modern symmetric ciphers, the S‐boxes are of static in nature. It will never depend or vary with respect to the message or the key, but dynamic S‐boxes are more resistant to linear and differential attacks when compared with the static S‐boxes. In this paper, we propose the design of a new dynamic colour table (DCT) that can be used as S‐box in symmetric ciphers and it depends upon a master key K. The same key can be used for encryption and decryption in symmetric ciphers. Dynamic colour table is a 64×4 table, having 256 entries. Each column of DCT has 64 unique values. The input to generate the DCT is 160 bit master key K. We have also developed a sub‐key generation algorithm for generating the sub keys and 4 seeds from the master key of 160 bits. These 4 seeds are used to generate the random values in DCT. Dynamic colour table uses the alpha red green blue (ARGB) colour model concept for each entry. Our DCT is so lightweight in nature. Our new DCT have a wide range of applications such as it can be used as S‐boxes in symmetric ciphers or it can be used as pseudorandom number generators. Finally, we show an implementation and the simulated results of DCT. The simulated results are used to analyse the strength of our DCT. The different criterions to verify that DCT has the characteristic of good S‐box are nonlinearity, strong avalanche criterion, bit Independence criterion, differential approximation probability, and linear approximation probability. The performance is measured in terms of time complexity and security. The results show that our DCT is cryptographically stronger to use in various symmetric encryption algorithms.

A Group Action Method for Construction of Strong Substitution Box

In this paper, the method to develop cryptographically strong substitution box is presented which can be used in multimedia security and data hiding techniques. The algorithm of construction depends on the action of a projective general linear group over the set of units of the finite commutative ring. The strength of substitution box and ability to create confusion is assessed with different available analyses. Moreover, the ability of resistance against malicious attacks is also evaluated. The substitution box is examined by bit independent criterion, strict avalanche criterion, nonlinearity test, linear approximation probability test and differential approximation probability test. This substitution box is equated with well-recognized substitution boxes such as AES, Gray, APA, S8, prime of residue, Xyi and Skipjack. The comparison shows encouraging results about the strength of the proposed box. The majority logic criterion is also calculated to analyze the strength and its practical implementation.

An algorithm for the construction of substitution box for block ciphers based on projective general linear group

The aim of this work is to synthesize 8*8 substitution boxes (S-boxes) for block ciphers. The confusion creating potential of an S-box depends on its construction technique. In the first step, we have applied the algebraic action of the projective general linear group PGL(2,GF(28)) on Galois field GF(28). In step 2 we have used the permutations of the symmetric group S256 to construct new kind of S-boxes. To explain the proposed extension scheme, we have given an example and constructed one new S-box. The strength of the extended S-box is computed, and an insight is given to calculate the confusion-creating potency. To analyze the security of the S-box some popular algebraic and statistical attacks are performed as well. The proposed S-box has been analyzed by bit independent criterion, linear approximation probability test, non-linearity test, strict avalanche criterion, differential approximation probability test, and majority logic criterion. A comparison of the proposed S-box with existing S-boxes shows that the analyses of the extended S-box are comparatively better.

A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system

Substitution Box (S-Box) is one of the most significant structures used to create an encryption which is strong and resistant against attacks in block encryption algorithms. S-Box plays an important role in data encryption. This paper presents a novel S-Box generation algorithm design based on scaled Zhongtang chaotic system. In this study, a new random number generator which uses the new scaled Zhongtang chaotic system with very complicated and interesting dynamic features is designed; also, a new effective and strong S-Box design algorithm utilizing this RNG (random number generator) is developed. Bits generated by RNG are put to NIST tests and they passed all the NIST tests. Non-linearity, bit independence criteria, strict avalanche criteria, differential approximation probability performance tests are run on the proposed S-Box produced by new S-Box design algorithm. The proposed S-Box is compared with other studies available in the literature, and it is proved stronger and more effective.

A highly nonlinear S-box based on a fractional linear transformation.

We study the structure of an S-box based on a fractional linear transformation applied on the Galois field GF(2^{8}). The algorithm followed is very simple and yields an S-box with a very high ability to create confusion in the data. The cryptographic strength of the new S-box is critically analyzed by studying the properties of S-box such as nonlinearity, strict avalanche, bit independence, linear approximation probability and differential approximation probability. We also apply majority logic criterion to determine the effectiveness of our proposed S-box in image encryption applications.

