import binascii
import struct
# return (g, x, y) a*x + b*y = gcd(x, y)
def egcd(a, b):
if a == 0:
return (b, 0, 1)
else:
g, x, y = egcd(b % a, a)
return (g, y - (b // a) * x, x)
def decryptRSA(p,q,e,ct):
# compute n
n = p * q
phi = (p - 1) * (q - 1)
gcd, a, b = egcd(e, phi)
d = a
print "d: " + str(d)
pt = pow(ct, d, n)
return pt
def encryptRSA(p,q,e,pt):
# compute n
n = p * q
phi = (p - 1) * (q - 1)
gcd, a, b = egcd(e, phi)
d = a
print "d: " + str(d)
ct = pow(pt, e, n)
return ct
def convert(int_value):
encoded = format(int_value, 'x')
length = len(encoded)
encoded = encoded.zfill(length+length%2)
return encoded.decode('hex')
# x = mulinv(b) mod n, (x * b) % n == 1
def mulinv(b, n):
g, x, _ = egcd(b, n)
if g == 1:
return x % n
def main():
# By implementing Chinese remainder algorithm
# 1) p and q are the primes
# 2) dp = d mod (p - 1)
# 3) dq = d mod (q - 1)
# 4) Qinv = 1/q mod p *This is not integer devision but multiplicative inverse
# 5) m1 = pow(c, dp, p)
# 6) m2 = pow(c, dq, q)
# 7-1) h = Qinv(m1 - m2) mod p ; if m1 < m2
# 7-2) h = Qinv * (m1 + q/p)
# 8) m = m2 + hq
# m = 65
# p = 61
# q = 53
# dp = 53
# dq = 49
# c = 2790
p = 7901324502264899236349230781143813838831920474669364339844939631481665770635584819958931021644265960578585153616742963330195946431321644921572803658406281
q = 12802918451444044622583757703752066118180068668479378778928741088302355425977192996799623998720429594346778865275391307730988819243843851683079000293815051
dp = 5540655028622021934429306287937775291955623308965208384582009857376053583575510784169616065113641391169613969813652523507421157045377898542386933198269451
dq = 9066897320308834206952359399737747311983309062764178906269475847173966073567988170415839954996322314157438770225952491560052871464136163421892050057498651
c = 62078086677416686867183857957350338314446280912673392448065026850212685326551183962056495964579782325302082054393933682265772802750887293602432512967994805549965020916953644635965916607925335639027579187435180607475963322465417758959002385451863122106487834784688029167720175128082066670945625067803812970871
Qinv = mulinv(q,p)
print "Qinv: " + str(Qinv)
m1 = pow(c, dp, p)
print "m1: " + str(m1)
m2 = pow(c, dq, q)
print "m2: " + str(m2)
h = (Qinv * (m1 - m2)) % p
print "h: " + str(h)
m = m2 + (h*q)
print "m: " + str(int(m))
hexadecimals = str(hex(m))[2:-1]
print "solved: " + str(binascii.unhexlify(hexadecimals))
# solved: Theres_more_than_one_way_to_RSA
if __name__ == "__main__":
main()
import struct
# return (g, x, y) a*x + b*y = gcd(x, y)
def egcd(a, b):
if a == 0:
return (b, 0, 1)
else:
g, x, y = egcd(b % a, a)
return (g, y - (b // a) * x, x)
def decryptRSA(p,q,e,ct):
# compute n
n = p * q
phi = (p - 1) * (q - 1)
gcd, a, b = egcd(e, phi)
d = a
print "d: " + str(d)
pt = pow(ct, d, n)
return pt
def encryptRSA(p,q,e,pt):
# compute n
n = p * q
phi = (p - 1) * (q - 1)
gcd, a, b = egcd(e, phi)
d = a
print "d: " + str(d)
ct = pow(pt, e, n)
return ct
def convert(int_value):
encoded = format(int_value, 'x')
length = len(encoded)
encoded = encoded.zfill(length+length%2)
return encoded.decode('hex')
# x = mulinv(b) mod n, (x * b) % n == 1
def mulinv(b, n):
g, x, _ = egcd(b, n)
if g == 1:
return x % n
def main():
# By implementing Chinese remainder algorithm
# 1) p and q are the primes
# 2) dp = d mod (p - 1)
# 3) dq = d mod (q - 1)
# 4) Qinv = 1/q mod p *This is not integer devision but multiplicative inverse
# 5) m1 = pow(c, dp, p)
# 6) m2 = pow(c, dq, q)
# 7-1) h = Qinv(m1 - m2) mod p ; if m1 < m2
# 7-2) h = Qinv * (m1 + q/p)
# 8) m = m2 + hq
# m = 65
# p = 61
# q = 53
# dp = 53
# dq = 49
# c = 2790
p = 7901324502264899236349230781143813838831920474669364339844939631481665770635584819958931021644265960578585153616742963330195946431321644921572803658406281
q = 12802918451444044622583757703752066118180068668479378778928741088302355425977192996799623998720429594346778865275391307730988819243843851683079000293815051
dp = 5540655028622021934429306287937775291955623308965208384582009857376053583575510784169616065113641391169613969813652523507421157045377898542386933198269451
dq = 9066897320308834206952359399737747311983309062764178906269475847173966073567988170415839954996322314157438770225952491560052871464136163421892050057498651
c = 62078086677416686867183857957350338314446280912673392448065026850212685326551183962056495964579782325302082054393933682265772802750887293602432512967994805549965020916953644635965916607925335639027579187435180607475963322465417758959002385451863122106487834784688029167720175128082066670945625067803812970871
Qinv = mulinv(q,p)
print "Qinv: " + str(Qinv)
m1 = pow(c, dp, p)
print "m1: " + str(m1)
m2 = pow(c, dq, q)
print "m2: " + str(m2)
h = (Qinv * (m1 - m2)) % p
print "h: " + str(h)
m = m2 + (h*q)
print "m: " + str(int(m))
hexadecimals = str(hex(m))[2:-1]
print "solved: " + str(binascii.unhexlify(hexadecimals))
# solved: Theres_more_than_one_way_to_RSA
if __name__ == "__main__":
main()
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