On decompositions of finite projective planes and their applications

Let PG(2; q) be the projective plane over the field Fq. Singer [19] notes that PG(2; q) has a cyclic group of order q2 + q + 1 that permutes the points of PG(2; q) in a single cycle. A k-arc set of k points no three of which are collinear. A k-arc is called complete if it is not contained in a (k + 1)-arc of PG(2; q). By taking the orbits of points under a proper subgroup of a single cycle, one can decompose the projective plane PG(2; qk) into disjoint copies of subplanes isomorphic to PG(2; q) if and only if k is not divisible by three. Moreover, by taking the orbits of points under a proper subgroup, one can decompose the projective plane PG(2; q2) into disjoint copies of complete (q2 - q + 1)-arcs. In this thesis, our main problem is to classify (up to isomorphism) the different types of decompositions of PG(2 ;q2) for q = 3; 4; 5; 7, namely subplanes and arcs. We further illustrate some of the connections between these subgeometry decompositions and other areas of combinatorial interest; in particular, we explain the relationship between coding theory and projective spaces and describe the links with Hermitian unital. Furthermore, projective codes are obtained by taking the disjoint union of such subgeometries

Noise-Resistant Image Encryption Scheme for Medical Images in the Chaos and Wavelet Domain

In this paper, a noise-resistant image encryption scheme is proposed. We have used a cubic-logistic map, Discrete Wavelet Transform (DWT), and bit-plane extraction method to encrypt the medical images at the bit-level rather than pixel-level. The proposed work is divided into three sections; In the first and the last section, the image is encrypted in the spatial domain. While the middle section of the proposed algorithm is devoted to the frequency domain encryption in which DWT is incorporated. As the frequency domain encryption section is a sandwich between the two spatial domain encryption sections, we called it a ”sandwich encryption.” The proposed algorithm is lossless because it can decrypt the exact pixel values of an image. Along with this, we have also gauge the proposed scheme's performance using statistical analysis such as entropy, correlation, and contrast. The entropy values of the cipher images generated from the proposed encryption scheme are more remarkable than 7.99, while correlation values are very close to zero. Furthermore, the number of pixel change rate (NPCR) and unified average change intensity (UACI) for the proposed encryption scheme is higher than 99.4% and 33, respectively. We have also tested the proposed algorithm by performing attacks such as cropping and noise attacks on enciphered images, and we found that the proposed algorithm can decrypt the plaintext image with little loss of information, but the content of the original image is visible

Efficient and secure image encryption using key substitution process with discrete wavelet transform

Over the past few years, there has been a rise in the utilization of chaotic encryption algorithms for securing images. The majority of chaos-based encryption algorithms adhere to the conventional model of confusion and diffusion, which typically involves either implementing multiple encryption rounds or employing a single round of intricate encryption to guarantee robust security. However, such kind of approaches reduces the computational efficiency of the encryption process but compromises security. There is a trade-off between security and computational efficiency. Prioritizing security may require high computational processes. To overcome this issue, a key substitution encryption process with discrete wavelet transform (KSP-DWT) is developed in the proposed image encryption technique (IET). Based on KSP-DWT and IET, the abbreviation of the proposed work is used in this paper as KSP-DWT-IET. The proposed KSP-DWT algorithm employs a key scheming technique to update the initial keys and uses a novel substitution method to encrypt digital images of different sizes. Additionally, the integration of DWT can result in the compression of frequency sub-bands of the source image, leading to lower computational overheads without compromising the security of the encryption. The KSP-DWT-IET performs a single encryption round and is highly secure and efficient. The simulation results and security analysis conducted on KSP-DWT-IET confirm its effectiveness in ensuring high-security image encryption while minimizing computational overhead. The proposed encryption technique undergoes various security analyses, including entropy, contrast, correlation, energy, NPCR (Number of Pixel Changes Rate), UACI (Unified Average Change Intensity) and computational complexity. The statistical values obtained for such parameters are 7.9991, 10.9889, 0.0001, 0.0152, 33.6767, and 33.6899, respectively, which indicate that the encryption technique performs very well in terms of security and computational efficiency. The proposed encryption scheme is also analyzed for its computational time in addition to its security. The analysis shows that the scheme can efficiently encrypt images of varying sizes with a high level of security in a short amount of time (i.e., 2 ms). Therefore, it is feasible to use this encryption scheme in real-time applications without causing any significant delays. Moreover, the key space of the proposed encryption scheme is large enough (i.e. Keyspace ) to resist the brute force attack

Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography

Substitution boxes are the key factor in symmetric-key cryptosystems that determines their ability to resist various cryptanalytic attacks. Creating strong substitution boxes that have multiple strong cryptographic properties at the same time is a challenging task for cryptographers. A significant amount of research has been conducted on S-boxes in the past few decades, but the resulting S-boxes have been found to be vulnerable to various cyberattacks. This paper proposes a new method for creating robust S-boxes that exhibit superior performance and possess high scores in multiple cryptographic properties. The hybrid S-box method presented in this paper is based on Chua’s circuit chaotic map, two-dimensional cellular automata, and an algebraic permutation group structure. The proposed 16×16 S-box has an excellent performance in terms of security parameters, including a minimum nonlinearity of 102, the absence of fixed points, the satisfaction of bit independence and strict avalanche criteria, a low differential uniformity of 5, a low linear approximation probability of 0.0603, and an auto-correlation function of 28. The analysis of the performance comparison indicates that the proposed S-box outperforms other state-of-the-art S-box techniques in several aspects. It possesses better attributes, such as a higher degree of inherent security and resilience, which make it more secure and less vulnerable to potential attacks

