Search Results (240)

Data integrity remains a critical requirement for secure communication in IoT environments. To address this challenge for resource-constrained IoT devices, lightweight cryptographic hash functions have been widely studied. However, static substitution layers in conventional hash functions might be vulnerable to advanced cryptanalysis. Dynamic substitution layers are constructed by exploring several methods such as key dependency, chaotic maps, DNA computations, and elliptic curves. Despite these efforts, existing dynamic substitution layers are not suitable for resource-efficient implementation. To achieve both enhanced security and practicality, this paper proposes a lightweight hash function based on a structure-varying self-coupled (SVSC) chaotic system and a dynamic substitution mechanism. A SVSC 4D chaotic map is first constructed using lightweight arithmetic and logical operations, including modular addition, bitwise shifts, and bitwise negation, thereby avoiding multiplication operations and enabling efficient hardware implementation. The chaotic map is then integrated with a generalized Feistel structure to construct a dynamic substitution layer, where the transformation behavior dynamically changes according to the internal chaotic state. This mechanism enhances nonlinear transformation diversity and contributes to improved diffusion characteristics. Finally, the dynamic substitution layer is incorporated into a sponge-based hash framework supporting flexible digest lengths. The results demonstrate that the proposed SVSC 4D chaotic system exhibits long cycle lengths in a 32-bit finite-precision implementation, mitigating the degradation caused by finite-precision effects and improving its suitability for practical cryptographic applications. Experimental evaluations demonstrate that the proposed methodology achieves a balanced tradeoff among security performance, hardware efficiency, and implementation complexity. Based on a 256-bit sponge state with a 192-bit capacity, DSLHash provides approximately 96-bit collision resistance, which is selected to balance security requirements and hardware resource consumption in lightweight applications. Full article

An algorithm of Ekerå and Gärtner, inspired by Regev’s factoring algorithm, computes discrete logarithms in multiplicative groups of prime fields. Asymptotically, it has the same qubit and gate complexity as Shor’s algorithm but splits the computation into d independent, parallel runs. The optimal value of this parameter is $d\sim \sqrt{n}$ where n is the bit size of the cryptographic group. We propose an extension of this algorithm to hyperelliptic curves. For curves of genus $g\sim \sqrt{n}$, which are not used in cryptography, we prove unconditionally that the optimal number of parallel runs $d\sim \sqrt{n}$ can still be achieved. For genus-two curves, we propose a heuristic algorithm. While its runtime speedup is difficult to quantify in general, we show that it can be expected to use up to $d=8$ parallel runs for specific curves relevant to cryptography, including GLV-friendly and pairing-friendly curves. Full article

Neural distinguishers are commonly developed and evaluated using cipher-specific data representations and model configurations. This paper presents a common CNN-Transformer differential-distinguisher architecture for the evaluated ARX cipher SPECK and the ARX-related addition–shift–XOR ciphers TEA and XTEA. The framework combines a supervised front-end purification gate, multi-scale convolutional feature extraction, multiple-ciphertext-pair representation, and self-attention-based aggregation. The purification gate is trained only on the training split and is treated as the first stage of an end-to-end classifier; samples rejected by the gate are not removed from the test-set evaluation. The same backbone architecture is trained separately for each evaluated cipher and round configuration. The resulting classifiers achieve accuracies of 98.64% for 7-round SPECK32/64 and 90.76% for 10-round TEA, and retain distinguishing capability for 5-cycle XTEA. These results demonstrate applicability across the evaluated word-oriented ciphers; they do not constitute an end-to-end key-recovery attack. Full article