A Watermarking Technique with Chaotic Fractional S-Box Transformation

In this paper, the system of non-linear ordinary differential equations which defines a continuous-time dynamical system that shows the fractal characteristics of attractor is used to construct chaotic S-box. In this new digital watermarking technique the priority is of importance of robustness along with chaos to create confusion. The inclusion of chaos along with watermarking in frequency domain ensures robustness. As we have proposed a frequency domain watermarking as which we embed watermark into the low or middle frequencies, these changes will be spread all over the image. The strength of fractional S-box is evaluated with the help of bit independence criterion, nonlinearity analysis, strict avalanche criterion, linear approximation probability and differential approximation probability. Additionally, some security analyses in the form of correlation, contrast, energy, entropy, homogeneity, mean square error and peak signal to noise ratio are performed for validity of proposed watermarking scheme. The confidence measure after these analyses indicates the survival aligned with malicious attacks like noise, cropping and compression.

Construction of Dynamical Non-linear Components Based on Lorenz System and Symmetric Group of Permutations

This paper is devoted to presenting a new technique for generating S-boxes based on a Lorenz system and S8 group of permutations. Within the algorithm, the initial condition is employed to drive the hyperchaotic Lorenz system to generate a chaotic sequence which is used to construct S-boxes. With different system conditions, many of distinct S-boxes can be obtained dynamically. Some cryptographic properties for a good S-box such as bijection, nonlinearity, SAC, BIC and differential approximation probability are found to hold in the obtained S-boxes from the proposed method. The analytic results indicate that all the criteria for designing robust S-boxes can be achieved. The comparison of the proposed S-box generating method with other chaos-based schemes indicates that our S-boxes have a better performance with respect to some properties. Classification of information security techniques and its applications

A Novel Ant Colony Optimization Based Scheme for Substitution Box Design

Abstract Efficient substitution boxes have crucial importance in the design of cryptographically strong modern block encryption algorithms. They are the only nonlinear blocks that decide the security strength of entire cryptosystem. In this paper, a meta-heuristic approach based on Ant Colony Optimization and chaos is put forward to retrieve a suitable configuration of strong 8×8 substitution box. The optimization is carried out by transforming initial S-box to travelling salesman problem through edge matrix. The cryptographic strength of optimized S-box is investigated against standard tests such as bijectivity, nonlinearity, strict avalanche criterion, output bits independence criterion and differential approximation probability. The performance comparison of generated S-box with some recent chaos-based S-boxes evidently proves that the proposed scheme is proficient to discover strong nonlinear component of block encryption systems.

Efficient method for designing chaotic S-boxes based on generalized Baker’s map and TDERC chaotic sequence

The theory of chaos is applied to the construction of substitution boxes used in encryption applications. The synthesis process of the proposed substitution boxes is presented, which is based on chaotic Baker’s map and TDERC chaotic sequences. The objectives of the new substitution box are to provide enhanced resistance against differential and linear cryptanalysis. The constructed substitution boxes uses Galois field elements and relies on discrete chaotic maps while keeping differential and linear approximation probabilities to desired levels.

A novel method for designing nonlinear component for block cipher based on TD-ERCS chaotic sequence

A substitution box is used to induce nonlinearity in plaintext for encryption systems. Recently, the application of chaotic maps to encryption applications has resulted in some interesting nonlinear transformations. In this paper, we propose an efficient method to design nonlinear components for block ciphers that are based on TD-ERCS chaotic sequence. The new substitution box is analyzed for nonlinearity, bit independence, strict avalanche criterion, generalized majority logic criterion, and differential and linear approximation probabilities. The results show high resistance to differential and linear cryptanalysis in comparison to some recently proposed chaotic substitution boxes.

A Novel Method for Designing Dynamical Key-Dependent S-Boxes based on Hyperchaotic System

The substitution box (S-box) is found in many block cipher, and it is a very important component. Since the chaotic system has several significant advantageous properties desirable for cryptosystem, the design of S-box using chaos has attracted a great deal of attention in recent years. In this paper, a novel method for designing key-dependent S-boxes based on a four-dimensional hyperchaotic Chen system has been presented. The design process for constructing S-boxes is described in detail and the results of numerical analysis indicate that all the criteria for S-boxes including bijection, nonlinearity, SAC, BIC and differential approximation probability can be fulfilled. Furthermore, the S-box’s sensitivity to the secret key is also conducted. All the results in this paper have shown that the presented method is a good candidate for designing dynamical S-boxes that can be widely used in block cipher.