Digital Images Security Technique Using Hénon and Piecewise Linear Chaotic Maps

The security of images has become a hot research area due to the widespread usage of the digital images all over the world. Literature review on chaotic image cryptography, on the other hand, indicates that many constructs have been employed for the realization of confusion operation while developing the image ciphers. To enhance the computational time, this study proposes a novel image cipher based on two chaotic maps and rectangle as a scrambler. As the given grayscale image is input, it is scrambled through dynamically generated rectangles. As a modus operandi, these rectangles are created in the given image with various dimensions and different location. The pixels lying on the boundary of the rectangle are rotated clockwise and anticlockwise with an arbitrary amount. These operations have been repeated a number of times to get the scrambling effects. The scrambled image has been further subjected to an XOR operation for embedding the diffusion effects in it. Two chaotic maps of Hénon and piecewise linear chaotic map have been used for the generation of random numbers. These numbers help in deciding the size, location, clockwise/anticlockwise movement of the pixels and the amount with which these pixels have to be rotated. The performance analysis and the machine simulation validate that the suggested cipher is sufficient enough to thwart the varied cryptanalytic attacks. In particular, we gained the computational speed of 0.5156 seconds and the information entropy of 7.9975. Besides, we posit that it has the ample prospects for its real world application

Image encryption scheme for multi-focus images for visual sensors network

Image fusion is the technique to obtain an image, possessing spatially and spectrally enhanced as compared to the individual high spatial and high spectral images. After obtaining a detailed image, propagation over an insecure channel is a critical issue to address. In this article, we have projected an image encryption structure for the fused image resulted from the multi-focus sensors. The projected scheme offered confusion as well as diffusion, which are the core parts of any symmetric cryptosystem. The projected cryptosystem has been tested against various security analysis and tabulated. The Number of Pixel Change Rate (NPCR) and Unified Average Change Intensity (UACI) are 99.62 and 33.49 shows the strength of the proposed encryption against differential attacks. For real-time implementation the time analysis is performed, for image fusion and encryption the algorithm only takes 1.268 s which makes it suitable for real-time implementation. The analysis is compared with the existing state-of-the-art techniques. The designed system is capable of obtaining spectrally and spatially enhanced image from multi-focus images and provide a high level of security

Block Ciphers Substitution Box Generation Based on Natural Randomness in Underwater Acoustics and Knights Tour Chain

The protection of confidential information is a global issue and block encryption algorithms are the most reliable option. The famous information theorist, Claude Shannon has given two desirable characteristics that should exist in a strong cipher which are substitution and permutation in their fundamental research on Communication Theory of Secrecy Systems. block ciphers strictly follow the substitution and permutation principle to generate a ciphertext. The actual strength of the block ciphers against several attacks is entirely based on its substitution characteristic, which is gained by using the S-Box. In the current literature, algebraic structure-based and chaos-based techniques are highly used for the construction of S-boxes because both these techniques have favourable features for S-box construction, but also various attacks of these techniques have been identified. True randomness has been universally recognized as the ideal method for cipher primitives design because true random numbers are unpredictable, irreversible, and unreproducible. The basic concept of the proposed technique is the extraction of true random bits from underwater acoustic waves and to design a novel technique for the dynamic generation of S-boxes using the chain of knights tour. The proposed method satisfies all standard evaluation tests of S-boxes construction and true random numbers generation. Two million bits have been analyzed using the NIST randomness test suite, and the results show that underwater sound waves are an impeccable entropy source for true randomness. Additionally, our dynamically generated S-boxes have better or equal strength, over the latest published S-boxes (2020 to 2021). According to our knowledge first time, this type of research has been done, in which natural randomness of underwater acoustic waves has been used for the construction of block cipher's S-BoxComment: 17 pages, 5 figures, Journa

A Low-Overhead Countermeasure against Differential Power Analysis for AES Block Cipher

This paper presents the employment of a DPA attack on the NIST (National Institute of Standards and Technology) standardized AES (advance encryption standard) protocol for key retrieval and prevention. Towards key retrieval, we applied the DPA attack on AES to obtain a 128-bit secret key by measuring the power traces of the computations involved in the algorithm. In resistance to the DPA attack, we proposed a countermeasure, or a new modified masking scheme, comprising (i) Boolean and (ii) multiplicative masking, for linear and non-linear operations of AES, respectively. Furthermore, we improved the complexity involved in Boolean masking by introducing Rebecca’s approximation. Moreover, we provide a novel solution to tackle the zero mask problem in multiplicative masking. To evaluate the power traces, we propose our custom correlation technique, which results in a decrease in the calculation time. The synthesis results for original implementation (without countermeasure) and inclusion of countermeasure are given on a Zynq 7020 FPGA (Artix-7 device). It takes 424 FPGA slices when implemented without considering the countermeasure, whereas 714 slices are required to implement AES with the inclusion of the proposed countermeasure. Consequently, the implementation results provide the acceptability of this work for area-constrained applications that require prevention against DPA attacks