def test_public_key(self):
p521 = _curves['p521']
point = EccPoint(p521.Gx, p521.Gy, 'p521')
key = EccKey(curve="P-384", point=point)
self.failIf(key.has_private())
self.assertEqual(key.pointQ, point)
def test_public_key(self):
p384 = _curves['p384']
point = EccPoint(p384.Gx, p384.Gy, 'p384')
key = EccKey(curve="P-384", point=point)
self.assertFalse(key.has_private())
self.assertEqual(key.pointQ, point)
def test_inplace_addition(self):
pointRx = 0x72b13dd4354b6b81745195e98cc5ba6970349191ac476bd4553cf35a545a067e
pointRy = 0x8d585cbb2e1327d75241a8a122d7620dc33b13315aa5c9d46d013011744ac264
pointR = self.pointS.copy()
pointR += self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = EccPoint.point_at_infinity()
# S + 0
pointR = self.pointS.copy()
pointR += pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai.copy()
pointR += self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai.copy()
pointR += pai
self.assertEqual(pointR, pai)
def test_generate(self):
key = ECC.generate(curve="P-256")
self.failUnless(key.has_private())
self.assertEqual(key.pointQ, EccPoint(_curve.Gx, _curve.Gy) * key.d)
# Other names
ECC.generate(curve="secp256r1")
ECC.generate(curve="prime256v1")
def test_generate(self):
curve = _curves['p521']
key = ECC.generate(curve="P-521")
self.assertTrue(key.has_private())
self.assertEqual(key.pointQ, EccPoint(curve.Gx, curve.Gy, "p521") * key.d)
# Other names
ECC.generate(curve="secp521r1")
ECC.generate(curve="prime521v1")
def test_generate(self):
curve = _curves['p384']
key = ECC.generate(curve="P-384")
self.failUnless(key.has_private())
self.assertEqual(key.pointQ, EccPoint(curve.Gx, curve.Gy, "p384") * key.d)
# Other names
ECC.generate(curve="secp384r1")
ECC.generate(curve="prime384v1")
def test_generate(self):
key = ECC.generate(curve="P-256")
self.assertTrue(key.has_private())
self.assertEqual(key.pointQ, EccPoint(_curves['p256'].Gx,
_curves['p256'].Gy) * key.d,
"p256")
# Other names
ECC.generate(curve="secp256r1")
ECC.generate(curve="prime256v1")
def test_generate(self):
key = ECC.generate(curve="P-192")
self.assertTrue(key.has_private())
self.assertEqual(key.pointQ, EccPoint(_curves['p192'].Gx,
_curves['p192'].Gy,
"P-192") * key.d,
"p192")
# Other names
ECC.generate(curve="secp192r1")
ECC.generate(curve="prime192v1")
def test_private_key(self):
key = EccKey(curve="P-256", d=1)
self.assertEqual(key.d, 1)
self.failUnless(key.has_private())
self.assertEqual(key.pointQ.x, _curve.Gx)
self.assertEqual(key.pointQ.y, _curve.Gy)
point = EccPoint(_curve.Gx, _curve.Gy)
key = EccKey(curve="P-256", d=1, point=point)
self.assertEqual(key.d, 1)
self.failUnless(key.has_private())
self.assertEqual(key.pointQ, point)
# Other names
key = EccKey(curve="secp256r1", d=1)
key = EccKey(curve="prime256v1", d=1)
def test_private_key(self):
key = EccKey(curve="P-224", d=1)
self.assertEqual(key.d, 1)
self.assertTrue(key.has_private())
self.assertEqual(key.pointQ.x, _curves['p224'].Gx)
self.assertEqual(key.pointQ.y, _curves['p224'].Gy)
point = EccPoint(_curves['p224'].Gx, _curves['p224'].Gy, curve='P-224')
key = EccKey(curve="P-224", d=1, point=point)
self.assertEqual(key.d, 1)
self.assertTrue(key.has_private())
self.assertEqual(key.pointQ, point)
# Other names
key = EccKey(curve="secp224r1", d=1)
key = EccKey(curve="prime224v1", d=1)
def test_private_key(self):
p521 = _curves['p521']
key = EccKey(curve="P-521", d=1)
self.assertEqual(key.d, 1)
