Comparative analysis of the scalar point multiplication algorithms in the NIST FIPS 186 elliptic curve cryptography

In today's world, the problem of information security is becoming critical. One of the most common cryptographic approaches is the elliptic curve cryptosystem. However, in elliptic curve arithmetic, the scalar point multiplication is the most expensive compared to the others. In this paper, we analyze the efficiency of the scalar multiplication on elliptic curves comparing Affine, Projective, Jacobian, Jacobi-Chudnovsky, and Modified Jacobian representations of an elliptic curve. For each coordinate system, we compare Fast exponentiation, Nonadjacent form (NAF), and Window methods. We show that the Window method is the best providing lower execution time on considered coordinate systems.

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

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.