FFT enabled ECC for WSN nodes without hardware multiplier support

Abstract

ECC is a popular cryptographic algorithm for key distribution in wireless sensor networks where power efficiency is desirable. A power efficient implementation of ECC without using hardware multiplier support was proposed earlier for wireless sensor nodes. The proposed implementation utilized the number theoretic transform to carry operands to the frequency domain, and conducted Montgomery multiplication, in addition to other finite field operations, in that domain. With this work, we perform in the frequency domain only polynomial multiplication and use the fast Fourier transform to carry operands between the time and frequency domains. Our ECC implementation over $GF((2^{13}-1)^{13})$ on the MSP430 microcontroller implements multiplications without using a hardware multiplier. It achieves scalar multiplication with fixed and random points in only 0.89 s and 1.74 s, respectively. Our implementation achieves ECC point multiplication of fixed and random points $10\%$ and $13\%$ faster, and consuming $12\%$ and $15\%$ less energy, in comparison to the existing work.