V-God Runic Scriptures Privacy Summoning :
- P = G * p, Q = G * q and R = G * r
- e(P,Q)
- e(P, Q + R) = e(P, Q) * e(P, R)
- e(P + S, Q) = e(P, Q) * e(S, Q)
- a + b = b + a, (a * b) * c = a * (b * c)
- (a * c) + (b * c) = (a + b) * c
- (a / b) * b = a
- (a + b) + c = a + (b + c)
- (a + b) * c = a * c + b * c
- a / b: (a * b^(p²-2)) % p
- f(x, y) = x — P_x
- [P] + [-P] — 2 * [O]
- ax + by + c = 0
- (F * G) = (F) + (G))
- f(x, y) = P_x — x
- (f³) = 3 * [P] + 3 * [-P] — 6 * [O]
- O ([P] + [Q] + [-P-Q] — 3 * [O]
- P + Q — P — Q — 3 * O = O
- (F_Q) = n * [Q] — n * [O]
- (g) = [P + Q] — [P] — [Q] + [O]
- n * [P] — n * [O] + n * [Q] — n * [O] + n * [P + Q] — n * [P] — n * [Q] + n * [O] = n * [P + Q] — n * [O]
- F_P * F_Q * g^n = F_(P + Q)
- z = (p¹² — 1) / n
- x ϵ F_p¹², x^(p¹² — 1) = 1
- F_P^z * F_Q^z = F_(P + Q)^z
Source : https://medium.com/@VitalikButerin/exploring-elliptic-curve-pairings-c73c1864e627
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