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# how to implement weil pairing

i am trying to implement weil pairing but seems very tough, is there a script for weil pairing ??

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This is indeed available in SageMath, see the relevant documentation.

An example from the documentation:

sage: F.<a>=GF(2^5)
sage: E=EllipticCurve(F,[0,0,1,1,1])
sage: P = E(a^4 + 1, a^3)
sage: Fx.<b>=GF(2^(4*5))
sage: Ex=EllipticCurve(Fx,[0,0,1,1,1])
sage: phi=Hom(F,Fx)(F.gen().minpoly().roots(Fx)[0][0])
sage: Px=Ex(phi(P.xy()[0]),phi(P.xy()[1]))
sage: O = Ex(0)
sage: Qx = Ex(b^19 + b^18 + b^16 + b^12 + b^10 + b^9 + b^8 + b^5 + b^3 + 1, b^18 + b^13 + b^10 + b^8 + b^5 + b^4 + b^3 + b)
sage: Px.weil_pairing(Qx,41) == b^19 + b^15 + b^9 + b^8 + b^6 + b^4 + b^3 + b^2 + 1
True
sage: Px.weil_pairing(17*Px,41) == Fx(1)
True
sage: Px.weil_pairing(O,41) == Fx(1)
True

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Asked: 2016-08-29 08:41:14 -0500

Seen: 505 times

Last updated: Aug 29 '16