self.failUnless(key.has_private())
self.assertEqual(key.pointQ.x, p521.Gx)
self.assertEqual(key.pointQ.y, p521.Gy)
point = EccPoint(p521.Gx, p521.Gy, "p521")
key = EccKey(curve="P-521", d=1, point=point)
self.assertEqual(key.d, 1)
self.failUnless(key.has_private())
self.assertEqual(key.pointQ, point)
# Other names
key = EccKey(curve="p521", d=1)
key = EccKey(curve="secp521r1", d=1)
key = EccKey(curve="prime521v1", d=1)
def test_private_key(self):
p384 = _curves['p384']
key = EccKey(curve="P-384", d=1)
self.assertEqual(key.d, 1)
self.failUnless(key.has_private())
self.assertEqual(key.pointQ.x, p384.Gx)
self.assertEqual(key.pointQ.y, p384.Gy)
point = EccPoint(p384.Gx, p384.Gy, "p384")
key = EccKey(curve="P-384", d=1, point=point)
self.assertEqual(key.d, 1)
self.failUnless(key.has_private())
self.assertEqual(key.pointQ, point)
# Other names
key = EccKey(curve="p384", d=1)
key = EccKey(curve="secp384r1", d=1)
key = EccKey(curve="prime384v1", d=1)
class TestEccPoint_PAI_P521(unittest.TestCase):
"""Test vectors from http://point-at-infinity.org/ecc/nisttv"""
curve = _curves['p521']
pointG = EccPoint(curve.Gx, curve.Gy, "p521")
def test_set(self):
pointW = EccPoint(0, 0)
pointW.set(self.pointS)
self.assertEqual(pointW, self.pointS)
class TestEccPoint_NIST(unittest.TestCase):
"""Tests defined in section 4.3 of https://www.nsa.gov/ia/_files/nist-routines.pdf"""
pointS = EccPoint(
0xde2444bebc8d36e682edd27e0f271508617519b3221a8fa0b77cab3989da97c9,
0xc093ae7ff36e5380fc01a5aad1e66659702de80f53cec576b6350b243042a256)
pointT = EccPoint(
0x55a8b00f8da1d44e62f6b3b25316212e39540dc861c89575bb8cf92e35e0986b,
0x5421c3209c2d6c704835d82ac4c3dd90f61a8a52598b9e7ab656e9d8c8b24316)
def test_set(self):
pointW = EccPoint(0, 0)
pointW.set(self.pointS)
self.assertEqual(pointW, self.pointS)
def test_copy(self):
pointW = self.pointS.copy()
self.assertEqual(pointW, self.pointS)
pointW.set(self.pointT)
self.assertEqual(pointW, self.pointT)
self.assertNotEqual(self.pointS, self.pointT)
def test_addition(self):
pointRx = 0x72b13dd4354b6b81745195e98cc5ba6970349191ac476bd4553cf35a545a067e
pointRy = 0x8d585cbb2e1327d75241a8a122d7620dc33b13315aa5c9d46d013011744ac264
pointR = self.pointS + self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = EccPoint.point_at_infinity()
# S + 0
pointR = self.pointS + pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai + self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai + pai
self.assertEqual(pointR, pai)
def test_inplace_addition(self):
pointRx = 0x72b13dd4354b6b81745195e98cc5ba6970349191ac476bd4553cf35a545a067e
pointRy = 0x8d585cbb2e1327d75241a8a122d7620dc33b13315aa5c9d46d013011744ac264
pointR = self.pointS.copy()
pointR += self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = EccPoint.point_at_infinity()
# S + 0
pointR = self.pointS.copy()
pointR += pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai.copy()
pointR += self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai.copy()
pointR += pai
self.assertEqual(pointR, pai)
def test_doubling(self):
pointRx = 0x7669e6901606ee3ba1a8eef1e0024c33df6c22f3b17481b82a860ffcdb6127b0
pointRy = 0xfa878162187a54f6c39f6ee0072f33de389ef3eecd03023de10ca2c1db61d0c7
pointR = self.pointS.copy()
pointR.double()
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 2*0
pai = self.pointS.point_at_infinity()
pointR = pai.copy()
pointR.double()
self.assertEqual(pointR, pai)
# S + S
pointR = self.pointS.copy()
