A Hardware-Efficient Elliptic Curve Cryptographic Architecture over GF (p)

Algorithm 4

Point addition and point doubling.

	Input: P1(x1, y1), P2(x2, y2),
	Output: P3(x3, x3) = P1 + P2
(1)	t2 = y1 − y2
(2)	t1 = x1 − x2
(3)	t1 = t2/t1
(4)	t2 = t1  t1
(5)	t2 = t2 − x1
(6)	t2 = t2 − x2
(7)	t2 = x2 − t2, x1 = t2
(8)	t2 = t1  t2
(9)	y1 = t2 − y2
(10)	return x3 = x1,y3 = y1
	Input: P1(x1, y1) = P2(x2, y2)
	Output: P3(x3, x3) = P1 + P2
(1)	t2 = x1  x1
(2)	t1 = t2 + t2
(3)	t1 = t2 + t1
(4)	t2 = t1 + a
(5)	t1 = y1 + y1
(6)	t1 = t2/t1
(7)	t2 = t1  t1
(8)	t2 = t2 − x1
(9)	t2 = t2 − x2
(10)	t2 = x2 − t2, x1 = t2,
(11)	t2 = t1 + t2
(12)	y1 = t2 − y2
(13)	return x3 = x1, y3 = y1