Traditional image encryption methods based on static permutation and diffusion are vulnerable to structural cryptanalysis and often exhibit limited robustness under imperfect communication conditions. To address these issues, this paper proposes a robust topology-evolving image encryption algorithm driven by complex hyperchaotic dynamics for secure visual data transmission. First, a two-dimensional Rosenbrock–Schwefel hyperchaotic map is constructed to generate high-quality pseudorandom sequences for both permutation and diffusion. Based on this map, a bidirectional oscillatory spatial permutation mechanism governed by a dynamic linked-list topology is developed. Unlike fixed-path permutation strategies, the proposed topology continuously evolves with the system state during image traversal, thereby increasing nonlinear path complexity and improving resistance to structural attacks. Furthermore, a plaintext-dependent adaptive diffusion mechanism is designed to enhance sensitivity to plaintext variations and produce a strong global avalanche effect. Experimental results demonstrate that the proposed algorithm achieves favorable encryption performance, with an information entropy of up to 7.9994, a Number of Pixels Change Rate (NPCR) of 99.6076%, and a Unified Average Changing Intensity (UACI) of 33.4683%. In addition, the algorithm maintains good recovery performance under cropping attacks and noise interference, indicating its robustness and applicability for secure image transmission in complex communication environments. Full article

The integer factorization problem is a hard problem in classical. Let $N=PQ$, where P and Q are large primes. Pollard’s P-1 Algorithm is an efficient integer factorization algorithm while all the prime factors of $P-1$ are small. However, the previous variants of Pollard’s P-1 algorithms require a strict bound on the prime factors, and the running time depends on the bound instead of the actual size of prime factors, which is undesirable. This paper firstly designs a dynamic scaling version of Pollard’s P-1 Algorithm (abbreviate as $\mathsf{DSP}$) to solve this problem and also accelerate the algorithm’s efficiency by applying a fast multiplication method to it. Additionally, $\mathsf{DSP}$ saves the cost in computing the product of prime factors with high enough exponent by repeatedly using product of primes with low exponent. We also give the complexity analysis for our proposed algorithm and the latest published variant of Pollard’s P-1 Algorithm named IPP1 (Kritsanapong Somsuk, Symmetry). Moreover, we give a theoretical comparison between IPP1 and our algorithm. In particular, we show that our algorithm costs less than IPP1 in more than 95% while in IPP1 the bound of prime factors of P-1 is set to at least 64. Additionally, we also test several instances in factoring 1024-bit integers $N=PQ$ in experiment. We firstly construct the $P-1$ as a product of several randomly generated 30-bit numbers to ensure its solvability by the Pollard’s P-1 Algorithm, then test four variants of Pollard’s P-1 Algorithm. The experimental result shows that our algorithm is most efficient among them. Its efficiency improvement performs more apparently while the exponent of a prime factor in $P-1$ is large. In factoring 1024-bit integer, our algorithm solves it nearly 23.5 times faster than IPP1, 16.4 times faster than the Original Pollard’s P-1 Algorithm (J. M. Pollard, MPCPS), 35.6 times faster than the trivial Pollard’s P-1 Algorithm (D. Bishop, Introduction to cryptography with Java applets). Full article

This paper provides a narrative review on the role of artificial intelligence in cryptography, with a substantial focus on the Advanced Encryption Standard (AES) and, where the distinction matters, on AES with 256-bit keys (AES-256), at the intersection of cryptanalysis, encrypted-traffic analysis, and post-quantum computing. Deep learning side-channel analysis has been evolving into a general-purpose attack tool; neural distinguishers have entered classical cryptanalysis; and encrypted-traffic analysis shows that payload confidentiality does not imply metadata privacy. We distinguish throughout between the security of the primitive, the security of a concrete implementation, and metadata privacy at the protocol level, since the results surveyed here bear on the latter two rather than on the first. AES-256 remains structurally robust, including against the Grover bound in an idealized quantum model, but should be deployed alongside hardened implementations, post-quantum key establishment such as ML-KEM, and protocol-level countermeasures, rather than treated as sufficient on its own. Full article

