Abstract One-dimensional (1D) chaotic maps play a pivotal role in diverse fields, including control systems, secure communication, and modeling complex systems, enabling to capture and analyze the intricate behaviors of dynamical processes. However, their limited control parameter ranges constrain their effectiveness in security applications such as cryptography and pseudo-random number generation. Addressing these concerns, the paper proposes a universal $$e$$ e -CM chaotification model, based on Euler’s number, to enhance the chaotic control parameter range of one-dimensional maps to infinity. The efficacy of the $$e$$ e -CM model has been assessed for thirteen 1D chaotic maps including, Chebyshev, Logistic, Sine, Cubic, Coupled Sine, Cubic Logistic, Quadratic, Renyi, Simple Quadratic, Sine-Sinh-Sine, Singer, Squared Sine Logistic, and Tent maps. Various tests have been conducted to evaluate the enhanced $$e$$ e -CM maps, such as Lyapunov exponents, bifurcation diagrams, approximate and sample entropies, time sensitivity analysis, 0–1 test, 2D and 3D phase plots, and cobweb plots. The findings indicate that $$e$$ e -CM-based maps exhibit complex chaotic dynamics characterized by elevated positive Lyapunov exponent values, the lack of periodic windows in the bifurcation plot, and higher sample and approximate entropy values. The 2D and 3D phase trajectory plots demonstrate that the points are evenly distributed across the entire phase space, while the cobweb plots illustrate densely packed irregular rectangular trajectories. The 0–1 test produces linear $$M-t$$ M - t and Brownian motion resembling chaotic $$p-q$$ p - q plots, alongside indicator value approaching the ideal value of $$1$$ 1 . Additionally, the $$e$$ e -CM-based enhanced 1D maps have been employed in designing a pseudo-random bit generator (PRBG). The PRBG has been evaluated in the MATLAB simulator for operational efficiency, bit-generation speed, and performance, alongside a rigorous assessment of its statistical randomness through the NIST tests. The PRBG has proven to be efficient in resource usage, faster in execution, and high-performing, while also successfully passing NIST tests. The PRBG has also been implemented and analyzed on the leading ARM Cortex-M $$4$$ 4 -based LPC $$4357$$ 4357 IoT development board to showcase its practical efficiency in RAM and ROM memory usage, execution time, current, energy, and power consumption. The results indicate that the PRBG demonstrates smaller memory usage, significantly reduced execution time, and minimal power and energy consumption. Thus, the $$e$$ e -CM based enhanced maps and PRBG stand out as an excellent choice for use in IoT environments, where security, efficiency, and performance are paramount.

Abstract Chaotic maps are employed in cryptography and secure communications due to their unpredictable and complex dynamics. However, existing chaotic maps, specifically the one-dimensional chaotic maps, often have limited chaotic control parameter ranges, which restricts their effectiveness and applicability in practical low-end applications. This paper proposes an enhanced Logistic map with an infinite chaotic control parameter range to address these limitations. The performance of the proposed map has been comprehensively evaluated using various chaos dynamical tests, including the bifurcation diagram, Lyapunov exponent, cobweb plots, 2D and 3D phase plots, approximate entropy, and sample entropy, time sensitivity analysis, and the 0–1 test. The results demonstrate that the improved Logistic map significantly outperforms its seed map across all evaluation metrics. Additionally, the enhanced Logistic map-based pseudorandom bit generator (PRBG) has been designed and evaluated for resource efficiency and security. The findings validate that the PRBG achieves significant implementation efficiency while also successfully qualifying the fifteen NIST tests, validating its statistical randomness. Thus, the proposed map and the PRBG position themselves as lightweight, highly secure solutions for safeguarding resource-limited smart IoT applications.

Chaotic maps have found applications in a wide range of fields. However, many existing one-dimensional (1-D) chaotic maps suffer from limitations. Their smaller chaotic regions restrict their effectiveness in areas like cryptography and nonlinear dynamics modeling, where randomness and security are crucial. This article proposes a novel approach that utilizes a Fibonacci sequence-based 1-D chaotic map model to address these limitations and achieve a more comprehensive chaotic range. The study compares the proposed model against six commonly used 1-D maps: 1) Logistic; 2) Sine; 3) Chebyshev; 4) Quadratic; 5) Simple Quadratic; and 6) Singer. We evaluate the enhanced chaotic maps using various chaos dynamical tests, including bifurcation diagrams, Lyapunov exponents, 2-D and 3-D phase plots, the 0-1 test, cobweb plots, and approximate and sample entropies. The results confirm that all FCM maps consistently exhibit chaotic behavior across the entire control parameter space, with higher positive Lyapunov exponents, and larger approximate and sample entropy values. The 0-1 test yields an indicator value near the ideal value of 1, with linear M-t plots and p-q plots exhibiting chaotic Brownian motion. The cobweb plot for all maps displayed intricate, dense trajectories, while the 2-D and 3-D plots displayed points filling the entire phase space. Additionally, the enhanced FCM map-based pseudorandom bit generator (PRBG) has been designed and assessed for operational efficiency, speed, and security. The findings validate that the PRBG achieves high resource efficiency, and successfully passes all 15 NIST tests for statistical randomness. The comprehensive evaluation results demonstrate the efficacy of the proposed maps and PRBG, making them a promising and preferable choice for various practical applications.

Abstract It is challenging to devise lightweight cryptographic primitives efficient in both hardware and software that can provide an optimum level of security to diverse Internet of Things applications running on low-end constrained devices. Therefore, an efficient hardware design approach that requires some specific hardware resource may not be efficient if implemented in software. Substitution bit Permutation Network based ciphers such as PRESENT and GIFT are efficient, lightweight cryptographic hardware design approaches. These ciphers introduce confusion and diffusion by employing a 4 × 4 static substitution box and bit permutations. The bit-wise permutation is realised by simple rerouting, which is most cost-effective to implement in hardware, resulting in negligible power consumption. However, this method is highly resource-consuming in software, particularly for large block-sized ciphers, with each single-bit permutation requiring multiple sub-operations. This paper proposes a novel software-based design approach for permutation operation in Substitution bit Permutation Network based ciphers using a bit-banding feature. The conventional permutation using bit rotation and the proposed approach have been implemented, analysed and compared for GIFT and PRESENT ciphers on ARM Cortex-M3-based LPC1768 development platform with KEIL MDK used as an Integrated Development Environment. The real-time performance comparison between conventional and the proposed approaches in terms of memory (RAM/ROM) footprint, power, energy and execution time has been carried out using ULINKpro and ULINKplus debug adapters for various code and speed optimisation scenarios. The proposed approach substantially reduces execution time, energy and power consumption for both PRESENT and GIFT ciphers, thus demonstrating the efficiency of the proposed method for Substitution bit Permutation Network based symmetric block ciphers.