First commit

.gitignore

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+cr/
+.venv/

lib/arithmetics.py

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+# Arithmetics functions implementaton
+
+def modpow(a: int, b: int, m: int) -> int:
+    result = 1 
+    while b > 0:
+        if (b & 1) > 0:
+            result = (result * a) % m
+        b = b >> 1 
+        a = (a * a) % m 
+    return result
+
+def gcd(a: int, b: int) -> int:
+    if b == 0:
+        return a
+    return gcd(b, a % b)
+
+def mod_inverse(A: int, M: int) -> int:
+    m0 = M
+    y = 0
+    x = 1
+    if (M == 1):
+        return 0
+    while (A > 1):
+        # q is quotient
+        q = A // M
+        t = M
+        # m is remainder now, process
+        # same as Euclid's algo
+        M = A % M
+        A = t
+        t = y
+        # Update x and y
+        y = x - q * y
+        x = t
+    # Make x positive
+    if (x < 0):
+        x = x + m0
+    return x
+

lib/diffie_hellman.py

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+# Python Diffie-Hillman implémentation
+
+import random
+
+import lib.miller_rabin as miller
+import lib.arithmetics as arithm
+
+def get_p_and_g(n: int) -> (int, int):
+    p = miller.get_random_prime(n)
+    g = random.randint(2**(n-1), p)
+    return (p, g)
+
+def get_x(n: int) -> int:
+    return random.randint(2**(n-1), 2**n - 1)
+
+def get_X(x: int, p: int, g: int) -> int:
+    return arithm.modpow(g, x, p)
+
+def get_K(X: int, y: int, p: int):
+    return arithm.modpow(X, y, p)
+

lib/miller_rabin.py

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+# Python Miller-Rabin implementation
+
+import random
+import lib.arithmetics as arithm
+
+def get_d_and_s(n: int) -> (int, int):
+    d = n - 1
+    s = 0
+    while d % 2 == 0:
+        d //= 2
+        s += 1
+    return (d, s)
+
+def rabin_witness(n: int, a: int) -> bool:
+    d, s = get_d_and_s(n)
+    x = arithm.modpow(a, d, n)
+    if x == 1 or x == n - 1:
+        return False
+    for _ in range(s - 1):
+        x = arithm.modpow(x, 2, n)
+        if x == n - 1:
+            return False
+    return True
+
+def miller_rabin(n: int, k: int) -> bool:
+    if n < 3: return False
+    for _ in range(k):
+        a = random.randint(2, n - 1)
+        if rabin_witness(n, a): return False
+    return True
+
+def is_prime(n: int) -> bool:
+    return miller_rabin(n, 25)
+
+def get_random_prime(n: int) -> int:
+    a = random.randint(2**(n-1), 2**(n) - 1)
+    while not is_prime(a):
+        a = random.randint(2**(n-1), 2**(n) - 1)
+    return a 
+

lib/rsa.py

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+# Python RSA implementation
+
+import random
+import sys
+
+import lib.arithmetics as arithm
+import lib.miller_rabin as miller
+
+def get_p_and_q(n: int) -> (int, int):
+    # Get two random prime numbers
+    p = miller.get_random_prime(n)
+    q = miller.get_random_prime(n)
+    # Ensure the two numbers are differents
+    while p == q:
+        q = get_random_prime(n)
+    return (p, q)
+
+def get_keys(l: int) -> int:
+    p, q = get_p_and_q(l // 2)
+    n = p * q 
+    phy_n = (p - 1) * (q - 1)
+    e = 65537
+    while arithm.gcd(e, phy_n) != 1:
+        p, q = get_p_and_q(l // 2)
+        n = p * q 
+        phy_n = (p - 1) * (q - 1)
+    d = arithm.mod_inverse(e, phy_n)
+    return (e, d, n)
+
+def encrypt(m: int, e: int, n: int) -> int:
+    return arithm.modpow(m, e, n)
+
+def decrypt(c: int, d: int, n: int) -> int:
+    return arithm.modpow(c, d, n)
+

main.py

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+import lib.rsa as rsa
+import lib.diffie_hellman as diffie
+from hashlib import sha256
+
+BITS = 32
+ALPH = {'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25, ' ': 26}
+LEN = BITS // 5
+
+def encode(text):
+    sum = 0
+    for i in range(len(text)):
+        sum += ALPH[text[i]] * 27 ** i
+    return sum
+
+def decode(num):
+    text = ""
+    while num > 0:
+        text += list(ALPH.keys())[num % 27]
+        num //= 27
+    return text
+
+def encrypt(text, e, n):
+    crypt = []
+    while len(text) > 0:
+        if len(text) >= LEN:
+            crypt.append(rsa.encrypt(encode(text[:LEN]), e, n))
+            text = text[LEN:]
+        else:
+            crypt.append(rsa.encrypt(encode(text), e, n))
+            text = ""
+    return crypt
+
+def decrypt(crypt, d, n):
+    text = ""
+    for i in range(len(crypt)):
+        text += decode(rsa.decrypt(crypt[i], d, n))
+    return text
+
+if __name__ == "__main__":
+    p, g = diffie.get_p_and_g(BITS)
+
+    a = diffie.get_x(BITS)
+    b = diffie.get_x(BITS)
+
+    A = diffie.get_X(a, p, g)
+    B = diffie.get_X(b, p, g)
+    
+    K_a = diffie.get_K(B, a, p)
+    K_b = diffie.get_K(A, b, p)
+
+    e, d, n = rsa.get_keys(BITS)
+
+    c_d = d ^ K_a
+    h_d = sha256(str(c_d).encode())
+
+    m = "hello world"
+    crypt = encrypt(m, e, n)
+    print(crypt)
+    print(decrypt(crypt, d, n))

requirements.txt

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+

tests.py

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+import lib.rsa as rsa
+import lib.arithmetics as arithm
+import lib.miller_rabin as miller
+
+for i in range(100):
+    for j in range(100):
+        assert arithm.modpow(i, j, 20) == pow(i, j, 20)
+
+for i in range(3, 100):
+    if miller.is_prime(i): print(i)
+
+e, d, n = rsa.get_keys(2048)
+c = rsa.encrypt(22, e, n)
+m = rsa.decrypt(c, d, n)
+print(m)
+