pointR += pointR
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_scalar_multiply(self):
d = 0xc51e4753afdec1e6b6c6a5b992f43f8dd0c7a8933072708b6522468b2ffb06fd
pointRx = 0x51d08d5f2d4278882946d88d83c97d11e62becc3cfc18bedacc89ba34eeca03f
pointRy = 0x75ee68eb8bf626aa5b673ab51f6e744e06f8fcf8a6c0cf3035beca956a7b41d5
pointR = self.pointS * d
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 0*S
pai = self.pointS.point_at_infinity()
pointR = self.pointS * 0
self.assertEqual(pointR, pai)
# -1*S
self.assertRaises(ValueError, lambda: self.pointS * -1)
def test_joing_scalar_multiply(self):
d = 0xc51e4753afdec1e6b6c6a5b992f43f8dd0c7a8933072708b6522468b2ffb06fd
e = 0xd37f628ece72a462f0145cbefe3f0b355ee8332d37acdd83a358016aea029db7
pointRx = 0xd867b4679221009234939221b8046245efcf58413daacbeff857b8588341f6b8
pointRy = 0xf2504055c03cede12d22720dad69c745106b6607ec7e50dd35d54bd80f615275
pointR = self.pointS * d + self.pointT * e
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_public_key(self):
point = EccPoint(_curve.Gx, _curve.Gy)
key = EccKey(curve="P-256", point=point)
self.failIf(key.has_private())
self.assertEqual(key.pointQ, point)
class TestEccPoint_PAI(unittest.TestCase):
"""Test vectors from http://point-at-infinity.org/ecc/nisttv"""
pointG = EccPoint(_curve.Gx, _curve.Gy)
class TestEccPoint_NIST_P224(unittest.TestCase):
"""Tests defined in section 4.2 of https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.204.9073&rep=rep1&type=pdf"""
pointS = EccPoint(
0x6eca814ba59a930843dc814edd6c97da95518df3c6fdf16e9a10bb5b,
0xef4b497f0963bc8b6aec0ca0f259b89cd80994147e05dc6b64d7bf22,
curve='p224')
pointT = EccPoint(
0xb72b25aea5cb03fb88d7e842002969648e6ef23c5d39ac903826bd6d,
0xc42a8a4d34984f0b71b5b4091af7dceb33ea729c1a2dc8b434f10c34,
curve='p224')
def test_set(self):
pointW = EccPoint(0, 0)
pointW.set(self.pointS)
self.assertEqual(pointW, self.pointS)
def test_copy(self):
pointW = self.pointS.copy()
self.assertEqual(pointW, self.pointS)
pointW.set(self.pointT)
self.assertEqual(pointW, self.pointT)
self.assertNotEqual(self.pointS, self.pointT)
def test_negate(self):
negS = -self.pointS
sum = self.pointS + negS
self.assertEqual(sum, self.pointS.point_at_infinity())
def test_addition(self):
pointRx = 0x236f26d9e84c2f7d776b107bd478ee0a6d2bcfcaa2162afae8d2fd15
pointRy = 0xe53cc0a7904ce6c3746f6a97471297a0b7d5cdf8d536ae25bb0fda70
pointR = self.pointS + self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = pointR.point_at_infinity()
# S + 0
pointR = self.pointS + pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai + self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai + pai
self.assertEqual(pointR, pai)
def test_inplace_addition(self):
pointRx = 0x236f26d9e84c2f7d776b107bd478ee0a6d2bcfcaa2162afae8d2fd15
pointRy = 0xe53cc0a7904ce6c3746f6a97471297a0b7d5cdf8d536ae25bb0fda70
pointR = self.pointS.copy()
pointR += self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = pointR.point_at_infinity()
# S + 0
pointR = self.pointS.copy()
pointR += pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai.copy()
pointR += self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai.copy()
pointR += pai
self.assertEqual(pointR, pai)
def test_doubling(self):
pointRx = 0xa9c96f2117dee0f27ca56850ebb46efad8ee26852f165e29cb5cdfc7
pointRy = 0xadf18c84cf77ced4d76d4930417d9579207840bf49bfbf5837dfdd7d
pointR = self.pointS.copy()
pointR.double()
