def test_decipher_rsa():
prk = rsa_private_key(2, 2, 1)
assert decipher_rsa(2, prk) == 2
prk = rsa_private_key(2, 3, 1)
assert decipher_rsa(2, prk) == 2
prk = rsa_private_key(5, 3, 3)
assert decipher_rsa(8, prk) == 2
def test_mutltiprime_rsa_full_example():
# Test example from
# https://iopscience.iop.org/article/10.1088/1742-6596/995/1/012030
puk = rsa_public_key(2, 3, 5, 7, 11, 13, 7)
prk = rsa_private_key(2, 3, 5, 7, 11, 13, 7)
assert puk == (30030, 7)
assert prk == (30030, 823)
msg = 10
encrypted = encipher_rsa(2 * msg - 15, puk)
assert encrypted == 18065
decrypted = (decipher_rsa(encrypted, prk) + 15) / 2
assert decrypted == msg
# Test example from
# https://www.scirp.org/pdf/JCC_2018032215502008.pdf
puk1 = rsa_public_key(53, 41, 43, 47, 41)
prk1 = rsa_private_key(53, 41, 43, 47, 41)
puk2 = rsa_public_key(53, 41, 43, 47, 97)
prk2 = rsa_private_key(53, 41, 43, 47, 97)
assert puk1 == (4391633, 41)
assert prk1 == (4391633, 294041)
assert puk2 == (4391633, 97)
assert prk2 == (4391633, 455713)
msg = 12321
encrypted = encipher_rsa(encipher_rsa(msg, puk1), puk2)
assert encrypted == 1081588
decrypted = decipher_rsa(decipher_rsa(encrypted, prk2), prk1)
assert decrypted == msg
def test_decipher_rsa():
prk = rsa_private_key(2, 2, 1)
assert decipher_rsa(2, prk) == 2
prk = rsa_private_key(2, 3, 1)
assert decipher_rsa(2, prk) == 2
prk = rsa_private_key(5, 3, 3)
assert decipher_rsa(8, prk) == 2
def test_rsa_private_key():
assert rsa_private_key(2, 3, 1) == (6, 1)
assert rsa_private_key(5, 3, 3) == (15, 3)
assert rsa_private_key(23,29,5) == (667,493)
assert rsa_private_key(8, 8, 8) is False
with warns_deprecated_sympy():
assert rsa_private_key(2, 2, 1) == (4, 1)
def test_rsa_private_key():
assert rsa_private_key(2, 3, 1) == (6, 1)
assert rsa_private_key(5, 3, 3) == (15, 3)
assert rsa_private_key(23, 29, 5) == (667, 493)
with warns(NonInvertibleCipherWarning):
assert rsa_private_key(2, 2, 1) == (4, 1)
assert rsa_private_key(8, 8, 8) is False
def test_rsa_private_key():
assert rsa_private_key(2, 3, 1) == (6, 1)
assert rsa_private_key(5, 3, 3) == (15, 3)
assert rsa_private_key(23, 29, 5) == (667, 493)
assert rsa_private_key(8, 8, 8) is False
with warns_deprecated_sympy():
assert rsa_private_key(2, 2, 1) == (4, 1)
def test_decipher_rsa():
prk = rsa_private_key(2, 3, 1)
assert decipher_rsa(2, prk) == 2
prk = rsa_private_key(5, 3, 3)
assert decipher_rsa(8, prk) == 2
with warns_deprecated_sympy():
prk = rsa_private_key(2, 2, 1)
assert decipher_rsa(2, prk) == 2
def test_decipher_rsa():
prk = rsa_private_key(2, 3, 1)
assert decipher_rsa(2, prk) == 2
prk = rsa_private_key(5, 3, 3)
assert decipher_rsa(8, prk) == 2
with warns_deprecated_sympy():
prk = rsa_private_key(2, 2, 1)
assert decipher_rsa(2, prk) == 2
def test_decipher_rsa():
prk = rsa_private_key(2, 3, 1)
assert decipher_rsa(2, prk) == 2
prk = rsa_private_key(5, 3, 3)
assert decipher_rsa(8, prk) == 2
with warns(NonInvertibleCipherWarning):
prk = rsa_private_key(2, 2, 1)
assert decipher_rsa(2, prk) == 2
def test_rsa_multipower_exhanstive():
from sympy.core.numbers import igcd
primes = [5, 5, 7]
e = 7
args = primes + [e]
puk = rsa_public_key(*args, multipower=True)
prk = rsa_private_key(*args, multipower=True)
n = puk[0]
for msg in range(n):
if igcd(msg, n) != 1:
continue
encrypted = encipher_rsa(msg, puk)
decrypted = decipher_rsa(encrypted, prk)
