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ec: frobenius map

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narodnik
2022-03-15 11:35:35 +01:00
parent 41855cd4a3
commit 9a6a22137a
1 changed files with 25 additions and 0 deletions
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script/research/ec/pairing/2.2.5-frobenius.sage Normal file
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q = 67
K.<x> = GF(q)[]
F1.<u> = K.extension(x^2 + 1)
F2.<v> = F1.extension(x^3 + 2)
E = EllipticCurve(F2, [4, 3])
print(E)
pi_i = F2.frobenius_endomorphism()
#print(pi)
def pi(p):
return E(pi_i(p[0]), pi_i(p[1]))
P1 = E(15, 50)
print(pi(P1))
P2 = E(2*u + 16, 30*u + 39)
print(pi(P2))
P3 = E(15*v^2 + 4*v + 8, 44*v^2 + 30*v + 21)
print(pi(P3))
print(pi(pi(P3)))
print(pi(pi(pi(P3))))