Faster Point Scalar Multiplication on Short Weierstrass Elliptic Curves over Fp using Twisted Hessian Curves over Fp2

This article shows how to use fast F_p2 arithmetic and twisted Hessian curves to obtain faster point scalar multiplication on elliptic curve E_SW in short Weierstrass form over F_p. It is assumed that p and #E_SW(F_p) are different large primes, #E(F_q) denotes number of points on curve E over field F_q and #E^t _SW (F_p), where E^t is twist of E, is divisible by 3. For example this method is suitable for two NIST curves over F_p: NIST P-224 and NIST P-256. The presented solution may be much faster than classic approach. Presented solution should also be resistant for side channel attacks and information about Y coordinate should not be lost (using for example Brier-Joye ladder such information may be lost). If coefficient A in equation of curve E_SW : y² =x³+Ax+B in short Weierstrass curve is not of special form, presented solution is up to 30% faster than classic approach. If A=−3, proposed method may be up to 24% faster.