Nawras H. Sabbry

ПОВЫШЕНИЕ ПРОИЗВОДИТЕЛЬНОСТИ И СНИЖЕНИЕ ПОТРЕБЛЕНИЯ РЕСУРСОВ ДЛЯ ЭЛЕКТРОННОЙ ПОДПИСИ НА 8-БИТНОМ МИКРОКОНТРОЛЛЕРЕ

Implementing elliptic curve point multiplication (ECPM), the core operation in elliptic curve cryptography (ECC), on microcontrollers is challenging due to limited processing power and memory, restricting its application in environments like embedded systems and autonomous vehicles, where security and performance are essential. This study presents an optimized ECPM approach for the Arduino Atmega 2560, leveraging low-level C and assembly programming for enhanced hardware resource control. By incorporating the cyclic group property of elliptic curve points, the additive inverse property in group theory, and the elimination of a curve-shaping parameter (specifically the parameter a, which influences point arithmetic in twisted Edwards curves) during doubling operations in the Extended Twisted Edwards Coordinates, along with the windowed method on Edwards25519, the approach achieves 14% to 71% reductions in execution time and cycle count, a 15% decrease in program storage space (flash memory) usage, and 77% to 80% lower dynamic memory (SRAM) consumption compared to previous studies. These results highlight the method’s efficiency, providing an optimal balance of speed, memory utilization, and security for constrained microcontroller applications.

Relevance. Ensuring secure cryptographic operations in resource-constrained environments presents challenges due to limited computational power and memory. With the rapid growth of Unmanned Vehicle Systems, the need for efficient and secure cryptographic solutions is increasing. Optimizing cryptographic algorithms for such systems becomes especially relevant given their limited computational resources and high security demands.The purpose of this study is to optimize Elliptic Curve Cryptography (ECC) digital signature operations for resource-limited systems, particularly in unmanned vehicle systems. The research aims to enhance computational efficiency and reduce memory usage, making ECC-based security mechanisms more feasible for embedded applications.The novelty of this study lies in its integration of multiple optimization techniques. It improves scalar point multiplication by leveraging cyclic group properties, additive inverses, and an enhanced windowed multiplication method. Additionally, it introduces a deterministic nonce generation approach inspired by EdDSA to further refine digital signature efficiency. These innovations collectively contribute to a more efficient cryptographic process suitable for constrained environments.The theoretical significance lies in the development of a new mathematical apparatus that makes it possible to optimize electronic signature operations.The practical significance of this study is its applicability in low-power embedded systems, where computational and memory resources are highly limited. By optimizing ECC operations, this research enhances the security and performance of cryptographic implementations in unmanned vehicle systems and similar embedded applications, ensuring secure communications without exceeding hardware constraints.The proposed method was implemented on the Arduino Atmega 2560 R3, achieves up to a 54,1 % results are showing reduction in cycle count and a 72,6 % decrease in SRAM usage for key generation, alongside significant performance improvements in signing and verification processes. Experimental results confirm its effectiveness in optimizing ECC operations for constrained devices of unmanned vehicle systems.

Elliptic curve cryptography (ECC) is widely acknowledged as a method for implementing public key cryptography on devices with limited resources thanks to its use of small keys. A crucial and complex operation in ECC calculations is scalar point multiplication. To improve its execution time and computational complexity in low-power devices, such as embedded systems, several algorithms have been suggested for scalar point multiplication, with each featuring different techniques and mathematical formulas. In this research, we focused on combining some techniques to produce a scalar point multiplication algorithm for elliptic curves over finite fields. The employed methodology involved mathematical analysis to investigate commonly used point multiplication methods. The aim was to propose an efficient algorithm that combined the best computational techniques, resulting in lower computational requirements. The findings show that the proposed method can overcome certain implementation issues found in other multiplication algorithms. In certain scenarios, the proposed method offers a more efficient approach by reducing the number of point doubling and point addition operations on elliptic curves using the inverse of the targeted point.

This research highlights the importance of error-correcting codes in ensuring secure and efficient data transmission over noisy channels. This paper aims to address the issue of limited information regarding the factors that contribute to the effectiveness of the implementation of Convolutional Codes in GPS systems. The research problem revolves around the insufficiency of scholarly sources elucidating the rationale behind the utilization of convolutional codes, specifically in GPS systems, rather than others. Through an in-depth analysis of these factors, this study strives to achieve a comprehensive understanding of the application of Convolutional Codes in GPS. To tackle this research problem, a novel methodology involving comparative analysis is employed. The coding techniques commonly used in satellite communication systems (such as BCH, LDPC, and turbo codes) are carefully examined and compared to the advantages and suitability of Convolutional codes and the Viterbi algorithm for GPS systems. Each coding technique is evaluated based on factors such as error detection and correction capabilities, bandwidth efficiency, computational complexity, and resilience to noise. The key findings of this study shed light on the unique advantages offered by Convolutional codes and the Viterbi algorithm for GPS systems. The analysis reveals that these coding techniques exhibit superior error detection and correction capabilities, efficient bandwidth utilization, and the ability to withstand noise in the GPS communication channel. The results also highlight the computational complexity associated with these techniques, providing valuable insights for the implementation of convolutional codes in GPS systems. Overall, this article contributes to the existing knowledge by providing a comprehensive understanding of the reasons behind the suitability of convolutional codes for GPS systems. The findings of this study serve as a resource for researchers, engineers, and practitioners in the field of satellite communication, aiding in the comprehensive understanding, advancement, and optimization of GPS system designs.

This research highlights the importance of error-correcting codes in ensuring secure and efficient data transmission over noisy channels. It discusses the application of Convolutional codes and the Viterbi algorithm for error detecting and correcting in applications where the data rate is high and the error probability is relatively low. This research extends beyond previous studies by conducting a comparative analysis of Convolutional codes, the Viterbi algorithm, and alternative coding methods utilized in satellite communication systems, by evaluating their effectiveness and efficiency relative to other coding approaches like BCH, LDPC, and turbo codes. The evaluation encompasses key performance metrics including error correction capabilities, computational complexity, and robustness against various error types. Additionally, practical implementation factors such as power consumption, computational requirements, and compatibility with existing hardware are considered. The analysis sheds light on the advantages and disadvantages of each coding method, offering insights into why convolutional codes and the Viterbi algorithm are particularly suitable for GPS systems.