try:
assert decrypted == msg
except AssertionError:
raise AssertionError(
"The RSA is not correctly decrypted "
"(Original : {}, Encrypted : {}, Decrypted : {})".format(
msg, encrypted, decrypted
)
)
def test_rsa_crt_extreme():
p = int(
"10177157607154245068023861503693082120906487143725062283406501"
"54082258226204046999838297167140821364638180697194879500245557"
"65445186962893346463841419427008800341257468600224049986260471"
"92257248163014468841725476918639415726709736077813632961290911"
"0256421232977833028677441206049309220354796014376698325101693"
)
q = int(
"28752342353095132872290181526607275886182793241660805077850801"
"75689512797754286972952273553128181861830576836289738668745250"
"34028199691128870676414118458442900035778874482624765513861643"
"27966696316822188398336199002306588703902894100476186823849595"
"103239410527279605442148285816149368667083114802852804976893"
)
r = int(
"17698229259868825776879500736350186838850961935956310134378261"
"89771862186717463067541369694816245225291921138038800171125596"
"07315449521981157084370187887650624061033066022458512942411841"
"18747893789972315277160085086164119879536041875335384844820566"
"0287479617671726408053319619892052000850883994343378882717849"
)
s = int(
"68925428438585431029269182233502611027091755064643742383515623"
"64321310582896893395529367074942808353187138794422745718419645"
"28291231865157212604266903677599180789896916456120289112752835"
"98502265889669730331688206825220074713977607415178738015831030"
"364290585369150502819743827343552098197095520550865360159439"
)
t = int(
"69035483433453632820551311892368908779778144568711455301541094"
"31487047642322695357696860925747923189635033183069823820910521"
"71172909106797748883261493224162414050106920442445896819806600"
"15448444826108008217972129130625571421904893252804729877353352"
"739420480574842850202181462656251626522910618936534699566291"
)
e = 65537
puk = rsa_public_key(p, q, r, s, t, e)
prk = rsa_private_key(p, q, r, s, t, e)
plaintext = 1000
ciphertext_1 = encipher_rsa(plaintext, puk)
ciphertext_2 = encipher_rsa(plaintext, puk, [p, q, r, s, t])
assert ciphertext_1 == ciphertext_2
assert decipher_rsa(ciphertext_1, prk) == decipher_rsa(
ciphertext_1, prk, [p, q, r, s, t]
)
def test_rsa_large_key():
# Sample from
# http://www.herongyang.com/Cryptography/JCE-Public-Key-RSA-Private-Public-Key-Pair-Sample.html
p = int('101565610013301240713207239558950144682174355406589305284428666'\
'903702505233009')
q = int('894687191887545488935455605955948413812376003053143521429242133'\
'12069293984003')
e = int('65537')
d = int('893650581832704239530398858744759129594796235440844479456143566'\
'6999402846577625762582824202269399672579058991442587406384754958587'\
'400493169361356902030209')
assert rsa_public_key(p, q, e) == (p*q, e)
assert rsa_private_key(p, q, e) == (p*q, d)
def test_rsa_large_key():
# Sample from
# http://www.herongyang.com/Cryptography/JCE-Public-Key-RSA-Private-Public-Key-Pair-Sample.html
p = int('101565610013301240713207239558950144682174355406589305284428666'\
'903702505233009')
q = int('894687191887545488935455605955948413812376003053143521429242133'\
'12069293984003')
e = int('65537')
d = int('893650581832704239530398858744759129594796235440844479456143566'\
'6999402846577625762582824202269399672579058991442587406384754958587'\
