METHOD OF POINT MULTIPLICATION ON THE EDWARDS25519 ELLIPTIC CURVE APPLIED TO RESOURCE-CONSTRAINED DEVICES

As secure communication becomes increasingly important for IoT devices, such as those used in smart city applications and healthcare, there is a critical need to improve the efficiency of cryptographic operations, especially on embedded microcontrollers with limited computational power and memory. Advanced optimization techniques are essential to enable efficient and secure cryptographic implementations in such environments. Elliptic Curve Cryptography (ECC) emerges as the optimal choice due to its combination of small key sizes and high security levels, making it particularly well-suited for resource-constrained devices. Implementing point multiplication on elliptic curves, which is the core operation of ECC applications such as digital signatures and Diffie-Hellman key exchange, poses a significant challenge in resource-constrained devices. To address these challenges, this study focuses on optimizing elliptic curve point multiplication in resource-constrained environments by proposing an optimized method tailored for the Arduino Atmega 2560 microcontroller as a resource-constrained device. By leveraging the Edwards25519 curve in a homogeneous coordinate system, the study introduces a technique that integrates principles of cyclic groups of elliptic curve points, the additive inverse property, and the windowing method for point multiplication. The proposed method is implemented using the C programming language and assembly code, using the Arduino IDE. The approach achieves notable improvements, including a reduction in computation cycles by up to 60 %, a decrease in SRAM usage by up to 78.66 %, and a reduction in Flash-memory consumption by up to 28.21 %, highlighting its suitability for resource-limited environments.