def test_Cl(self):
Cl23 = fg.ClassGroup(Delta=-23)
secgrp = mpc.SecGrp(Cl23)
secint = secgrp.sectype
g = Cl23.generator
self.assertFalse(mpc.run(mpc.output(secgrp(g) != g)))
self.assertEqual(mpc.run(secgrp.repeat_public(g, -secint(2))), g)
self.assertEqual(mpc.run(mpc.output(g**secint(-2))), g)
self.assertEqual(mpc.run(mpc.output(g * secgrp(g))), Cl23((2, -1, 3)))
Cl227 = fg.ClassGroup(Delta=-227) # Example 9.6.2 from Buchman&Vollmer
secgrp = mpc.SecGrp(Cl227)
g = Cl227((3, 1, 19))
self.assertEqual(mpc.run(mpc.output(secgrp(g) ^ 5)), g ^ 5)
Cl1123 = fg.ClassGroup(
Delta=-1123) # Example 9.7.5 from Buchman&Vollmer
secgrp = mpc.SecGrp(Cl1123)
self.assertEqual(Cl1123((1, 1, 281)), Cl1123.identity)
g = Cl1123((7, 5, 41))
self.assertEqual(mpc.run(mpc.output(secgrp(g) ^ 5)), g ^ 5)
self.assertEqual(mpc.run(mpc.output(secgrp(g)**3)), g ^ 3)
group = fg.ClassGroup(l=28)
secgrp = mpc.SecGrp(group)
g = group.generator
a = secgrp(g) ^ 6
self.assertEqual(mpc.run(mpc.output(a)), g ^ 6)
self.assertEqual(mpc.run(mpc.output(a * (a ^ -1))), group.identity)
m, z = group.encode(5)
self.assertEqual(
mpc.run(mpc.output(secgrp.decode(secgrp(m), secgrp(z)))), 5)
self.assertRaises(ValueError, secgrp, [0])
def test_group_caching(self):
S3_cached = fg.SymmetricGroup(3)
self.assertEqual(self.S3, S3_cached)
self.assertEqual(self.S3(), S3_cached())
QR11_cached = fg.QuadraticResidues(l=4)
self.assertEqual(self.QR11, QR11_cached)
Cl23_cached = fg.ClassGroup(Delta=-23)
self.assertEqual(self.Cl23, Cl23_cached)
self.assertEqual(self.Cl23(), Cl23_cached())
Cl23_cached = fg.ClassGroup(l=5)
self.assertEqual(self.Cl23, Cl23_cached)
def test_Cl(self):
Cl3 = fg.ClassGroup() # trivial class group D=-3 with 1 elt
g = Cl3((1, 1, 1))
self.assertEqual(g * (1 / g) @ g ^ 2, Cl3.identity)
self.assertEqual({g, 1 / g, 1 / g}, {g, g, 1 / g})
Cl23 = self.Cl23 # discriminant -23
self.assertEqual(Cl23.order, 3)
self.assertTrue(Cl23.is_multiplicative)
g = Cl23.generator
self.assertEqual(g, Cl23((2, 1, 3)))
self.assertEqual(g * g, Cl23((2, -1)))
self.assertEqual((g ^ 2) @ g, Cl23.identity)
self.assertEqual(g @ g.inverse(), Cl23.identity)
Cl227 = fg.ClassGroup(Delta=-227) # Example 9.6.2 from Buchman&Vollmer
self.assertEqual(Cl227.order, 5)
self.assertEqual(Cl227((1, 1, 57)), Cl227.identity)
g = Cl227((3, 1, 19))
self.assertEqual(g ^ 5, Cl227.identity)
Cl1123 = fg.ClassGroup(
Delta=-1123) # Example 9.7.5 from Buchman&Vollmer
self.assertEqual(Cl1123((1, 1, 281)), Cl1123.identity)
g = Cl1123((7, 5, 41))
self.assertEqual(g ^ 5, Cl1123.identity)
self.assertEqual(g ^ 3, Cl1123((17, 13, 19)))
self.assertRaises(ValueError, Cl23, (1, 1, 2))
self.assertRaises(ValueError, Cl23, (2, 2, 2))
Cl_2_16 = fg.ClassGroup(l=16)
g = Cl_2_16.generator
a = (g ^ 10000) ^ 128
self.assertEqual(a @ (a ^ -1), Cl_2_16.identity)
Cl_2_32 = fg.ClassGroup(l=32)
self.assertEqual(Cl_2_32.generator ^ 20021, Cl_2_32.identity)
self.assertEqual(Cl_2_32.decode(*Cl_2_32.encode(24)), 24)
self.assertRaises(ValueError, fg.ClassGroup, -13)
self.assertRaises(ValueError, fg.ClassGroup, 13)
self.assertRaises(ValueError, fg.ClassGroup, -12)
self.assertRaises(ValueError, Cl23, (-2, 1, -3))
def setUp(self):
self.S3 = fg.SymmetricGroup(3)
self.QR11 = fg.QuadraticResidues(11)
self.SG11 = fg.SchnorrGroup(11, 5, 4)
self.Cl23 = fg.ClassGroup(Delta=-23)