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 2*0
pai = self.pointS.point_at_infinity()
pointR = pai.copy()
pointR.double()
self.assertEqual(pointR, pai)
# S + S
pointR = self.pointS.copy()
pointR += pointR
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_scalar_multiply(self):
d = 0xa78ccc30eaca0fcc8e36b2dd6fbb03df06d37f52711e6363aaf1d73b
pointRx = 0x96a7625e92a8d72bff1113abdb95777e736a14c6fdaacc392702bca4
pointRy = 0x0f8e5702942a3c5e13cd2fd5801915258b43dfadc70d15dbada3ed10
pointR = self.pointS * d
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 0*S
pai = self.pointS.point_at_infinity()
pointR = self.pointS * 0
self.assertEqual(pointR, pai)
# -1*S
self.assertRaises(ValueError, lambda: self.pointS * -1)
# Reverse order
pointR = d * self.pointS
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pointR = Integer(d) * self.pointS
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_joing_scalar_multiply(self):
d = 0xa78ccc30eaca0fcc8e36b2dd6fbb03df06d37f52711e6363aaf1d73b
e = 0x54d549ffc08c96592519d73e71e8e0703fc8177fa88aa77a6ed35736
pointRx = 0xdbfe2958c7b2cda1302a67ea3ffd94c918c5b350ab838d52e288c83e
pointRy = 0x2f521b83ac3b0549ff4895abcc7f0c5a861aacb87acbc5b8147bb18b
pointR = self.pointS * d + self.pointT * e
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_sizes(self):
self.assertEqual(self.pointS.size_in_bits(), 224)
self.assertEqual(self.pointS.size_in_bytes(), 28)
class TestEccPoint_NIST_P521(unittest.TestCase):
"""Tests defined in section 4.5 of https://www.nsa.gov/ia/_files/nist-routines.pdf"""
pointS = EccPoint(
0x000001d5c693f66c08ed03ad0f031f937443458f601fd098d3d0227b4bf62873af50740b0bb84aa157fc847bcf8dc16a8b2b8bfd8e2d0a7d39af04b089930ef6dad5c1b4,
0x00000144b7770963c63a39248865ff36b074151eac33549b224af5c8664c54012b818ed037b2b7c1a63ac89ebaa11e07db89fcee5b556e49764ee3fa66ea7ae61ac01823,
"p521")
pointT = EccPoint(
0x000000f411f2ac2eb971a267b80297ba67c322dba4bb21cec8b70073bf88fc1ca5fde3ba09e5df6d39acb2c0762c03d7bc224a3e197feaf760d6324006fe3be9a548c7d5,
0x000001fdf842769c707c93c630df6d02eff399a06f1b36fb9684f0b373ed064889629abb92b1ae328fdb45534268384943f0e9222afe03259b32274d35d1b9584c65e305,
"p521")
def test_set(self):
pointW = EccPoint(0, 0)
pointW.set(self.pointS)
self.assertEqual(pointW, self.pointS)
def test_copy(self):
pointW = self.pointS.copy()
self.assertEqual(pointW, self.pointS)
pointW.set(self.pointT)
self.assertEqual(pointW, self.pointT)
self.assertNotEqual(self.pointS, self.pointT)
def test_negate(self):
negS = -self.pointS
sum = self.pointS + negS
self.assertEqual(sum, self.pointS.point_at_infinity())
def test_addition(self):
pointRx = 0x000001264ae115ba9cbc2ee56e6f0059e24b52c8046321602c59a339cfb757c89a59c358a9a8e1f86d384b3f3b255ea3f73670c6dc9f45d46b6a196dc37bbe0f6b2dd9e9
pointRy = 0x00000062a9c72b8f9f88a271690bfa017a6466c31b9cadc2fc544744aeb817072349cfddc5ad0e81b03f1897bd9c8c6efbdf68237dc3bb00445979fb373b20c9a967ac55
pointR = self.pointS + self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = pointR.point_at_infinity()
# S + 0
pointR = self.pointS + pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai + self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai + pai
self.assertEqual(pointR, pai)
def test_inplace_addition(self):
pointRx = 0x000001264ae115ba9cbc2ee56e6f0059e24b52c8046321602c59a339cfb757c89a59c358a9a8e1f86d384b3f3b255ea3f73670c6dc9f45d46b6a196dc37bbe0f6b2dd9e9
