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 dual layer security scheme for medical images using Hessenberg and singular value decompositions

Due to the recent advancement in the field of the Internet of Medical things (IoMT). To facilitate doctors and patients, in the process of diagnosis and treatment, the medical imaging equipment is connected to the IoMT. During communication over the network, these medical images are subjected to various threads. In this work, we have proposed a dual-layer data confidentiality scheme, firstly it encrypts the secret medical images followed by a data hiding scheme. The encryption scheme possesses diffusion and confusion, for confusion the encryption scheme utilizes logistic and tent maps for the generation of S-boxes. For data hiding, it utilizes Hessenberg and singular value decomposition (SVD). The proposed scheme is applied to highly correlated medical images. The proposed technique provides dual security to the confidential information and makes it difficult for the intruder to extract the confidential information. The encryption scheme is evaluated by using the standard performance indicators including statistical analysis, differential analysis, and NIST analysis, etc. The encrypted images have the highest practically achievable entropy of 7.999 which is closest to the ideal value of 8. The data hiding scheme is evaluated by using statistical analysis, Distance-based analysis, analysis based on pixel difference, and information theory. Both the analysis of encryption and data hiding are satisfactory and the results show the strength of the dual-layer security scheme.

     

A image encryption algorithm based on chaotic Lorenz system and novel primitive polynomial S-boxes

We have proposed a robust, secure and efficient image encryption algorithm based on chaotic maps and algebraic structure. Nowadays, the chaotic cryptosystems gained more attention due to their efficiency, the assurance of robustness and high sensitivity corresponding to initial conditions. In literature, there are many encryption algorithms that can simply guarantees security while the schemes based on chaotic systems only promises the uncertainty, both of them can not encounter the needs of current scenario. To tackle this issue, this article proposed an image encryption algorithm based on Lorenz chaotic system and primitive irreducible polynomial substitution box. First, we have proposed 16 different S-boxes based on projective general linear group and 16 primitive irreducible polynomials of Galois field of order 256, and then utilized these S-boxes with combination of chaotic map in image encryption scheme. Three chaotic sequences can be produced by the disturbed of Lorenz chaotic system corresponding to variables x, y and z. We have constructed a new pseudo random chaotic sequence k_i based on x, y and z. The plain image is encrypted by the use of chaotic sequence k_i and XOR operation to get a ciphered image. To show the strength of presented image encryption, some renowned analyses are performed.

     

Correction to: A dual layer security scheme for medical images using Hessenberg and singular value decompositions

Multimedia Tools and Applications -     

Cryptanalysis and Improvement of Novel Image Encryption Technique Using Hybrid Method of Discrete Dynamical Chaotic Maps and Brownian Motion

Multimedia Tools and Applications - Recently, an encryption technique depending on discrete dynamical chaotic maps and Brownian motion was offered. The authors of the understudy cryptosystem claim...     

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.