In this article coset diagrams of the action of PSL(2,Z) on a [Formula: see text] are obtained, through parametrization, which yields one of the eight finite generalized triangle groups which are homomorphic images or quotients of PSL(2,Z). Other than this we analyzed the coset diagrams for the parameter for three finite generalized triangle groups. One of the most dependable methods for achieving data security has been the block cipher. S-Boxes constructed using algebraic structure have gained popularity recently because of their advantageous cryptographic properties and high non-linearity have been found in these structures, which attract researchers. With the help of these parametrized actions, a novel algebraic method to create [Formula: see text] S-Boxe was established. The S-Box provides strong cryptographic qualities of nonlinearity 112, differential uniformity 6, linear approximation probability of 0.0576 and differential attack probability of 0.0039. To assess the practical applicability of our S-box, we integrate it into an image encryption scheme and present experimental results to showcase its efficacy in real-world scenarios. When used with an image encryption framework, the following results were obtained: NPCR = 0.9959, UACI = 0.3348, and approx. Entropy 7.98. Therefore, GTG based parametrisation has been shown to be an effective and secure alternative to traditional algebraic construction method for S-Boxes.

This article presents general methodologies for plaintext attacks on block ciphers using the Tabu Search algorithm. These methods treat the cipher as a black box, with the objective of finding the session key. The primary innovation of our approach is the division of the key space into subsets based on a divisor, enabling the attack to focus on a specific portion of the total space. The following investigation demonstrates the successful application of these methods to a member of a block cipher family that includes the Advanced Encryption Standard (AES) cipher. One of the proposed methodologies, the subregions path attack, enables navigation of the key session space by applying specific predetermined strategies within these subregions.

This paper presents an extended investigation into deep learning-based cryptanalysis of block ciphers by introducing and evaluating a multi-server attack environment. Building upon our prior work in centralized settings, we explore the practicality and scalability of deploying such attacks across multiple distributed edge servers. We assess the vulnerability of five representative block ciphers—DES, SDES, AES-128, SAES, and SPECK32/64—under two neural attack models: Encryption Emulation (EE) and Plaintext Recovery (PR), using both fully connected neural networks and Recurrent Neural Networks (RNNs) based on bidirectional Long Short-Term Memory (BiLSTM). Our experimental results show that the proposed federated learning-based cryptanalysis framework achieves performance nearly identical to that of centralized attacks, particularly for ciphers with low round complexity. Even as the number of edge servers increases to 32, the attack models maintain high accuracy in reduced-round settings. We validate our security assessments through formal statistical significance testing using two-tailed binomial tests with 99% confidence intervals. Additionally, our scalability analysis demonstrates that aggregation times remain negligible (<0.01% of total training time), confirming the computational efficiency of the federated framework. Overall, this work provides both a scalable cryptanalysis framework and valuable insights into the design of cryptographic algorithms that are resilient to distributed, deep learning-based threats.

Abstract Partial neural distinguishers limit the available ciphertext bit combinations in differential neural cryptanalysis. When the training data size and the number of bits are not appropriately selected, label collisions can occur, which adversely affects key recovery efficiency. This paper conducts an analysis to investigate the correlation between the number of bits and the data size, aiming to address the aforementioned issue. It develops a strategy to control collisions and mitigate the impact of these collisions on model performance. A Collision-Aware Key Recovery (CAKR) framework is proposed tailored for high-collision data based on this strategy. This framework leverages the distribution characteristics of labels, eliminating the need for training neural distinguishers and significantly reducing both time and resource consumption. Experimental results show that the CAKR framework reduces the key recovery time by 96.8%, 95.5%, and 91.0% for the Speck32/64, Speck64/96, and Speck96/128, respectively. Additionally, a bit search algorithm is proposed that incorporates a differential evolution strategy and uses the non-uniformity of the ciphertext difference distribution among positive samples as the fitness criterion. Frequent calls to the neural distinguisher are avoided by our method, reducing the search time from 3.286 h to 7.464 s for 8-bit combinations in Speck32/64. The CAKR framework also offers a quantum version that theoretically further reduces time complexity.

