def test_intpow_unary_p4_mod(self):
"""
Check if 2^4 = 5 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 2)
self.assertEqual(a.intpow(4), FP2Value(11, 5))
def test_serialize_attestation_many(self):
"""
Check if an Attestation can be serialized and unserialized correctly with twenty bitpairs.
"""
p = 884546864135123153155516635631631
g = FP2Value(p, 58468546584635416356, 51468468484864846451)
h = FP2Value(p, 651465444864846456151, 31213216564)
a = FP2Value(p, 64168498535685461646, 6846513216165165)
b = FP2Value(p, 32184987216545974, 987984116541354132132165464)
c = FP2Value(p, 13265, 848464848609849840645102)
bitpair = BitPairAttestation(a, b, c)
key = BonehPublicKey(p, g, h)
bitpairs = [bitpair] * 20
attest = Attestation(key, bitpairs)
serialized = attest.serialize()
unserialized = Attestation.unserialize(serialized)
self.assertEqual(p, unserialized.PK.p)
self.assertEqual(g, unserialized.PK.g)
self.assertEqual(h, unserialized.PK.h)
for bp in unserialized.bitpairs:
self.assertEqual(bitpair.a, bp.a)
self.assertEqual(bitpair.b, bp.b)
self.assertEqual(bitpair.complement, bp.complement)
def test_inverse(self):
"""
Check if (4/3)^-1 = 3/4 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 4, aC=3)
self.assertEqual(a.inverse(), FP2Value(11, 3, aC=4))
def test_intpow_x_p2(self):
"""
Check if x^2 = x^2 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, b=1)
self.assertEqual(a.intpow(2), FP2Value(11, c=1))
def test_intpow_combined_p2(self):
"""
Check if (x + 1)^2 = x^2 + 2x + 1 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 1, 1)
self.assertEqual(a.intpow(2), FP2Value(11, 1, 2, 1))
def test_intpow_unary_p2(self):
"""
Check if 2^2 = 4 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 2)
self.assertEqual(a.intpow(2), FP2Value(11, 4))
def test_intpow_unary_p3(self):
"""
Check if 2^3 = 8 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 2)
self.assertEqual(a.intpow(3), FP2Value(11, 8))
def test_inverse_normalized(self):
"""
Check if (4/3)^-1 = 9 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 4, aC=3)
self.assertEqual(a.inverse().normalize(), FP2Value(11, 9))
def test_div_x(self):
"""
Check if 9x / 3x = 3 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, b=9)
b = FP2Value(11, b=3)
self.assertEqual((a / b).normalize(), FP2Value(11, 3))
def test_mul_unary(self):
"""
Check if 2 * 5 = 10 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 2)
b = FP2Value(11, 5)
self.assertEqual(a * b, FP2Value(11, 10))
def test_spob_esum(self):
"""
Check if EC sum of the point of infinity with another point equals the other point.
"""
P = (FP2Value(11, 1), FP2Value(11, 2))
self.assertEqual(esum(11, P, "O"), P)
self.assertEqual(esum(11, "O", P), P)
def test_div_combined_mod(self):
"""
Check if (x^2 + 2x + 1) / (x + 1) = x + 1 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 1, 2, 1)
b = FP2Value(11, 1, 1)
self.assertEqual((a / b).normalize(), FP2Value(11, 1, 1))
def test_div_x_mod(self):
"""
Check if 4x / 3x = 5 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, b=4)
b = FP2Value(11, b=3)
self.assertEqual((a / b).normalize(), FP2Value(11, 5))
def test_add_x(self):
"""
Check if 2x + 5x = 7x mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, b=2)
b = FP2Value(11, b=5)
self.assertEqual(a + b, FP2Value(11, b=7))
def test_div_unary_mod(self):
"""
Check if 4 / 3 = 5 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 4)
b = FP2Value(11, 3)
self.assertEqual((a / b).normalize(), FP2Value(11, 5))
def test_div_unary(self):
"""
Check if 9 / 3 = 3 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 9)
b = FP2Value(11, 3)
self.assertEqual(a / b, FP2Value(11, 3))
def test_add_unary_mod(self):
"""
Check if 5 + 7 = 1 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 5)
b = FP2Value(11, 7)
self.assertEqual(a + b, FP2Value(11, 1))
def test_mul_x(self):
"""
Check if 2x * 5x = 10x^2 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, b=2)
b = FP2Value(11, b=5)
self.assertEqual(a * b, FP2Value(11, c=10))
def test_mul_unary_mod(self):
"""
Check if 3 * 5 = 4 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 3)
b = FP2Value(11, 5)
self.assertEqual(a * b, FP2Value(11, 4))
def test_sub_x2_mod(self):
"""
Check if x^2 - (x^2 + 1) = 10 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, c=1)
b = FP2Value(11, 1, 0, 1)
self.assertEqual(a - b, FP2Value(11, 10))
def test_sub_combined_mod(self):
"""
Check if x^2 + 5x + 5 - (x^2 + 7x + 7) = 9x + 9 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 5, 5, 1)
b = FP2Value(11, 7, 7, 1)
self.assertEqual(a - b, FP2Value(11, 9, 9))
def test_sub_x(self):
"""
Check if 5x - 2x = 3x mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, b=5)
b = FP2Value(11, b=2)
self.assertEqual(a - b, FP2Value(11, b=3))
def test_sub_x_mod(self):
"""
Check if 2x + 5x = 8x mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, b=2)
b = FP2Value(11, b=5)
self.assertEqual(a - b, FP2Value(11, b=8))
def test_add_unary(self):
"""
Check if 2 + 5 = 7 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 2)
b = FP2Value(11, 5)
self.assertEqual(a + b, FP2Value(11, 7))
def test_sub_unary_mod(self):
"""
Check if 2 - 5 = 8 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 2)
b = FP2Value(11, 5)
self.assertEqual(a - b, FP2Value(11, 8))
def test_sub_unary(self):
"""
Check if 5 - 2 = 3 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 5)
b = FP2Value(11, 2)
self.assertEqual(a - b, FP2Value(11, 3))
def test_add_combined_mod(self):
"""
Check if x^2 + 5x + 5 + x^2 + 7x + 7 = 10x + 10 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 5, 5, 1)
b = FP2Value(11, 7, 7, 1)
self.assertEqual(a + b, FP2Value(11, 10, 10))
def test_add_x2_mod(self):
"""
Check if x^2 + x^2 = 9x + 9 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, c=1)
b = FP2Value(11, c=1)
self.assertEqual(a + b, FP2Value(11, 9, 9))
def test_add_x_mod(self):
"""
Check if 5x + 7x = 1x mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, b=5)
b = FP2Value(11, b=7)
self.assertEqual(a + b, FP2Value(11, b=1))
def test_mul_combined_mod(self):
"""
Check if (5) * (x^2 + x + 1) = 5x^2 + 5x + 5 = 0 mod 11 mod x^2 + x + 1.
"""
a = FP2Value(11, 5)
b = FP2Value(11, 1, 1, 1)
self.assertEqual(a * b, FP2Value(11, 5, 5, 5))
self.assertEqual(a * b, FP2Value(11, 0))