Prime Field ECDSA Signature Processing for Reconfigurable Embedded Systems

Algorithm 4

Scalar multiplication in 𝐸.

Input:  Point 𝑃∈𝐸; Integer 𝑘=∑^𝑙−1_𝑖=0𝑘_𝑖2^𝑖

      with 𝑘_𝑖∈{0,1} and 𝑘_𝑙−1=1.

Output:  Point 𝑄=𝑘𝑃∈𝐸.

(1)  𝑃₁=𝑃

(2)  𝑃₂=2𝑃

(3)  for 𝑖=𝑙−2 downto 0  do

(4)   if 𝑘=0  then

(5)    𝑃^new₁=2𝑃^old₁

(6)    𝑃^new₂=𝑃^old₁+𝑃^old₂

(7)   else

(8)    𝑃^new₁=𝑃^old₁+𝑃^old₂

(9)    𝑃^new₂=2𝑃^old₂

(10)  end  if

(11)  end  for

(12)  return 𝑄=𝑃₁