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Jan 24th, 2013
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- F.<x> = GF(8111)[]
- K.<x> = GF(8111^3, name='x', modulus=x^3 + 4*x - 11)
- E = EllipticCurve(GF(8111), [1,300])
- E_ = EllipticCurve(K, [1,300])
- n = E.order()
- P = E.random_element()
- Q = ZZ.random_element(n) * P
- P_ = E_(P)
- Q_ = E_(Q)
- R = E_.random_element() * (E_.order() // E.order()^2)
- W1 = P_.weil_pairing(R, n)
- W2 = Q_.weil_pairing(R, n)
- u = log(W2, W1)
- assert(P*u == Q)
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