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Copy pathRSA.StringInput.py
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RSA.StringInput.py
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import random
import math
def mod_power(a, b, n):
#Function that returns a**b (mod n) where a, b, n are integers
#Returns the remainder when a**b is divided by n
#Implementation done without using pow() function as a challenge
r = 1
x = a%n
while b > 0:
if ((b%2) == 1):
r = (r*a)%n
b = b >>1
a = (a*a)%n
return r
def bezout_solver(a,b,k):
# given integers a, b, k return the integer solution to the equation: # a*x + b*y = k
# return the greatest common divisor of a and b as well
# if a solution does not exist, return None, None, gcd(a,b)
#Finding the gcd of a and b without using gcd() function
gcd = None
l = max(a,b) # From the values passed into the parameters a and b, assign the larger value to local variable l
s = min(a,b) # From the values passed into the parameters a and b, assign the lesser value to local variable s
while s > 0:
gcd = s
s = l%s
l = gcd
# check if gcd divdes k, if it does, run Bezout's algorithm
if(k%gcd != 0 ):
return None ,None , gcd
else: #Bezout Algorithm
x = 0; x0 = 1
y = 1; y0 = 0
r = min(a,b); r0 = max(a,b)
while r != 0:
quo = r0//r
r0, r = r, r0 - quo*r
y0, y = y, y0 - quo*y
x0, x = x, x0 - quo*x
c = k//gcd
#The lines below assign the variables to the correct values based on the values of a and b
if(a == max(a,b)):
return c*x0, c*y0, gcd
elif(b == max(a,b)):
return c*y0, c*x0, gcd
else: # in case a and b are equal
return c*x0, c*y0, gcd
def rsa_setup(p,q):
n, e, d = 0, 0, 0
n = p * q
gcd = 0
totient = (p-1) * (q-1)
e = 0
for i in range(3, totient):
gcd = math.gcd(i, totient)
if(gcd == 1):
e = i
a, _, _ = bezout_solver(e,totient,1)
d = mod_power(a, 1, totient)
return n, e, d
def encrypt(n, e, message):
return mod_power(message, e, n)
def decrypt(n, d, encrypted_message):
return mod_power(encrypted_message, d, n)
#Algorithm Testing Code
#List of small prime numbers
primes = [11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779]
#Number of trials to run for the test program
trials = 1
count = 0
for i in range(trials):
p , q = random.sample(primes, 2)
n, e, d = rsa_setup(p,q)
print(p,q,n,e,d)
message = random.randint(0, n-1)
en = encrypt(n, e, message)
if message != decrypt(n, d, en):
print("Error for p={0} q={1}".format(p,q))
count += 1
print(f"Error rate {count/trials}")
ints = []
def str2ints(message):
# supports utf-8 encoded message string parameter
# function converts that string into a list of integers where the integer is the number associated with the binary representation of the character
#ints = []
for ch in message:
ints.append(ord(ch))
concatenated_int = int(''.join(str(i) for i in ints))
return concatenated_int
def ints2str(message_list):
# given a list of integers where each integer represents a character, return the string message it represents
# reverses the str2ints function
string = ""
for i in message_list:
string += chr(i)
return string
# Algorithm Testing with message strings
primes = [11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779]
#Number of trials to run for the test program
trials = 1
count = 0
for i in range(trials):
p , q = random.sample(primes, 2)
n, e, d = rsa_setup(p,q)
print(p,q,n,e,d)
#message = random.randint(0, n-1)
message = str2ints("me")
print(str2ints("me"))
en = encrypt(n, e, message)
if message != decrypt(n, d, en):
print("Error for p={0} q={1}".format(p,q))
count += 1
print(ints2str(ints))
print(f"Error rate {count/trials}")