Symmetry is crucial in lattice cryptography, where secure signatures rely on structural invariants over polynomial rings. This paper conducts a rigorous security and correctness analysis on Falcon-M, a lightweight signature scheme. We first demonstrate a fundamental correctness failure through an explicit experimental instantiation of the scheme: because the signing algorithm is algebraically decoupled from the secret key, no honestly generated signature was accepted in our tested experiments. Furthermore, we reveal that removing the NTRU trapdoor breaks the essential computational asymmetry, causing the verification equation to degenerate into a publicly solvable linear system. Consequently, for invertible public keys, an adversary can execute a direct universal forgery attack purely from public data via pointwise algebraic inversion in the frequency domain with $\mathcal{O}\left(n\log n\right)$ time complexity. For non-invertible keys, we further identify a practical existential forgery utilizing a localized salt-search. Ultimately, these practical cryptanalytic results mathematically invalidate the claimed security under the analyzed instantiation. Full article

In certain variants of the RSA cryptosystem with a modulus $N=pq$, the public exponent e and the private exponent d are related by the equation $ed\equiv 1\left(\mathrm{mod}{\phi }_n\left(N\right)\right)$ or $ed\equiv 1\left(\mathrm{mod}{\psi }_n\left(N\right)\right)$, where ${\phi }_n\left(N\right)=(p^n-1)(q^n-1)$ and ${\psi }_n\left(N\right)={\displaystyle \frac{(p^n-1)(q^n-1)}{(p-1)(q-1)}}$ are defined for a positive integer $n\ge 1$. In this paper, we introduce a new attack against the RSA variants when two public exponents $e_1$ and $e_2$ are given, satisfying $e_i{d}_i\equiv 1\left(\mathrm{mod}{\phi }_n\left(N\right)\right)$ or $e_i{d}_i\equiv 1\left(\mathrm{mod}{\psi }_n\left(N\right)\right)$ for $i=1,2$. Specifically, we show that when the prime factors of N share an amount of their least significant bits, and $d_1$ and $d_2$ share an amount of their most significant bits, the factorization of N can be computed in polynomial time. Our method is based on an extension of Coppersmith’s technique and lattice basis reduction and achieves improved bounds as the number of shared bits increases. The proposed attacks are heuristic in nature, relying on the standard assumption that the polynomials obtained after lattice reduction are algebraically independent. Full article

Fractional-order chaotic systems have gained immense popularity in image encryption due to their complex nonlinear dynamics and infinite memory effects. However, their excessive computational complexity remains a persistent bottleneck, severely hindering real-time engineering applications. To address this issue, a lightweight Two-Dimensional Fractional-Order Discrete Cross-Coupled Map (2D-FODCCM) is constructed based on the Short Memory Principle (SMP). This simplified map exhibits excellent dynamical behaviors and cryptographic properties, while its physical realizability and computational efficiency are successfully verified on an STM32 microcontroller. Furthermore, guided by modern cryptanalysis, an efficient and robust image cryptosystem is developed. It integrates a plaintext-associated mechanism to thwart chosen-plaintext attacks, a dynamic fractal Dragon Curve for global spatial permutation, and an innovative pixel fusion strategy to significantly boost encryption throughput. Comprehensive experimental validations demonstrate that the proposed scheme achieves a massive key space of $2^{511}$, exceptional execution efficiency of 123.61 Mbit/s for standard $512\times 512\times 3$ color images, and outstanding robustness against severe noise and data occlusion, offering a highly practical solution for secure real-time multimedia communication. Full article

Lattice-based cryptanalysis has become one of the most powerful tools for evaluating the security of the RSA cryptosystem. Most existing attacks rely on the classical key equation $ed-k\phi \left(N\right)=1$ and are effective mainly when the decryption exponent is sufficiently small or when significant information about the RSA prime factors is available. However, the dependence on this classical equation restricts the applicability of existing attacks and limits the range of weak exponents that can be targeted. In this paper, we propose a generalized lattice-based technique for solving the extended key equation $er-x\phi \left(N\right)=s$ when an approximation of one of the RSA primes is known and the parameters r, x, and s are suitably small. By transforming this relation into an appropriate modular equation and applying Coppersmith’s method, we derive conditions under which the RSA modulus can be factored in polynomial time, even when the corresponding private exponent is large. Our analysis encompasses several well-known attacks as special cases and significantly enlarges the class of vulnerable RSA exponents. Consequently, the proposed framework remains effective in settings where classical lattice-based approaches are no longer applicable. Full article

