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elgamal.py

+from typing import Tuple
+from random import randint
+from sys import argv
+from math import sqrt
+
+INPUT_NAME="fichier.txt"
+SIGNATURE_NAME="fichier.signed.txt"
+PUBKEY_FILE="pubkey.txt"
+PRIVKEY_FILE="privkey.txt"
+
+class Pubkey:
+    p: int
+    g: int
+    A: int
+
+    def __init__(self, p: int, g: int, A: int) -> None:
+        self.p = p
+        self.g = g
+        self.A = A
+    
+    def write(self, filename: str) -> None:
+        with open(filename, "w") as f:
+            f.write(f"{self.p} {self.g} {self.A}")
+
+    def read(filename: str) -> "Pubkey":
+        with open(filename, "r") as f:
+            p, g, A = map(int, f.read().split())
+            return Pubkey(p, g, A)
+
+class Privkey:
+    p: int
+    g: int
+    a: int
+
+    def __init__(self, p: int, g: int, a: int) -> None:
+        self.p = p
+        self.g = g
+        self.a = a
+
+    def write(self, filename: str) -> None:
+        with open(filename, "w") as f:
+            f.write(f"{self.p} {self.g} {self.a}")
+
+    def read(filename: str) -> "Privkey":
+        with open(filename, "r") as f:
+            p, g, a = map(int, f.read().split())
+            return Privkey(p, g, a)
+
+class Signature:
+    Y: int
+    S: int
+
+    def __init__(self, Y: int, S: int) -> None:
+        self.Y = Y
+        self.S = S
+    
+    def write(self, filename: str, data: str) -> None:
+        with open(filename, "w") as f:
+            f.write(f"{self.Y} {self.S}\n{data}")
+
+    def read(filename: str) -> Tuple["Signature", str]:
+        with open(filename, "r") as f:
+            Y, S = map(int, f.readline().split())
+            data = f.read()
+            return Signature(Y, S), data
+
+def hash(m: str) -> int:
+    return sum(ord(c) for c in m)
+
+def sign(m: int, k: int, privkey: Privkey) -> Signature:
+    p = privkey.p
+    g = privkey.g
+    a = privkey.a
+
+    Y = pow(g, k, p)
+    S = pow((m - a * Y) * k, -1, p - 1)
+    return Signature(Y, S)
+
+def verify(m: int, sig: Signature, pubkey: Pubkey) -> bool:
+    Y = sig.Y
+    S = sig.S
+
+    p = pubkey.p
+    g = pubkey.g
+    A = pubkey.A
+
+    return (pow(A, Y, p) * pow(Y, S, p)) % p == pow(g, m, p)
+
+def is_prime(n: int) -> bool:
+    if n <= 1:
+        return False
+    
+    for i in range(3, int(sqrt(n)) + 1, 2):
+        if n % i == 0:
+            return False
+
+    return True
+
+def get_random_prime(min: int, max: int) -> int:
+    # trouver un nombre premier aléatoire entre min et max
+    while True:
+        n = randint(min, max)
+        if is_prime(n):
+            print(f"Found prime: {n}")
+            return n
+
+def get_all_generators(p: int) -> int:
+    return [g for g in range(2, p) if all(pow(g, i, p) != 1 for i in range(1, p - 1))]
+
+def get_random_generator(p: int) -> int:
+    generators = get_all_generators(p)
+    rand = randint(0, len(generators) - 1)
+    return generators[1]
+
+def generate_key_pair() -> Tuple[Privkey, Pubkey]:
+    p = get_random_prime(1000, 10_000)
+    g = get_random_generator(p)
+    a = randint(0, p - 1)
+    A = pow(g, a, p)
+    return Privkey(p, g, a), Pubkey(p, g, A)
+
+def main(mode):
+    if mode == 0:
+        # open the fichier.txt file and read its content into a string
+        m = ""
+        with open(INPUT_NAME, "r") as f:
+            m = f.read()
+
+        # algorithm
+        privkey, pubkey = generate_key_pair()
+        signature = sign(hash(m), 5, privkey)
+
+        # write our files
+        pubkey.write(PUBKEY_FILE)
+        privkey.write(PRIVKEY_FILE)
+        signature.write(SIGNATURE_NAME, m)
+    elif mode == 1:
+        signature, m = Signature.read(SIGNATURE_NAME)
+        pubkey = Pubkey.read(PUBKEY_FILE)
+        is_valid = verify(hash(m), signature, pubkey)
+        print("Signature is valid" if is_valid else "Signature is invalid")
+    else:
+        print("Usage: python elgamal.py [mode]")
+        print("mode: 0 for signing, 1 for verifying")
+        exit(1)
+
+main(int(argv[1]) if len(argv) == 2 else -1)
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fichier.signed.txt

+1117 2077
+Il faut pas respirer la compote, ça fait tousser.
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fichier.txt

+Il faut pas respirer la compote, ça fait tousser.
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privkey.txt

+6659 6 337
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pubkey.txt

+6659 6 1575
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