'400493169361356902030209')
assert rsa_public_key(p, q, e) == (p * q, e)
assert rsa_private_key(p, q, e) == (p * q, d)
def test_rsa_private_key():
assert rsa_private_key(2, 3, 1) == (6, 1)
assert rsa_private_key(5, 3, 3) == (15, 3)
assert rsa_private_key(23,29,5) == (667,493)
assert rsa_private_key(8, 8, 8) is False
raises(SymPyDeprecationWarning, lambda: rsa_private_key(2, 2, 1))
with warns_deprecated_sympy():
assert rsa_private_key(2, 2, 1) == (4, 1)
def test_rsa_private_key():
assert rsa_private_key(2, 3, 1) == (6, 1)
assert rsa_private_key(5, 3, 3) == (15, 3)
assert rsa_private_key(23,29,5) == (667,493)
assert rsa_private_key(8, 8, 8) is False
raises(SymPyDeprecationWarning, lambda: rsa_private_key(2, 2, 1))
with warns_deprecated_sympy():
assert rsa_private_key(2, 2, 1) == (4, 1)
def test_rsa_exhaustive():
p, q = 61, 53
e = 17
puk = rsa_public_key(p, q, e, totient='Carmichael')
prk = rsa_private_key(p, q, e, totient='Carmichael')
for msg in range(puk[0]):
encrypted = encipher_rsa(msg, puk)
decrypted = decipher_rsa(encrypted, prk)
try:
assert decrypted == msg
except AssertionError:
raise AssertionError(
"The RSA is not correctly decrypted " \
"(Original : {}, Encrypted : {}, Decrypted : {})" \
.format(msg, encrypted, decrypted)
)
def test_rsa_multiprime_exhanstive():
primes = [3, 5, 7, 11]
e = 7
args = primes + [e]
puk = rsa_public_key(*args, totient='Carmichael')
prk = rsa_private_key(*args, totient='Carmichael')
n = puk[0]
for msg in range(n):
encrypted = encipher_rsa(msg, puk)
decrypted = decipher_rsa(encrypted, prk)
try:
assert decrypted == msg
except AssertionError:
raise AssertionError(
"The RSA is not correctly decrypted " \
"(Original : {}, Encrypted : {}, Decrypted : {})" \
.format(msg, encrypted, decrypted)
)
def rsa(msg, pqe, **kwargs):
nd = rsa_private_key(*pqe)
ne = rsa_public_key(*pqe)
nlength = len(str(ne[0]))
m = []
for x in msg:
ordinal = ord(x)
m.append(ordinal)
cipher = []
for i in m:
enciphered = encipher_rsa(i, ne)
cipher.append(enciphered)
m = []
for c in cipher:
m.append(decipher_rsa(c, nd))
dt = "".join([chr(x) for x in m])
return cipher, dt
def test_rsa_private_key():
assert rsa_private_key(2, 2, 1) == (4, 1)
assert rsa_private_key(2, 3, 1) == (6, 1)
assert rsa_private_key(5, 3, 3) == (15, 3)
assert rsa_private_key(23,29,5) == (667,493)
assert rsa_private_key(8, 8, 8) is False
def test_rsa_private_key():
assert rsa_private_key(2, 2, 1) == (4, 1)
assert rsa_private_key(2, 3, 1) == (6, 1)
assert rsa_private_key(5, 3, 3) == (15, 3)
assert rsa_private_key(23,29,5) == (667,493)
assert rsa_private_key(8, 8, 8) is False
from sympy.crypto.crypto import rsa_private_key, rsa_public_key, encipher_rsa, decipher_rsa a, b, c = 11, 13, 17 rsa_private_key(a, b, c) publickey = rsa_public_key(a, b, c) pt = 8 encipher_rsa(pt, publickey) privatekey = rsa_private_key(a, b, c) ct = 112 decipher_rsa(ct, privatekey)
rsa_public_key(p, q, 30) # In[5]: # 从SymPy中导入RSA私钥模块 from sympy.crypto.crypto import rsa_private_key # In[6]: # p, q是两个不同的素数，d与e模(p-1)(q-1)互逆，即de = 1 (mod (p-1)(q-1)). p, q, e = 3, 5, 7 # In[7]: # 生成公钥(n,d)，其中n = pq. rsa_private_key(p, q, e) # In[8]: # 若上面的任何假定不满足，则返回False。 rsa_private_key(p, q, 30) # In[14]: from sympy.crypto.crypto import encipher_rsa, rsa_public_key # 准备公钥，选取p,q两个不同素数。 p, q, e = 13, 5, 7 # 生成公钥pub_key pub_key = rsa_public_key(p, q, e)