pointRy = 0x00000062a9c72b8f9f88a271690bfa017a6466c31b9cadc2fc544744aeb817072349cfddc5ad0e81b03f1897bd9c8c6efbdf68237dc3bb00445979fb373b20c9a967ac55
pointR = self.pointS.copy()
pointR += self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = pointR.point_at_infinity()
# S + 0
pointR = self.pointS.copy()
pointR += pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai.copy()
pointR += self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai.copy()
pointR += pai
self.assertEqual(pointR, pai)
def test_doubling(self):
pointRx = 0x0000012879442f2450c119e7119a5f738be1f1eba9e9d7c6cf41b325d9ce6d643106e9d61124a91a96bcf201305a9dee55fa79136dc700831e54c3ca4ff2646bd3c36bc6
pointRy = 0x0000019864a8b8855c2479cbefe375ae553e2393271ed36fadfc4494fc0583f6bd03598896f39854abeae5f9a6515a021e2c0eef139e71de610143f53382f4104dccb543
pointR = self.pointS.copy()
pointR.double()
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 2*0
pai = self.pointS.point_at_infinity()
pointR = pai.copy()
pointR.double()
self.assertEqual(pointR, pai)
# S + S
pointR = self.pointS.copy()
pointR += pointR
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_scalar_multiply(self):
d = 0x000001eb7f81785c9629f136a7e8f8c674957109735554111a2a866fa5a166699419bfa9936c78b62653964df0d6da940a695c7294d41b2d6600de6dfcf0edcfc89fdcb1
pointRx = 0x00000091b15d09d0ca0353f8f96b93cdb13497b0a4bb582ae9ebefa35eee61bf7b7d041b8ec34c6c00c0c0671c4ae063318fb75be87af4fe859608c95f0ab4774f8c95bb
pointRy = 0x00000130f8f8b5e1abb4dd94f6baaf654a2d5810411e77b7423965e0c7fd79ec1ae563c207bd255ee9828eb7a03fed565240d2cc80ddd2cecbb2eb50f0951f75ad87977f
pointR = self.pointS * d
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 0*S
pai = self.pointS.point_at_infinity()
pointR = self.pointS * 0
self.assertEqual(pointR, pai)
# -1*S
self.assertRaises(ValueError, lambda: self.pointS * -1)
def test_joing_scalar_multiply(self):
d = 0x000001eb7f81785c9629f136a7e8f8c674957109735554111a2a866fa5a166699419bfa9936c78b62653964df0d6da940a695c7294d41b2d6600de6dfcf0edcfc89fdcb1
e = 0x00000137e6b73d38f153c3a7575615812608f2bab3229c92e21c0d1c83cfad9261dbb17bb77a63682000031b9122c2f0cdab2af72314be95254de4291a8f85f7c70412e3
pointRx = 0x0000009d3802642b3bea152beb9e05fba247790f7fc168072d363340133402f2585588dc1385d40ebcb8552f8db02b23d687cae46185b27528adb1bf9729716e4eba653d
pointRy = 0x0000000fe44344e79da6f49d87c1063744e5957d9ac0a505bafa8281c9ce9ff25ad53f8da084a2deb0923e46501de5797850c61b229023dd9cf7fc7f04cd35ebb026d89d
t = self.pointS * d
pointR = self.pointS * d
pointR += self.pointT * e
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_sizes(self):
self.assertEqual(self.pointS.size_in_bits(), 521)
self.assertEqual(self.pointS.size_in_bytes(), 66)
class TestEccPoint_NIST_P384(unittest.TestCase):
"""Tests defined in section 4.4 of https://www.nsa.gov/ia/_files/nist-routines.pdf"""
pointS = EccPoint(
0xfba203b81bbd23f2b3be971cc23997e1ae4d89e69cb6f92385dda82768ada415ebab4167459da98e62b1332d1e73cb0e,
0x5ffedbaefdeba603e7923e06cdb5d0c65b22301429293376d5c6944e3fa6259f162b4788de6987fd59aed5e4b5285e45,
"p384")
pointT = EccPoint(
0xaacc05202e7fda6fc73d82f0a66220527da8117ee8f8330ead7d20ee6f255f582d8bd38c5a7f2b40bcdb68ba13d81051,
0x84009a263fefba7c2c57cffa5db3634d286131afc0fca8d25afa22a7b5dce0d9470da89233cee178592f49b6fecb5092,
"p384")
def test_set(self):
pointW = EccPoint(0, 0, "p384")
pointW.set(self.pointS)
self.assertEqual(pointW, self.pointS)
def test_copy(self):
pointW = self.pointS.copy()