In this work, a novel method was introduced for the construction of the S-box based on delayed nonlinear chaotic systems coupled with a hybrid hash whitening mechanism. The evidence for strong nonlinear dynamical behavior is the strongly positive Lyapunov exponent with uniform statistical distribution of the generated binary sequence. Optimized 8-bit → 8-bit S-boxes, displayed in 16 × 16 hexadecimal format, were achieved by applying Fisher–Yates permutation to the chaotic sequences and further enhancing them with affine transformations over GF(2). Nonlinearity, differential uniformity, avalanche effect, strict avalanche criterion, linear approximation table, difference distribution table, and algebraic degree are cryptographic metrics that reveal very strong resistance against linear and differential attacks. Image encryption with the generated S-box further validates the confusion properties. The results confirm that the hybrid approach achieves high-quality S-boxes suitable for symmetric cryptography. Full article

We introduce the Hamiltonian pseudorandom function (HPRF), a new symmetric cryptographic primitive in which the function family $\left\{F_k\right\}$ is defined by $F_k\left(q\right)=\nabla S_k\left(q\right)$, the gradient of the generating function of a secret Lagrangian submanifold $L_k$ on the symplectic torus ${\mathbb{T}}^{2n}$. The key k specifies a composition of kicked-rotor maps in the strongly chaotic regime, whose classical Lyapunov exponents grow as $log(K/2)$ per kick. The HPRF is best understood as a seeded one-way function with high min-entropy output: $F_k$ is smooth ($C^{\infty }$), so its raw output is not directly usable as a uniform keystream, but it is computationally hard to invert. We construct three symmetric encryption modes—Mode A (key-dependent coordinate frame), Mode C (Lagrangian keystream), and Mode AC (hybrid)—in which the HPRF supplies the hardness and a key derivation function (HKDF) supplies bit-level uniformity. Standard symmetric composition then yields IND-CPA and IND-CCA2 security. Classical security reduces to the Lagrangian identification problem (LIP), shown as equivalent to the Hamiltonian inversion problem of recovering the kick parameters, which we state as an explicit hardness assumption supported by a precision/sample-complexity obstruction from the positive Lyapunov exponents, by the empirical failure of concrete attacks, and (more heuristically) by topological suggestiveness from the Arnold conjecture and Floer theory. We validate a gradient-fitting attack and an algebraic-structure attack and show that both fail. For quantum security, we propose what we believe is the right framing: that the composed Floquet operator ${\widehat{U}}_K^r$ is a candidate pseudorandom unitary (PRU) in the sense of Ji–Liu–Song. We provide three independent pillars of evidence—Wigner–Dyson spectral statistics, Lyapunov-rate scrambling, and conjectural approximate-design behaviour—and reduce the HPRF quantum security to the PRU conjecture for ${\widehat{U}}_K^r$. We then retire the dynamical-localisation argument of previous drafts as inapplicable at cryptographic parameters; the chaotic-pseudorandomness regime that the operator actually inhabits is, we argue, a stronger foundation than the one that localisation would have provided. A deterministic fixed-point arithmetic core ensures cross-platform bit-exact consistency. A reference implementation validates correctness across all modes, and an NIST SP 800-90B analysis of the output min-entropy fixes the parameter sets. As a foundational proposal, the HPRF is intended for settings that seek a symmetric hardness assumption structurally independent of the algebraic problems underlying current cryptography, for example, as a hedge primitive in defence-in-depth designs, or as a basis for further study of geometry- and chaos-based cryptography, rather than as a drop-in replacement for AES or lattice-based schemes at this stage. Full article

