A method of calculating the x-coordinate(xM) of a point mapping in an elliptic curve Diffie-Hellman key exchange protocol (EC-DHKF), wherein the point mapping is defined as sG+H, where sG is a point (xS,yS) on an elliptic curve and H is a point (xH,yH) on the elliptic curve, including: computing V=yS2 based upon the elliptic curve and xS; computing W=yH2 based upon the elliptic curve and xH; computing U=sqrt(W·V)mod p, where p is a large prime number; choosing U′=U or U′=p−U such that U′ based upon a characteristic agreed upon by the parties to the EC-DHKF; computing xM based upon V, W, U′, xS, xH, and p.