Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform

Abstract

We implement elliptic curve cryptography on the MSP430 which is a commonly used microcontroller in wireless sensor network nodes. We use the number theoretic transform to perform finite field multiplication and squaring as required in elliptic curve scalar point multiplication. We take advantage of the fast Fourier transform for the first time in the literature to speed up the number theoretic transform for an efficient realization of elliptic curve cryptography. Our implementation achieves elliptic curve scalar point multiplication in only 0.65 s and 1.31 s for multiplication of fixed and random points, respectively, and has similar or better timing performance compared to previous works in the literature.

Keywords

• elliptic curve cryptography
• fast fourier transform
• number theoretic transform
• wireless sensor network
• finite field multiplication