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jack4818
GitHub Repository: jack4818/Castryck-Decru-SageMath
 Path: blob/main/dead-code/FromJacToJac.sage
323 views
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def FromJacToJac(h, D11, D12, D21, D22, a):

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    R.<x> = h.parent()

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    Fp2 = R.base()

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    J = Jacobian(HyperellipticCurve(h))

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    D1 = J(D11, D12)

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    D2 = J(D21, D22)

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    G1 = (2^(a-1)*D1)[0]

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    G2 = (2^(a-1)*D2)[0]

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    G3 = h / (G1*G2)

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    delta = Matrix(Fp2, 3, 3, [Coefficient(G1, 0), Coefficient(G1, 1), Coefficient(G1, 2),

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                              Coefficient(G2, 0), Coefficient(G2, 1), Coefficient(G2, 2),

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                              Coefficient(G3, 0), Coefficient(G3, 1), Coefficient(G3, 2)])

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    delta = delta.determinant()^(-1)

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    H1 = delta*(derivative(G2)*G3 - G2*derivative(G3))

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    H2 = delta*(derivative(G3)*G1 - G3*derivative(G1))

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    H3 = delta*(derivative(G1)*G2 - G1*derivative(G2))

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    hnew = H1*H2*H3

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    Jnew = Jacobian(HyperellipticCurve(hnew))

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    # now compute image points

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    # first the point [D11, D12]:

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    u0 = Coefficient(D11, 0)

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    u1 = Coefficient(D11, 1)

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    v0 = Coefficient(D12, 0)

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    v1 = Coefficient(D12, 1)

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    S.<x1,y1,y2,x2> = PolynomialRing(Fp2, 4)

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    # TODO: How is this computed in sage?

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    # pr = hom<S -> R | 0, 0, 0, x>

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    eq1 = x1^2 + u1*x1 + u0

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    eq2 = v1*x1 + v0 - y1

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    # TODO: What is evaluate doing?

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    # eq3 = Evaluate(G1, x1)*Evaluate(H1, x2) + Evaluate(G2, x1)*Evaluate(H2, x2)

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    # eq4 = y1*y2 - Evaluate(G1, x1)*Evaluate(H1, x2)*(x1 - x2)

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    # eq5 = y1^2 - Evaluate(h, x1)

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    I = Ideal([eq1, eq2, eq3, eq4, eq5])

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    G = GroebnerBasis(I) # last two are in non-reduced Mumford form: y2 + cubic(x2), quartic(x2)

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    # TODO what is pr?

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    # unew = pr(G[len(G)])

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    # vnew = -pr(G[len(G)-1])

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    # sanity check: (vnew^2 - hnew) mod unew

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    # TODO what is pr?

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    # imD1 = Jnew(pr(G[len(G)]), -pr(G[len(G)-1]))

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    # now same for the point [D21, D22]:

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    u0 = Coefficient(D21, 0)

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    u1 = Coefficient(D21, 1)

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    v0 = Coefficient(D22, 0)

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    v1 = Coefficient(D22, 1)

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    eq1 = x1^2 + u1*x1 + u0

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    eq2 = v1*x1 + v0 - y1

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    I = Ideal([eq1, eq2, eq3, eq4, eq5])

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    G = GroebnerBasis(I)

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    # TODO what is pr?

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    # unew = pr(G[len(G)])

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    # vnew = -pr(G[len(G)-1])

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    # TODO what is pr?

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    # imD2 = Jnew(pr(G[len(G)]), -pr(G[len(G)-1]))

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    return hnew, imD1[0], imD1[1], imD2[0], imD2[1]

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