Abstract In lightweight block cipher designs, involutory components are often employed to minimize circuit area. However, these components can also introduce security vulnerabilities. Loong is a family of lightweight block ciphers based on the Substitution-Permutation Network (SPN) structure. Each round of Loong incorporates two involutory MDS matrices and two involutory S-boxes, resulting in a fully involutory round function. While these operations provide high diffusion and a substantial algebraic degree, the involutory nature of the design makes Loong vulnerable to weak-key attacks. In this paper, we present several notable observations regarding the round function of Loong. By exploiting the unique properties of its involutory round function, we identify weak-key differential characteristics for all three full-round variants of Loong. Specifically, the probabilities of weak-key differential characteristics for Loong-64, Loong-80, and Loong-128 are $$2^{-26.83}$$ 2 - 26.83 , $$2^{-37.42}$$ 2 - 37.42 and $$2^{-46.66}$$ 2 - 46.66 , respectively. The corresponding weak-key spaces are of sizes $$2^{36}$$ 2 36 , $$2^{52}$$ 2 52 and $$2^{96}$$ 2 96 . These findings effectively compromise the security of Loong. Furthermore, we conducted experiments on a personal computer and identified practical differential characteristics for Loong-64. Additionally, we analyze the security of block ciphers with involutory round functions in general. Our findings indicate that such designs are more prone to weak-key attacks and are even more vulnerable to general differential cryptanalysis. While the use of involutory round functions reduces circuit area and improves cipher efficiency, it also introduces significant security weaknesses.

The explosive growth of AI-driven services has led to cloud-based Field Programmable Gate Array (FPGA) accelerators as key enablers of high-performance training and inference in modern data centers. Since 2024, the demand for deploying large AI workloads, especially Large Language Model (LLM), in the cloud has increased dramatically, intensifying competition among cloud providers and increasing pressure on shared FPGA infrastructures. This increasing reliance highlights the need for robust hardware security measures for cloud FPGAs. A particularly serious threat is fault injection attacks, which exploit dynamic voltage fluctuations to induce timing faults, potentially compromising functional integrity and bypassing cryptographic protections. However, existing verification procedures and structural Design Rule Check (DRC) remain blind to attacks embedded in benign-looking circuits. In this paper, we present Power-Wasting Neural Network (PWNN), a novel adversarial technique that leverages the inherent switching behavior of neural network operations to act as a power-waster circuit under adversarial input patterns. We systematically explore network architectures, and input patterns to craft configurations that induce voltage fluctuations capable of triggering timing faults for successful Differential Fault Analysis (DFA). Our PWNN implementation uses a standard open-source tool chain and passes all pre-implementation verification checks, while covertly inducing faults at runtime. We demonstrate on both the AMD ZCU104 and PYNQ-Z2 that PWNN can reliably cause timing faults on the critical path of a co-located AES-128 block cipher, enabling the rapid collection of correct/faulty ciphertext pairs needed for DFA-based key recovery. These results show that functionally correct, DRC compliant accelerators can serve as powerful, adaptive fault injectors that invalidate assumptions about bitstream security and hardware isolation.

As probably the most widespread block cipher, the AES has attracted tremendous cryptanalytical efforts since its standardization. In the single secret-key setting, Demirci-Selcuk Meet-in-the-Middle (DS-MitM) attacks have remained the state of the art on most rounds and have the lowest time complexities on all AES versions. However, after the research intensity had peaked with Derbez et al.'s seminal works from Eurocrypt'13 and FSE'13 and Li et al.'s improvements on the AES-192 at FSE'14, the generic technical evolution on DS-MitM attacks stagnated. Subsequent works automated the technique or concentrated on ciphers other than the AES. But it took one decade until Dong et al. (DCC'24) advanced the progress on DS-MitM attacks. Their approach uses constraints in both the offline and online phases, which produced improved attacks on AES-192 and -256 in the chosen-plaintext setting and on all versions in the practical-data setting. In this work, we demonstrate that Dong et al.'s use of constraints could be further improved, leading to better attacks on all versions of the AES with practical data complexity. We emphasize that our attacks do not threaten the security of the full AES versions but refine our understanding of their security margins under practical data settings.

