Algorithm A3:Atomic patterns using special mixed Jacobian–affine coordinates for EC point addition and doubling for ECs over GF(p) with the parameter a = −3, corresponding to [13].
Nr	point addition	point doubling
1	R1 ←Xq ∙ Z2	R0 ← I ∙ Z2
2	R1 ← R1 − X	R1 ← X − R0
3	⁕ ←⁕ +⁕	R2 ← Y + Y
4	R2 ← R1 ∙ R1	Z22 ← Y ∙ R2
5	⁕ ←⁕ +⁕	Y2 ← Z22 + Z22
6	R3 ← X ∙ R2	R3 ← R2 ∙ Z
7	R0 ←Yq ∙ Z3	R2 ←Y2 ∙ X
8	⁕ ←⁕ +⁕	X2 ← X + R0
9	Z3 ←R1 ∙ R2	R0 ←R1 ∙ X2
10	R2 ← Z ∙ R1	R1 ← Z22 ∙ Y2
11	X3 ←R3 + R3	X2 ← R0 + R0
12	X3 ← Z3 + X3	R0 ← R0 + X2
13	Z32 ←(R2)2	X2 ← (R0)2
14	R0 ← R0 − Y	X2 ← X2 − R2
15	R1 ←(R0)2	Z22 ← (R3)2
16	X3 ←R1 − X3	X2 ← X2 − R2
17	R1 ←R3 − X3	R2 ← R2 − X2
18	R3 ← R1 ∙ R0	Z23 ← Z22 ∙ R3
19	R0 ← Y ∙ Z3	Y2 ← R0 ∙ R2
20	Y3 ←R3 − R0	Y2 ← Y2 − R1
21	Z3 ← R2	Z2 ← R3