A Resource-Efficient Edwards25519 Point Multiplication Technique for Resource-Constrained Devices

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.