inverse de k

elgamal.py

@@ -3,10 +3,11 @@ from random import randint
 from sys import argv
 from math import sqrt, gcd
 
-INPUT_NAME="fichier.txt"
-SIGNATURE_NAME="fichier.signed.txt"
-PUBKEY_FILE="pubkey.txt"
-PRIVKEY_FILE="privkey.txt"
+INPUT_NAME = "fichier.txt"
+SIGNATURE_NAME = "fichier.signed.txt"
+PUBKEY_FILE = "pubkey.txt"
+PRIVKEY_FILE = "privkey.txt"
+
 
 class Pubkey:
     p: int
@@ -17,7 +18,7 @@ class Pubkey:
         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}")
@@ -27,6 +28,7 @@ class Pubkey:
             p, g, A = map(int, f.read().split())
             return Pubkey(p, g, A)
 
+
 class Privkey:
     p: int
     g: int
@@ -46,6 +48,7 @@ class Privkey:
             p, g, a = map(int, f.read().split())
             return Privkey(p, g, a)
 
+
 class Signature:
     Y: int
     S: int
@@ -53,7 +56,7 @@ class Signature:
     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}")
@@ -64,18 +67,25 @@ class Signature:
             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)
+    inverse = xgcd(k, p)[1] % (p - 1)
+    S = ((m - a * Y) * inverse) % (p - 1)
+    print(
+        f"Y  = {Y}, S = {S}, p = {p}, g = {g} a = {a}, k = {k}, m = {m}, A = {pow(g,a,p)}"
+    )
     return Signature(Y, S)
 
+
 def verify(m: int, sig: Signature, pubkey: Pubkey) -> bool:
     Y = sig.Y
     S = sig.S
@@ -86,16 +96,18 @@ def verify(m: int, sig: Signature, pubkey: Pubkey) -> bool:
 
     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:
@@ -104,40 +116,47 @@ def get_random_prime(min: int, max: int) -> int:
             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]
+    return generators[rand]
+
 
 def generate_key_pair() -> Tuple[Privkey, Pubkey]:
-    # p = get_random_prime(1000, 10_000)
-    # g = get_random_generator(p)
-    # a = randint(0, p - 1)
-    p = 7297
-    g = 14
-    a = 7057
+    p = get_random_prime(1000, 10_000)
+    g = get_random_generator(p)
+    a = randint(0, p - 1)
+    # p = 7297
+    # g = 852
+    # a = 12
     A = pow(g, a, p)
+    print(f"Found generator : {g}")
     return Privkey(p, g, a), Pubkey(p, g, A)
 
-def xgcd(a,b):
-    prevx , x = 1 , 0 
-    prevy , y = 0 , 1 
+
+def xgcd(a, b):
+    prevx, x = 1, 0
+    prevy, y = 0, 1
     while b:
-        q = a//b
-        x, prevx = prevx - q*x, x 
-        y, prevy = prevy - q*y, y
-        a, b = b, a % b
+        q = a // b
+        x, prevx = prevx - q * x, x
+        y, prevy = prevy - q * y, y
+        a, b = b, a - q * b
     return a, prevx, prevy
 
+
 def generate_k(p: int) -> int:
     k = randint(1, p - 2)
     while gcd(k, p - 1) != 1:
         k = randint(1, p - 2)
     return k
 
+
 def main(mode):
     if mode == 0:
         # open the fichier.txt file and read its content into a string
@@ -164,4 +183,5 @@ def main(mode):
         print("mode: 0 for signing, 1 for verifying")
         exit(1)
 
-main(int(argv[1]) if len(argv) == 2 else -1)
\ No newline at end of file
+
+main(int(argv[1]) if len(argv) == 2 else -1)