Algorithm A1: Calculation of u∙P + v·Q using the Straus–Shamir trick.

Input: u = (ul−1 … u1 u0)2, v = (vl−1 … v1 v0)2 with (ul−1,vl−1) ≠ (0,0);

P, Q are points of EC over GF(p), P ≠ Q

Output: R = u∙P + v·Q

Precompute: W = P + Q

R = ul−1 ·P+ vl−1 ·Q

for i from l − 2 downto 0 do

R = 2·R

if ui = 1 and vi = 1 then R = R + W

else if ui = 1 and vi  = 0 then R = R + P

else if ui = 0 and vi = 1 then R = R + Q

end for

return R