X =
00
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
Y =
00
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
X ↔ Y
Ext-GCD(12, 14) → Twos = 1 → Ext-GCD(6, 7) :
i
GCD
Bezout
AOdd :
AEven :
A
↔
B
ax
ay
bx
by
|A-B|
A↔B
Sx
Sy
ax ←
Sx' ay ←
Sy' A ←
A/2 ax ←
ax + Y ay ←
ay + X ax ←
ax/2 ay ←
ay/2
0
6
7
1
0
0
1
1
6
7
1
0
0
1
1
3
8
6
4
3
2
3
7
4
3
0
1
4
1
4
4
4
4
2
Even
Even
2
2
3
2
↔
3
2
2
4
3
1
1
Even
Even
1
1
4
1
↔
3
1
1
4
3
2
1
5
4
5
4
1
12
10
6
5
5
1
1
6
5
1
1
0
6
1
1
6
5
1
1
0
7
1
1
6
5
1
1
0
(6)(12) - (5)(14) = 2