Efficiency is essential in lightweight cryptography to ensure robust protection within constrained environments. This paper introduces a lightweight block cipher built on a Non-Linear Feedback Shift Register (NFSR), referred to as the NFSR-Based Block Cipher (NFBC). The cipher is designed for constrained environments where both efficiency and strong security are critical. NFBC operates as a Nonce-based Authenticated Encryption with Associated Data (NAEAD) scheme, providing confidentiality and authenticity within a single framework. The design achieves robust protection while maintaining minimal hardware overhead. NFBC operates on 128-bit data, key, and nonce sizes, fully aligning with National Institute of Standards and Technology (NIST) lightweight cryptography requirements. The design integrates a Non-Linear Feedback Shift Register (NFSR) for generating high-entropy round subkeys, dynamic chaotic substitution box (S-boxes) for strong confusion, and a Group Permutation (GRP) mechanism that ensures rapid diffusion with hardware-friendly efficiency. Security is rigorously evaluated across multiple dimensions. NFBC passes all 15 NIST Statistical Test Suite (STS) tests, achieves near-ideal avalanche and Bit Independence Criterion (BIC), and demonstrates consistently high nonlinearity across 200 independent chaotic S-box instances. The S-box achieves a maximum differential probability of 10/256 and maximum linear probability of (72/256)^{2}, confirming strong resistance to classical attacks. To strengthen theoretical guarantees, a provable branch-number analysis is introduced, establishing conservative lower bounds on active S-boxes (ge 45 across 20 rounds), with corresponding differential and linear probabilities that are vanishingly small. Formal AEAD security is ensured through an Encrypt-then-MAC (EtM) construction. Implementation on a Xilinx Artix-7 FPGA confirms practicality: NFBC achieves superior throughput-per-area compared to several NIST Round-2 lightweight candidates (SPOC, SPOOK, GIFT-COFB, ESTATE, SAEAES, Oribatida) and CAESAR finalists (Ascon-128, Ascon-small, CLOC-AES, SILC-AES). Estimated countermeasure overheads for masking and fault detection demonstrate feasibility against side-channel and fault attacks. These results confirm NFBC as a secure, efficient, and practically deployable lightweight cryptographic solution.

In the contemporary digital landscape, the security and confidentiality of information exchange have emerged as paramount concerns due to the increasing sophistication of cyber threats. This study proposes an integrated security framework through the development of "PrivaSel," a hybrid application that synergizes advanced cryptography and steganography to achieve dual-layer protection. The system employs the Advanced Encryption Standard (AES) with a robust 256-bit key length, implemented in Cipher Block Chaining (CBC) mode to ensure high-level data confidentiality and resistance against frequency analysis attacks. Key derivation is further strengthened using the PBKDF2 algorithm with 100,000 iterations and a random salt to mitigate brute-force vulnerabilities. For the covert layer, the system utilizes the End-of-File (EOF) steganography technique, which embeds encrypted payloads into diverse container media including images and videos without altering the spatial pixel data. Developed using a Python-based FastAPI backend and a responsive HTML5/Tailwind CSS frontend, the application facilitates seamless asynchronous processing. Empirical testing through histogram analysis confirms that the EOF method maintains absolute visual integrity, yielding a Mean Squared Error (MSE) of 0.00 and an infinite Peak Signal-to-Noise Ratio (PSNR). The results demonstrate that while the file size increases linearly relative to the payload and metadata overhead, the hidden information remains imperceptible to statistical analysis and can be flawlessly retrieved only with the authorized password, providing a reliable solution for secure multi-file data transmission.

The ILLcipher family of low-latency block ciphers for industrial internet of things

