Faster Cryptographic Key Exchange on Hyperelliptic Curves

We present a new approach to key exchange based on divisor arithmetic for the real model of a hyperelliptic curve over a finite field, as opposed to the imaginary representation that is normally used for cryptographic applications. Using generic divisor arithmetic, our protocol is almost fifteen percent faster than conventional key exchange using hyperelliptic curves, with the most significant improvements occurring for low genus (2 and 3). This speed-up is established theoretically and confirmed numerically. Although explicit formulas for low genus curves are not considered, our results provide strong evidence that once such formulas are developed for the real case, our protocol will still be faster than that using the imaginary model.