Input:
Output:
(1) Compute the NAF form of ;
(2) Add leading 0's in so that the number of bits in
is multiple of 2, ,
;
(3) ;
(4) While do
(4.1) if and = (0, 0)) then
(4.2) if then
(4.3)  set and
;
(4.4) else if then
(4.5)  set
;
(4.6) else if then
(4.7)  set and
;
(4.8) else if then
(4.9)  set and
;
(4.10) else
(4.11)  set and
;
(4.12) else
(4.13) ;
(5) Pre-computation
;
;
   ;
(6) ;
(7) For from downto 0 do
(7.1) ;
(7.2) ;
(7.3) if then
(7.4)  ;
(7.5) else if then
(7.6)  if then
(7.7 )   ;
(7.8) else
(7.9)   ;
(7.10) else
(7.11)  ;
(8) Return .
Algorithm 6: New multi-scalar multiplication algorithm.