Cryptographic Randomness Testing of Block Ciphers: SAC Tests

HDHL: A hybrid GSP lightweight block cipher with two-round high diffusion

ABSTRACT The substitution box (S‐box) is a core nonlinear component in modern block ciphers, providing confusion and resistance against cryptanalytic attacks. Traditionally, S‐boxes are constructed over Galois fields, which are algebraically simple but limited in structural diversity. In this work, we present a novel S‐box designed over the non‐chain ring introducing richer algebraic characteristics compared to conventional chain ring or field‐based designs. The choice of allows for a greater number of units and zero divisors, enhancing the algebraic complexity of the transformation while maintaining manageable memory requirements 24 × 2 8 bits compared to the large storage demands of GF (2 24 ). The proposed S‐box demonstrates strong algebraic complexity due to the complex algebraic operations of the ring. For validation, the S‐box is applied in a 24‐bit RGB image encryption framework, where pixels from red, green, and blue channels are combined into 24‐bit vectors, substituted, and then permuted through affine transformations defined over the ring Z 2 32 . The resulting encrypted images exhibit uniform histograms, low correlation, and high entropy, confirming the robustness of the proposed scheme. Overall, this study highlights the novel use of a non‐chain ring structure for efficient and secure S‐box design, offering a promising alternative to field‐based cryptographic constructions.

The rapid expansion of Internet of Things (IoT) and mobile devices has intensified the demand for lightweight cryptographic algorithms capable of delivering strong security with minimal computational overhead. This work presents the SMA, a Secure Matrix-Based lightweight block cipher designed to meet these requirements through a 64-bit block and 80-bit key Substitution–Permutation Network (SPN) optimized for constrained environments. The SMA combines a nibble-wise PRESENT S-box with a fully index-based 2D matrix permutation to provide high non-linearity and efficient full-bit diffusion, supported by an enhanced key schedule that increases round-key diversity and mitigates key-dependent weaknesses. The proposed method replaces the complex linear diffusion layers used in existing lightweight ciphers such as GIFT, RECTANGLE, and PRESENT with a low-cost two-dimensional permutation that improves practical performance. Experimental evaluation demonstrates that the SMA achieves 98.5% non-correlated outputs, an average 50% bit error rate under both plaintext and key variations, and a 100% pass rate across fifteen NIST SP 800-22 statistical tests in nine data categories. Software-based implementation further confirms the correctness and applicability of the SMA for IoT-oriented simulation environments. Moreover, no exploitable differential or linear trails were identified across the full 20-round design. These results indicate that the SMA provides strong confusion, diffusion, and statistical randomness while maintaining competitive performance for secure IoT and mobile encryption applications.

The object of the study is the AES-128 (Advanced Encryption Standard) – based image-encryption scheme. The problem solved is the persistence of residual image structure and sub-ideal statistical security when classical AES is naively applied to visual data. The generated cipher images yield near-maximal entropy with low pixel correlations and uniform histograms. Encrypted-image Chi-square values concentrate around 200–310 (close to a uniform distribution), the NPCR (Number Of Changing Pixel Rate) consistently 99.623–99.657% with a best case 99.6547%, and the UACI (Unified Averaged Changed Intensity) ≈ 33.64% per channel (RGB combined ≈ 22%). Robustness tests show ≈ 30.7 dB at 50% cropping and ≈ 39.5–39.7 dB at 0.01 salt-and-pepper noise and 6.25% cropping. These outcomes are explained by the bit-level, state-dependent permutations introduced by the surjective automaton (boosting diffusion) and by the nonlinear S-box synthesized under strict criteria (e. g., bounded differential uniformity, high nonlinearity) that heighten confusion, and operation in CBC (Cipher Block Chaining) mode supplies semantic security. Other unique features that facilitate the solution are the substituting of ShiftRows/MixColumns with surjective finite automata; a custom, criteria-optimized S-box; and a 10-round AES-128 CBC pipeline with a random. Taking all of this together yielding observed statistical uniformity, a high NPCR/UACI, and stable robustness under degradation. Lastly, the findings demonstrate the applicability to secure multimedia transmission and storage in channels prone to noise or partial data loss, and being data-agnostic, that the transformations can generalize to text and generic binary data when carefully managed

