Aхbоrоt tехnоlоgiyalari univеrsitеti - bet 14

Ilova
def gcd(a, b): while a != 0:
a, b = b % a, a return b
def findModInverse(a, m): if gcd(a, m) != 1:
return None
u1, u2, u3 = 1, 0, a v1, v2, v3 = 0, 1, m
while v3 != 0: q = u3 // v3
v1, v2, v3, u1, u2, u3 = (u1 - q * v1), (u2 - q * v2), (u3 - q *v3), v1, v2, v3 return u1 % m
import random
def rabinMiller(num):
s = num - 1
t = 0
while s % 2 == 0:
s = s // 2
t += 1
for trials in range(5):
a = random.randrange(2, num - 1) v = pow(a, s, num)
if v != 1: i = 0
while v != (num - 1): if i == t - 1:
return False else:
i = i + 1
v = (v ** 2) % num return True
def isPrime(num):
if (num < 2): return False
lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191,
193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257,
263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331,
337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401,
409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563,
569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631,
641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709,
719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797,
809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877,
881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967,
971, 977, 983, 991, 997]
if num in lowPrimes: return True
for prime in lowPrimes: if (num % prime) == 0:
return False
return rabinMiller(num)
def generateLargePrime(keysize = 1024):
while True:
num = random.randrange(2 ** (keysize - 1), 2 ** (keysize)) if isPrime(num):
return num
if name == ' main ':
num = generateLargePrime() print('Prime number:', num) print('isPrime:', isPrime(num))
import random, sys, os
import rabin_miller as rabinMiller, cryptomath_module as cryptoMath def main():
print('Making key files...') makeKeyFiles('rsa', 1024)
print('Key files generation successful.') def generateKey(keySize):
print('Generating prime p...')
p = rabinMiller.generateLargePrime(keySize) print('Generating prime q...')
q = rabinMiller.generateLargePrime(keySize) n = p * q
print('Generating e that is relatively prime to (p - 1) * (q - 1)...') while True:
e = random.randrange(2 ** (keySize - 1), 2 ** (keySize)) if cryptoMath.gcd(e, (p - 1) * (q - 1)) == 1:
break
print('Calculating d that is mod inverse of e...')
d = cryptoMath.findModInverse(e, (p - 1) * (q - 1)) publicKey = (n, e)
privateKey = (n, d)
return (publicKey, privateKey) def makeKeyFiles(name, keySize):
if os.path.exists('%s_pubkey.txt' % (name)) or os.path.exists('%s_privkey.txt' % (name)): print('\nWARNING:')
print('"%s_pubkey.txt" or "%s_privkey.txt" already exists. \nUse a different name or delete these files and re-run this program.' % (name, name))
sys.exit()
publicKey, privateKey = generateKey(keySize) print('\nWriting public key to file %s_pubkey.txt...' % name) with open('%s_pubkey.txt' % name, 'w') as fo:
fo.write('%s,%s,%s' % (keySize, publicKey[0], publicKey[1])) print('Writing private key to file %s_privkey.txt...' % name)
with open('%s_privkey.txt' % name, 'w') as fo: fo.write('%s,%s,%s' % (keySize, privateKey[0], privateKey[1]))
if name == ' main ': main()
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