Efficient ECC Processor Designs for IoT Using Edwards Curves and Exploiting FPGA Embedded Components

Abstract

Elliptic Curve Cryptography (ECC) provides high security with shorter key sizes and higher performance. Internet of Things (IoT) is the interconnected network where a vast number of connected devices require high security to ensure data integrity and privacy. Field programmable gate arrays (FPGAs) are configurable hardware fabrics enhancing the performance of applications. We propose two FPGA-based high performance and lightweight ECC processors for IoT devices. One of the ECC processor is serial with less area and the other is parallel with higher speed. The proposed ECC processors use Edwards curves and perform frequency domain multiplication utilizing FPGA-embedded digital signal processors (DSPs) or lookup tables. The proposed ECC processors work over prime characteristic finite fields of the form $GF((2^{n}-1)^{n})$ . Three such prime characteristic finite fields are investigated for each processor: $n=13,~17$ and 19, providing the key lengths of 169, 289 and 361 bits, respectively. Synthesis results, targeting different FPGAs, show that the proposed ECC processors outperform similar existing ECC processors in terms of area and speed. For example, over Virtex5 FPGA, compared to the lowest area ECC implementations in the literature over the same finite fields, our serial ECC processor without DSPs occupies 19.07% to 26.06% fewer slices while being $2.17\times $ to $3.57\times $ faster. Compared to the fastest ECC implementations, our parallel ECC processor without DSPs occupies 20.42% to 27.38% fewer slices while being $1.76\times $ to $2.22\times $ faster, and our parallel ECC processor that use DSPs is $1.93\times $ to $2.50\times $ faster.

Keywords

• Elliptic curve cryptography
• edwards curve
• embedded multiplier
• FPGA
• discrete Fourier transform
• modular multiplication