Fast hashing onto elliptic curves over fields of characteristic 3

We describe a fast hash algorithm that maps arbitrary messages onto points of an elliptic curve defined over a finite field of characteristic 3. Our new scheme runs in time O(m) for curves over F3m . The best previous algorithm for this task runs in time O(m). Experimental data confirms the speedup by a factor O(m), or approximately a hundred times for practical m values. Our results apply for both standard and normal basis representations of F3m .