SoC FPGA hardware implementation of radix-2w arithmetic-based elliptic curve cryptography point multiplication

Abstract

Elliptic Curve Cryptography (ECC) is widely recognized for its strength in cryptographic applications, particularly for small key sizes, offering improved security with reduced compu- tational requirements. However, efficient ECC operations, such as point and double-point mul- tiplication, continue to present challenges. This study focuses on addressing these challenges by developing a hardware design and implementation of Elliptic Curve Point Multiplication (ECPM) that integrates Radix-2 w arithmetic, a method aimed at reducing addition operations without increasing doubling operations. The primary objective is to demonstrate the superiority of this approach and provide a mechanism to explore its potential integration in ECC applica- tions. To achieve this, a detailed design for all the necessary building blocks of ECPM is de- veloped. High-Level Synthesis (HLS) tools are utilized to implement the hardware components required for the Radix-2 w point multiplication algorithm and binary field arithmetic, with a spe- cific focus on key sizes of 163 bits. Multiple optimization techniques are applied to exploit FPGA parallelism, resulting in significant performance improvements. Moreover, to facilitate seamless integration of the hardware module into system-level applications, an appropriate in- terfacing approach is devised, and the developed ECPM module is integrated into a System-on- Chip (SoC) system which includes a Processing System. This integration includes the develop- ment of a high-level abstraction software driver tailored for the implemented point multiplica- tion kernel, enabling its utilization in cryptographic applications. The use of a SoC FPGA as the development platform is due to the advantages of combining software control with hardware acceleration, enabling efficient implementation and utilization of our created ECPM module for enhanced security and performance Experimental results validate the superiority of the developed Radix-2 w ECPM module, ex- hibiting a 28% faster execution time compared to the traditional binary method. These findings contribute to a deeper understanding of the achievable performance gains in ECPM operations through the integration of Radix-2 w arithmetic. The developed hardware module serves as a testament to the potential benefits of incorporating specialized cryptographic hardware that in- tegrates Radix-2 w arithmetic in ECC applications. It provides a practical framework for the seamless integration of the hardware module into real cryptographic systems, effectively en- hancing their performance and security.