self.assertEqual(pointW, self.pointS)
pointW.set(self.pointT)
self.assertEqual(pointW, self.pointT)
self.assertNotEqual(self.pointS, self.pointT)
def test_negate(self):
negS = -self.pointS
sum = self.pointS + negS
self.assertEqual(sum, self.pointS.point_at_infinity())
def test_addition(self):
pointRx = 0x12dc5ce7acdfc5844d939f40b4df012e68f865b89c3213ba97090a247a2fc009075cf471cd2e85c489979b65ee0b5eed
pointRy = 0x167312e58fe0c0afa248f2854e3cddcb557f983b3189b67f21eee01341e7e9fe67f6ee81b36988efa406945c8804a4b0
pointR = self.pointS + self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = pointR.point_at_infinity()
# S + 0
pointR = self.pointS + pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai + self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai + pai
self.assertEqual(pointR, pai)
def _test_inplace_addition(self):
pointRx = 0x72b13dd4354b6b81745195e98cc5ba6970349191ac476bd4553cf35a545a067e
pointRy = 0x8d585cbb2e1327d75241a8a122d7620dc33b13315aa5c9d46d013011744ac264
pointR = self.pointS.copy()
pointR += self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = pointR.point_at_infinity()
# S + 0
pointR = self.pointS.copy()
pointR += pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai.copy()
pointR += self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai.copy()
pointR += pai
self.assertEqual(pointR, pai)
def test_doubling(self):
pointRx = 0x2a2111b1e0aa8b2fc5a1975516bc4d58017ff96b25e1bdff3c229d5fac3bacc319dcbec29f9478f42dee597b4641504c
pointRy = 0xfa2e3d9dc84db8954ce8085ef28d7184fddfd1344b4d4797343af9b5f9d837520b450f726443e4114bd4e5bdb2f65ddd
pointR = self.pointS.copy()
pointR.double()
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 2*0
pai = self.pointS.point_at_infinity()
pointR = pai.copy()
pointR.double()
self.assertEqual(pointR, pai)
# S + S
pointR = self.pointS.copy()
pointR += pointR
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_scalar_multiply(self):
d = 0xa4ebcae5a665983493ab3e626085a24c104311a761b5a8fdac052ed1f111a5c44f76f45659d2d111a61b5fdd97583480
pointRx = 0xe4f77e7ffeb7f0958910e3a680d677a477191df166160ff7ef6bb5261f791aa7b45e3e653d151b95dad3d93ca0290ef2
pointRy = 0xac7dee41d8c5f4a7d5836960a773cfc1376289d3373f8cf7417b0c6207ac32e913856612fc9ff2e357eb2ee05cf9667f
pointR = self.pointS * d
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 0*S
pai = self.pointS.point_at_infinity()
pointR = self.pointS * 0
self.assertEqual(pointR, pai)
# -1*S
self.assertRaises(ValueError, lambda: self.pointS * -1)
def test_joing_scalar_multiply(self):
d = 0xa4ebcae5a665983493ab3e626085a24c104311a761b5a8fdac052ed1f111a5c44f76f45659d2d111a61b5fdd97583480
e = 0xafcf88119a3a76c87acbd6008e1349b29f4ba9aa0e12ce89bcfcae2180b38d81ab8cf15095301a182afbc6893e75385d
pointRx = 0x917ea28bcd641741ae5d18c2f1bd917ba68d34f0f0577387dc81260462aea60e2417b8bdc5d954fc729d211db23a02dc
pointRy = 0x1a29f7ce6d074654d77b40888c73e92546c8f16a5ff6bcbd307f758d4aee684beff26f6742f597e2585c86da908f7186
t = self.pointS * d
pointR = self.pointS * d + self.pointT * e
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_sizes(self):
self.assertEqual(self.pointS.size_in_bits(), 384)
self.assertEqual(self.pointS.size_in_bytes(), 48)
def test_public_key(self):
point = EccPoint(_curves['p224'].Gx, _curves['p224'].Gy, curve='P-224')
key = EccKey(curve="P-224", point=point)
self.assertFalse(key.has_private())
self.assertEqual(key.pointQ, point)
