Twisted Hessian curves.

This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, $$8.77\\mathbf{M}$$8.77M per bit for 256-bit variable-base single-scalar multiplication when curve parameters are chosen properly. This is faster than the best results known for cofactor﾿1, showing for the first time that points of order 3 are useful for performance and narrowing the gap to the speeds of curves with cofactor 4.