The basic building block of a modern block cipher is the substitution box (S-box), which provides the nonlinearity that is required when fending off advanced cryptanalytic methods. The novel approach introduced in the present work is computationally efficient, but it is still a robust algorithm for generating an 8 8 S-box through an operation of a specifically defined bijective mapping over the Galois Field GF(28). The proposed S-box was strictly tested on a broad range of standard security criteria to prove its cryptographic integrity. A good performance has been identified in the analysis with a nonlinearity of 112 and linear approximation probability (LAP) of 0.0625, and the outstanding element of differential approximation probability (DAP) of 0.0156. Using a strong cryptographic construction, the new AES structure implements an S-box whose avalanche-like properties are best shown by a low value of the strict avalanche criterion (SAC) 0.4995 and strong bit independence (BIC) scores. The experimental results have supported the hypothesis that the proposed S-box has a much greater resistance to both the differential and the linear attacks compared with the state-of-the-art algebraic, heuristic, and chaos-based designs. In order to show how applicable the S-box can be in practical terms, a framework of image encryption incorporates the use of the S-box in it, whereby it operates as the basis element of a block cipher. The resulting cipher image achieved an entropy of 7.9978, which demonstrates a very high degree of randomness and strong resistance to statistical attacks. The feature article introduces a significant step towards systematizing cryptographic design through the introduction of a sound and carefully defined framework for the construction of high-security S-boxes.

This paper examines a new theoretical differential attack on the IDEA block cipher and several related ciphers from the same design family, such as PES and MESH. We present an analysis of the most probable differentials, which characterise the ciphers' security against the proposed attack. We also propose a design modification targeting the cipher's key-adding function to enhance its security against the attack.

This work presents a comprehensive comparative analysis of four fundamental cryptographic algorithms that form the basis of security in modern information systems: the symmetric block ciphers AES and DES, as well as the asymmetric systems RSA and ECC. The research includes a detailed description of the mathematical models and structural features of each algorithm, supported by relevant mathematical derivations. A thorough analysis of the evolution of cryptanalytic attacks on these schemes is conducted, ranging from classical methods (differential and linear cryptanalysis) to prospective quantum algorithms (Shor's and Grover's), with an assessment of their complexity and conditions for practical feasibility by 2025. Contemporary and prospective defense mechanisms are systematized, including the transition to quantum-resistant standards. Based on the conducted analysis, it is concluded that the only method known to date that ensures complete data confidentiality in the context of the development of quantum computing at all stages of its life cycle (storage, transmission, and processing) is Fully Homomorphic Encryption (FHE).

This paper presents a systematized study of algebraic cryptanalysis for symmetric ciphers. It explains how encryption algorithms can be expressed as systems of polynomial equations over finite fields and analyzed using algebraic and logical solvers. The study beginsby detailing block and stream ciphers through the lens of difference algebra, interpreting state updates and key additions as polynomial mappings. It then outlines the main solving strategies used in algebraic cryptanalysis, starting from Gröbner-basis and SAT approaches and progressing to hybrid solving. It next focuses on multistep and oracle-based strategies, which adjust variable guessing according to the hardness of each instance. These strategies extend classical hybrid attacks and make the solving process more efficient. Four case studies on Bluetooth E0, Bivium, Trivium, and Aradi illustrate these ideas. Each example shows how algebraic modeling and adaptive solving reveal structural properties and solvability thresholds in the cipher design. The results show that multistep reasoning reduces computational effort compared with static hybrids and provides a unified way to understand algebraic complexity in both stream and block ciphers.

Data encryption is a core mechanism in modern security services for protecting confidential data at rest and in transit. This work introduces the Super Encryption Standard (SES), a symmetric block cipher that follows the overall workflow of the Advanced Encryption Standard (AES) but adopts a key-dependent design to enlarge the effective key space and improve execution efficiency. The SES accepts a user-supplied key file and a selectable block dimension, from which it derives per-block round material and a dynamic substitution box generated using SHA-512. Each round relies only on XOR and a conditional half-byte swap driven by key-derived row and column vectors, enabling lightweight diffusion and confusion with low implementation cost. Experimental evaluation using multiple color images of different sizes shows that the proposed SES algorithm achieves faster encryption than the AES baseline and produces a ciphertext that behaves statistically like random noise. The encrypted images exhibit very low correlation between adjacent pixels, strong sensitivity to even minor changes in the plaintext and in the key, and resistance to standard statistical and differential attacks. Analysis of the SES substitution box also indicates favorable differential and linear properties that are comparable to those of the AES. The SES further supports a very wide key range, scaling well beyond typical fixed-length keys, which substantially increases brute-force difficulty. Therefore, the SES is a promising cipher for image encryption and related data-protection applications.