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64 lines
1.7 KiB
Python
64 lines
1.7 KiB
Python
load("div.sage")
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# Initialize an elliptic curve
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p = 115792089237316195423570985008687907853269984665640564039457584007908834671663
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r = 115792089237316195423570985008687907852837564279074904382605163141518161494337
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Fp = GF(p) # Base Field
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Fr = GF(r) # Scalar Field
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A = 0
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B = 7
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E = EllipticCurve(GF(p), [A, B])
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assert(E.cardinality() == r)
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K.<x> = PolynomialRing(Fp, implementation="generic")
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L.<y> = PolynomialRing(K, implementation="generic")
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M.<z> = L[]
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eqn = y^2 - x^3 - A * x - B
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P1 = LabelPoint(E.random_element(), {"P₁": 1})
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P2 = LabelPoint(E.random_element(), {"P₂": 1})
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P3 = LabelPoint(E.random_element(), {"P₃": 1})
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P4 = LabelPoint(E.random_element(), {"P₄": 1})
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P5 = LabelPoint(E.random_element(), {"P₅": 1})
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Q = -(P1.P + P2.P + P3.P + P4.P + P5.P)
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Q = LabelPoint(Q, {"Q": 1})
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assert P1.P + P2.P + P3.P + P4.P + P5.P + Q.P == E(0)
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L1 = div_line(P1, P2)
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Q1 = P1 + P2
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print(f"L₁ = {L1}")
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print(f"Q₁ = P₁ + P₂")
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L2 = div_line(P3, P4)
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Q2 = P3 + P4
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print(f"L₂ = {L2}")
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print(f"Q₂ = P₃ + P₄")
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L3 = div_line(P5, Q)
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Q3 = P5 + Q
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print(f"L₃ = {L3}")
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print(f"Q₃ = P₅ + Q")
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print()
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ℓ4 = div_line(Q1, Q2)
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L4 = ℓ4 + L1 + L2 - div_line(Q1, -Q1) - div_line(Q2, -Q2)
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Q4 = Q1 + Q2
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print(f"ℓ₄ = {ℓ4}")
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print(f"L₄ = ℓ₄ + L₁ + L₂ - div(x - Q₁) - div(x - Q₂)")
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print(f" = {L4}")
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print(f"Q₄ = Q₁ + Q₂")
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print("Carry L₃ to next level")
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print()
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ℓ5 = div_line(Q4, Q3)
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L5 = ℓ5 + L4 + L3 - div_line(Q4, -Q4) - div_line(Q3, -Q3)
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print(f"ℓ₅ = {ℓ5}")
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print(f"L₅ = ℓ₅ + L₄ + L₃ - div(x - Q₄) - div(x - Q₃)")
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print(f" = {L5}")
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print()
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# We should get the same result here:
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load("construct.sage")
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points = [P1, P2, P3, P4, P5, Q]
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L = construct(points)
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print(f"L = {L}")
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