## Cryptology ePrint Archive: Report 2010/373

Hashing into Hessian Curves

Reza Rezaeian Farashahi

Abstract: We describe a hashing function from the elements of the finite field $\F_q$ into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fibers compared with the other known hashing functions for elliptic curves. Moreover, a point on the image set of the function is uniquely given by its abscissa. For ordinary Hessian curves, the cardinality of the image set of the function is exactly given by $(q+i)/2$ for some $i=1,2,3$.

Category / Keywords: public-key cryptography / Elliptic curve cryptography, Hessian curve, hashing