class TestEccPoint_NIST_P192(unittest.TestCase):
"""Tests defined in section 4.1 of https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.204.9073&rep=rep1&type=pdf"""
pointS = EccPoint(
0xd458e7d127ae671b0c330266d246769353a012073e97acf8,
0x325930500d851f336bddc050cf7fb11b5673a1645086df3b,
curve='p192')
pointT = EccPoint(
0xf22c4395213e9ebe67ddecdd87fdbd01be16fb059b9753a4,
0x264424096af2b3597796db48f8dfb41fa9cecc97691a9c79,
curve='p192')
def test_set(self):
pointW = EccPoint(0, 0)
pointW.set(self.pointS)
self.assertEqual(pointW, self.pointS)
def test_copy(self):
pointW = self.pointS.copy()
self.assertEqual(pointW, self.pointS)
pointW.set(self.pointT)
self.assertEqual(pointW, self.pointT)
self.assertNotEqual(self.pointS, self.pointT)
def test_negate(self):
negS = -self.pointS
sum = self.pointS + negS
self.assertEqual(sum, self.pointS.point_at_infinity())
def test_addition(self):
pointRx = 0x48e1e4096b9b8e5ca9d0f1f077b8abf58e843894de4d0290
pointRy = 0x408fa77c797cd7dbfb16aa48a3648d3d63c94117d7b6aa4b
pointR = self.pointS + self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = pointR.point_at_infinity()
# S + 0
pointR = self.pointS + pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai + self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai + pai
self.assertEqual(pointR, pai)
def test_inplace_addition(self):
pointRx = 0x48e1e4096b9b8e5ca9d0f1f077b8abf58e843894de4d0290
pointRy = 0x408fa77c797cd7dbfb16aa48a3648d3d63c94117d7b6aa4b
pointR = self.pointS.copy()
pointR += self.pointT
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pai = pointR.point_at_infinity()
# S + 0
pointR = self.pointS.copy()
pointR += pai
self.assertEqual(pointR, self.pointS)
# 0 + S
pointR = pai.copy()
pointR += self.pointS
self.assertEqual(pointR, self.pointS)
# 0 + 0
pointR = pai.copy()
pointR += pai
self.assertEqual(pointR, pai)
def test_doubling(self):
pointRx = 0x30c5bc6b8c7da25354b373dc14dd8a0eba42d25a3f6e6962
pointRy = 0x0dde14bc4249a721c407aedbf011e2ddbbcb2968c9d889cf
pointR = self.pointS.copy()
pointR.double()
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 2*0
pai = self.pointS.point_at_infinity()
pointR = pai.copy()
pointR.double()
self.assertEqual(pointR, pai)
# S + S
pointR = self.pointS.copy()
pointR += pointR
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_scalar_multiply(self):
d = 0xa78a236d60baec0c5dd41b33a542463a8255391af64c74ee
pointRx = 0x1faee4205a4f669d2d0a8f25e3bcec9a62a6952965bf6d31
pointRy = 0x5ff2cdfa508a2581892367087c696f179e7a4d7e8260fb06
pointR = self.pointS * d
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
# 0*S
pai = self.pointS.point_at_infinity()
pointR = self.pointS * 0
self.assertEqual(pointR, pai)
# -1*S
self.assertRaises(ValueError, lambda: self.pointS * -1)
# Reverse order
pointR = d * self.pointS
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
pointR = Integer(d) * self.pointS
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_joing_scalar_multiply(self):
d = 0xa78a236d60baec0c5dd41b33a542463a8255391af64c74ee
e = 0xc4be3d53ec3089e71e4de8ceab7cce889bc393cd85b972bc
pointRx = 0x019f64eed8fa9b72b7dfea82c17c9bfa60ecb9e1778b5bde
pointRy = 0x16590c5fcd8655fa4ced33fb800e2a7e3c61f35d83503644
pointR = self.pointS * d + self.pointT * e
self.assertEqual(pointR.x, pointRx)
self.assertEqual(pointR.y, pointRy)
def test_sizes(self):
self.assertEqual(self.pointS.size_in_bits(), 192)
self.assertEqual(self.pointS.size_in_bytes(), 24)