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307 lines
8.6 KiB
307 lines
8.6 KiB
# Test libsecp256k1' group operation implementations using prover.sage
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import sys
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load("group_prover.sage")
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load("weierstrass_prover.sage")
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def formula_secp256k1_gej_double_var(a):
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"""libsecp256k1's secp256k1_gej_double_var, used by various addition functions"""
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rz = a.Z * a.Y
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rz = rz * 2
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t1 = a.X^2
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t1 = t1 * 3
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t2 = t1^2
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t3 = a.Y^2
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t3 = t3 * 2
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t4 = t3^2
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t4 = t4 * 2
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t3 = t3 * a.X
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rx = t3
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rx = rx * 4
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rx = -rx
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rx = rx + t2
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t2 = -t2
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t3 = t3 * 6
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t3 = t3 + t2
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ry = t1 * t3
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t2 = -t4
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ry = ry + t2
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return jacobianpoint(rx, ry, rz)
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def formula_secp256k1_gej_add_var(branch, a, b):
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"""libsecp256k1's secp256k1_gej_add_var"""
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if branch == 0:
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return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), b)
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if branch == 1:
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return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
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z22 = b.Z^2
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z12 = a.Z^2
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u1 = a.X * z22
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u2 = b.X * z12
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s1 = a.Y * z22
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s1 = s1 * b.Z
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s2 = b.Y * z12
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s2 = s2 * a.Z
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h = -u1
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h = h + u2
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i = -s1
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i = i + s2
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if branch == 2:
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r = formula_secp256k1_gej_double_var(a)
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return (constraints(), constraints(zero={h : 'h=0', i : 'i=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}), r)
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if branch == 3:
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return (constraints(), constraints(zero={h : 'h=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={i : 'i!=0'}), point_at_infinity())
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i2 = i^2
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h2 = h^2
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h3 = h2 * h
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h = h * b.Z
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rz = a.Z * h
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t = u1 * h2
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rx = t
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rx = rx * 2
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rx = rx + h3
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rx = -rx
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rx = rx + i2
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ry = -rx
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ry = ry + t
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ry = ry * i
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h3 = h3 * s1
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h3 = -h3
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ry = ry + h3
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return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
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def formula_secp256k1_gej_add_ge_var(branch, a, b):
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"""libsecp256k1's secp256k1_gej_add_ge_var, which assume bz==1"""
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if branch == 0:
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return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(nonzero={a.Infinity : 'a_infinite'}), b)
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if branch == 1:
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return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a)
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z12 = a.Z^2
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u1 = a.X
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u2 = b.X * z12
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s1 = a.Y
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s2 = b.Y * z12
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s2 = s2 * a.Z
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h = -u1
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h = h + u2
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i = -s1
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i = i + s2
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if (branch == 2):
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r = formula_secp256k1_gej_double_var(a)
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return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
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if (branch == 3):
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return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
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i2 = i^2
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h2 = h^2
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h3 = h * h2
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rz = a.Z * h
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t = u1 * h2
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rx = t
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rx = rx * 2
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rx = rx + h3
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rx = -rx
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rx = rx + i2
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ry = -rx
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ry = ry + t
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ry = ry * i
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h3 = h3 * s1
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h3 = -h3
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ry = ry + h3
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return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
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def formula_secp256k1_gej_add_zinv_var(branch, a, b):
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"""libsecp256k1's secp256k1_gej_add_zinv_var"""
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bzinv = b.Z^(-1)
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if branch == 0:
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return (constraints(), constraints(nonzero={b.Infinity : 'b_infinite'}), a)
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if branch == 1:
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bzinv2 = bzinv^2
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bzinv3 = bzinv2 * bzinv
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rx = b.X * bzinv2
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ry = b.Y * bzinv3
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rz = 1
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return (constraints(), constraints(zero={b.Infinity : 'b_finite'}, nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz))
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azz = a.Z * bzinv
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z12 = azz^2
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u1 = a.X
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u2 = b.X * z12
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s1 = a.Y
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s2 = b.Y * z12
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s2 = s2 * azz
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h = -u1
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h = h + u2
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i = -s1
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i = i + s2
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if branch == 2:
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r = formula_secp256k1_gej_double_var(a)
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return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r)
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if branch == 3:
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return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity())
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i2 = i^2
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h2 = h^2
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h3 = h * h2
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rz = a.Z
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rz = rz * h
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t = u1 * h2
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rx = t
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rx = rx * 2
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rx = rx + h3
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rx = -rx
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rx = rx + i2
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ry = -rx
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ry = ry + t
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ry = ry * i
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h3 = h3 * s1