A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems

In cryptographic systems, the encryption process relies on the nonlinear mapping of original data or plaintext to the secure data. The mapping of data is facilitated by the application of the substitution process embedded in the cipher. It is desirable to have resistance against differential cryptanalysis, which assists in providing clues about the composition of keys, and linear secret system, where a simple approximation is created to emulate the original cipher characteristics. In this work, we propose the use of nonlinear functional chaos-based substitution process which employs a continuous time Lorenz system. The proposed substitution system eliminates the need of independent round keys in a substitution-permutation network. The performance of the new substitution box is evaluated by nonlinearity analysis, strict avalanche criterion, bit independence criterion, linear approximation probability, and differential approximation probability.

A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm

A substitution box (S-box) plays a central role in cryptographic algorithms. In this paper, an efficient method for designing S-boxes based on chaotic maps is proposed. The proposed method is based on the NCA (nonlinear chaotic algorithm) chaotic maps. The S-box so constructed has very optimal nonlinearity, bit independence criterion (BIC), strict avalanche criterion (SAC), differential and linear approximation probabilities. The proposed S-box is more secure against differential and linear cryptanalysis compared to recently proposed chaotic S-boxes.

A group theoretic approach to construct cryptographically strong substitution boxes

In this paper, we present a method to construct a substitution box used in encryption applications. The proposed algorithm for the construction of substitution box relies on the linear fractional transform method. The design methodology is simple, while the confusion-creating ability of the new substitution box is complex. The strength of the proposed substitution box is evaluated, and an insight is provided to quantify the confusion-creating ability. In addition, tests are performed to assess the vulnerability of the encrypted data to algebraic and statistical attacks. The substitution box is critically analyzed by strict avalanche criterion, bit independent criterion, differential approximation probability test, linear approximation probability test, non-linearity test, and majority logic criterion. The performance of the proposed substitution box is also compared with those of some of the well-known counterparts including AES, APA, Gray, S8, Skipjack, Xyi, and prime of residue substitution boxes. It is apparent that the performance, in terms of confusion-creating ability, of the new substitution box is better than those of some of the existing non-linear components used in encryption systems. The majority logic criterion is applied to these substitution boxes to further evaluate the strength and usefulness.

A projective general linear group based algorithm for the construction of substitution box for block ciphers

The substitution boxes are used in block ciphers with the purpose to induce confusion in data. The design of a substitution box determines the confusion ability of the cipher; therefore, many different types of boxes have been proposed by various authors in literature. In this paper, we present a novel method to design a new substitution box and compare its characteristics with some prevailing boxes used in cryptography. The algorithm proposed in this paper apply the action of projective linear group PGL(2, GF(28)) on Galois field GF(28). The new substitution box corresponds to a particular type of linear fractional transformation (35z + 15)/(9z + 5). In order to test the strength of the proposed substitution box, we apply non-linearity test, bit independence criterion, linear approximation probability method, differential approximation probability method, strict avalanche criterion, and majority logic criterion. This new technique to synthesize a substitution box offers a powerful algebraic complexity while keeping the software/hardware complexity within manageable parameters.

A Novel Approach for Designing Dynamical S-Boxes Using Hyperchaotic System

In the information security field, the substitution boxes (S-boxes) have been extensively used in many cryptographic systems. This paper presents a novel approach for generating dynamically cryptographically S-boxes using a four-dimensional hyperchaotic Lorenz system. Within the algorithm, the initial condition is employed to drive the hyper-chaotic system to generate a chaotic sequence which is used to construct a chaotic key-dependent S-box. With different system initial conditions, many of distinct S-boxes can be obtained dynamically. Some cryptographic properties for a good S-box such as bijection, nonlinearity, SAC (Strict Avalanche Criterion), BIC (Bit Independence Criterion), and differential approximation probability are found to hold in the obtained S-boxes. The analytic results indicated that all the criteria for designing strong S-boxes can be achieved. The comparison of the proposed method for generating S-boxes with other chaos-based schemes indicates that our S-boxes have a better performance with respect to some properties. Finally, the authors give an example of a digital image encryption algorithm using their S-box and the results of image statistical analysis show that the algorithm has the desirable cryptographic properties.