Point inequality

[hridambasu]

Halo2 Example: Prove knowledge of a point (x, y) that is NOT equal to reference point (x0, y0)
This circuit demonstrates proving that a witness point (x, y) is different from
a public reference point (x0, y0). The inequality is proven by showing that

• either x != x0 OR y != y0 (or both).
  We solve this by:
• Computing the inverses of the differences of the points inv_dx and inv_dy
• Computing the terms is_dx_nz and is_dy_nz which are flags for checking if dx and dy are 0 or not
• Checking whether these flags are boolean or not
• Checking whether (1 - is_dx_nz)(1 - is_dy_nz) = 0

The Circuit looks like:

Row | I0 | A0 | A1 | F0 | F1 | S0 | S1 | S2
----+-----+--------------------------------------------------------------------+--------------------------------------------------------------------+-----+----+----+----+---
0 | 0x5 | 0xa | 0 | 0 | 0 | 0 | 0 | 0
1 | 0x7 | 0xc | 0 | 0 | 0 | 0 | 0 | 0
2 | 0 | 0x5 | 0 | 0 | 0 | 0 | 0 | 0
3 | 0 | 0x7 | 0 | 0 | 0 | 0 | 0 | 0
4 | 0 | 0xa | 0x5 | 0x2 | 0 | 0 | 1 | 0
5 | 0 | 0x5 | 0 | 0 | 0 | 0 | 0 | 0
6 | 0 | 0xc | 0x7 | 0x2 | 0 | 0 | 1 | 0
7 | 0 | 0x5 | 0 | 0 | 0 | 0 | 0 | 0
8 | 0 | 0x19999999999999999999999999999999a74f7064d0853071707879f866666667 | 0 | 0 | 0 | 0 | 0 | 0
9 | 0 | 0x19999999999999999999999999999999a74f7064d0853071707879f866666667 | 0 | 0 | 0 | 0 | 0 | 0
10 | 0 | 0x5 | 0x19999999999999999999999999999999a74f7064d0853071707879f866666667 | 0 | 1 | 0 | 0 | 1
11 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0
12 | 0 | 0x5 | 0x19999999999999999999999999999999a74f7064d0853071707879f866666667 | 0 | 1 | 0 | 0 | 1
13 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0
14 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0
15 | 0 | 1 | 1 | 0x2 | 0 | 0 | 1 | 0
16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
17 | 0 | 1 | 1 | 0x2 | 0 | 0 | 1 | 0
18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
19 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1
20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
21 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1
22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
23 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1