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h3 = -h3
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ry = ry + h3
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return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz))
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def formula_secp256k1_gej_add_ge(branch, a, b):
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"""libsecp256k1's secp256k1_gej_add_ge"""
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zeroes = {}
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nonzeroes = {}
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a_infinity = False
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if (branch & 4) != 0:
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nonzeroes.update({a.Infinity : 'a_infinite'})
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a_infinity = True
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else:
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zeroes.update({a.Infinity : 'a_finite'})
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zz = a.Z^2
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u1 = a.X
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u2 = b.X * zz
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s1 = a.Y
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s2 = b.Y * zz
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s2 = s2 * a.Z
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t = u1
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t = t + u2
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m = s1
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m = m + s2
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rr = t^2
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m_alt = -u2
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tt = u1 * m_alt
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rr = rr + tt
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degenerate = (branch & 3) == 3
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if (branch & 1) != 0:
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zeroes.update({m : 'm_zero'})
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else:
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nonzeroes.update({m : 'm_nonzero'})
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if (branch & 2) != 0:
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zeroes.update({rr : 'rr_zero'})
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else:
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nonzeroes.update({rr : 'rr_nonzero'})
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rr_alt = s1
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rr_alt = rr_alt * 2
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m_alt = m_alt + u1
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if not degenerate:
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rr_alt = rr
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m_alt = m
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n = m_alt^2
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q = n * t
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n = n^2
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if degenerate:
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n = m
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t = rr_alt^2
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rz = a.Z * m_alt
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infinity = False
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if (branch & 8) != 0:
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if not a_infinity:
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infinity = True
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zeroes.update({rz : 'r.z=0'})
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else:
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nonzeroes.update({rz : 'r.z!=0'})
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rz = rz * 2
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q = -q
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t = t + q
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rx = t
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t = t * 2
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t = t + q
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t = t * rr_alt
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t = t + n
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ry = -t
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rx = rx * 4
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ry = ry * 4
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if a_infinity:
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rx = b.X
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ry = b.Y
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rz = 1
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if infinity:
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return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), point_at_infinity())
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return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), jacobianpoint(rx, ry, rz))
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def formula_secp256k1_gej_add_ge_old(branch, a, b):
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"""libsecp256k1's old secp256k1_gej_add_ge, which fails when ay+by=0 but ax!=bx"""
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a_infinity = (branch & 1) != 0
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zero = {}
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nonzero = {}
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if a_infinity:
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nonzero.update({a.Infinity : 'a_infinite'})
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else:
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zero.update({a.Infinity : 'a_finite'})
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zz = a.Z^2
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u1 = a.X
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u2 = b.X * zz
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s1 = a.Y
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s2 = b.Y * zz
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s2 = s2 * a.Z
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z = a.Z
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t = u1
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t = t + u2
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m = s1
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m = m + s2
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n = m^2
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q = n * t
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n = n^2
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rr = t^2
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t = u1 * u2
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t = -t
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rr = rr + t
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t = rr^2
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rz = m * z
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infinity = False
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if (branch & 2) != 0:
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if not a_infinity:
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infinity = True
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else:
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return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(nonzero={z : 'conflict_a'}, zero={z : 'conflict_b'}), point_at_infinity())
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zero.update({rz : 'r.z=0'})
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else:
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nonzero.update({rz : 'r.z!=0'})
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rz = rz * (0 if a_infinity else 2)
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rx = t
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q = -q
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rx = rx + q
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q = q * 3
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t = t * 2
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t = t + q
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t = t * rr
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t = t + n
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ry = -t
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rx = rx * (0 if a_infinity else 4)
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ry = ry * (0 if a_infinity else 4)
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t = b.X
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t = t * (1 if a_infinity else 0)
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rx = rx + t
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t = b.Y
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t = t * (1 if a_infinity else 0)
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ry = ry + t
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t = (1 if a_infinity else 0)
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rz = rz + t
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if infinity:
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return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), point_at_infinity())
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return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), jacobianpoint(rx, ry, rz))
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if __name__ == "__main__":
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check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var)
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check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var)
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check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var)
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check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge)
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check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old)
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if len(sys.argv) >= 2 and sys.argv[1] == "--exhaustive":
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check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43)
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check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43)
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check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43)
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check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43)
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check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43)
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