How did you get y2-y1 to equal that? When I did it it ends up being a negative number.
Also, where does modp come into it all?
You've answered your own question here.
The secp256k1 curve which bitcoin uses is defined over the field
p. So all calculations must be done modulo
p.
p is defined as:
FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F
2
256 - 2
32 - 2
9 - 2
8 - 2
7 - 2
6 - 2
4 - 1
115792089237316195423570985008687907853269984665640564039457584007908834671663
With the coordinates you have given above, y2 - y1 gives:
-21239012392863529345032835584268763069528848989720309668369416382715921184388
Take that number mod
p, and you get:
94553076844452666078538149424419144783741135675920254371088167625192913487275