In this study, we propose a hybrid cryptanalytic technique targeting the RSA cryptosystem when instantiated with small private exponents. By integrating the continued fraction approach with Coppersmith’s lattice-based technique, we formulate a novel vulnerability framework. Utilizing an innovative relationship extracted from continued fraction convergents, we deduce an improved upper bound for the secret key: $d<N^{1-\alpha /3-\gamma /2}$. In this context, $\alpha :={log}_{N}e$ and $\gamma :={log}_N|p+q-S|$, where S serves as a known approximation of the prime sum $p+q$. As an extension of our preliminary conference proceedings, this paper supplies comprehensive proofs for all theoretical propositions, performs a comprehensive parameter sensitivity evaluation, and provides bounds for partial prime exposure scenarios. Empirical evaluations confirm the theoretical mechanics of our framework, demonstrating that it offers improved bounds in specific partial leakage scenarios compared to traditional lattice-only baselines. Full article

The growing need for secure image transmission across public networks requires robust encryption algorithms. Traditional chaos-based image ciphers typically have a small key space, weak avalanche behavior, or are susceptible to differential cryptanalysis. To overcome such inadequacies, this paper suggests a new adaptive image cryptosystem that combines a fractional-order memristive chaotic engine and a non-linear hybrid encryption kernel. The system uses piano-inspired feedback; the keystream generator dynamically adapts to the previously encrypted pixel, enabling powerful Cipher Block Chaining (CBC)-style chaining and content-dependent diffusion. A four-dimensional memristive system is solved by the use of fractional-order calculus, which gives an ultra-large key space (>10⁸⁰) and very high sensitivity to initial conditions—confirmed by a positive largest Lyapunov exponent (1.7199). The encryption kernel maps the traditional Exclusive OR (XOR) with the reversible two-step operation: the modular addition of the plaintext with the first keystream byte and the XOR with the second keystream one, both of which increase non-linearity and confusion. Large-scale experiments with six standard 256 × 256 colour images indicate almost ideal entropy (7.9994), Number of Pixel Change Rate (NPCR) which is 99.62, Unified Average Changing Intensity (UACI) which is 33.43, correlation coefficients are near to zero, very low Gray-Level Co-occurrence Matrix (GLCM) homogeneity (≈0.017) and high contrast (≈4843) and low energy (≈0.006 The ciphertext passes seven National Institute of Standards and Technology (NIST) SP-800-22 statistical tests, is extremely sensitive to keys (a perturbation of 1 × 10⁻¹⁴ alters >99.6% of ciphertext) and resists chosen-plaintext and known-plaintext attacks. Decryption has linear time complexity O(N), and average encryption and decryption times are 3.40 s and 2.75 s for 256 × 256 images. The proposed cryptosystem provides an attractive security–performance trade-off that can be used in high-security systems like medical image protection, privacy-preserving multimedia transmission, and secure cloud storage. Full article

The Internet of Drones (IoD) has become an important platform for applications such as smart agriculture, industrial monitoring, and large-scale aerial sensing. However, securing IoD communications remains challenging because drones often operate in open environments and have limited computation, storage, and energy resources. Existing authentication and key agreement protocols still face practical limitations, including high computational overhead, exposure to physical capture attacks, and reliance on centralized servers for session-key generation. In this paper, we first analyze a recent IoD authentication scheme and show that it is vulnerable to session-key disclosure, offline identity/password guessing, and mobile device/drone impersonation attacks. To address these issues, we propose a lightweight Physically Unclonable Function (PUF)-based end-to-end authentication protocol for IoD environments. The proposed scheme avoids storing long-term secret keys in drone memory and enables the mobile device and drone to establish a session key directly, without involving the Ground Station Server in key derivation. The security of the proposed protocol is evaluated through informal analysis, BAN logic, the Real-or-Random model, and AVISPA simulation. The results show that the scheme resists common attacks, including replay, impersonation, stolen verifier, physical capture, and offline password guessing attacks. Performance evaluation further indicates that the protocol maintains low computational cost while providing stronger security guarantees, making it suitable for resource-constrained IoD deployments. Full article