elgamal done

Elgamal.py

@@ -0,0 +1,70 @@
+import hashlib
+import random
+def extended_gcd(a, b):
+ if b == 0:
+ return (a, 1, 0)
+ else:
+ d, x, y = extended_gcd(b, a % b)
+ return (d, y, x - (a // b) * y)
+
+def mod_inverse(a, m):
+ d, x, y = extended_gcd(a, m)
+ if d != 1:
+ raise ValueError("Modular inverse does not exist")
+ else:
+ return x % m
+
+def generate_k(q):
+ while True:
+ k = random.randint(1, q-1)
+ if gcd(k, q-1) == 1:
+ return k 
+
+def gcd(a, b):
+ while b != 0:
+ a, b = b, a % b
+ return a
+
+def readFile():
+ with open("publickeys.txt", "r") as file:
+ keys = file.read().split()
+ q = int(keys[0])
+ alpha = int(keys[1])
+ return q,alpha
+
+def generate_private_key(q):
+ Xa = random.randint(1, q-1)
+ return Xa
+
+def generate_public_key(q, alpha):
+ Ya = pow(alpha, Xa,q)
+ return Ya
+
+def hash_message(M):
+ return int(hashlib.sha1(M.encode()).hexdigest(), 16)
+
+def sign(m, q, alpha,Xa):
+ k = generate_k(q)
+ s1 = pow(alpha, k, q)
+ k_inv=mod_inverse(k,q-1);
+ s2 = k_inv * (m-Xa*s1) % (q-1)
+ return (s1, s2)
+
+def verify(alpha,m,q,Ya,s1,s2):
+ v1=pow(alpha,m,q)
+ v2= (pow(Ya,s1)*pow(s1,s2)) %q
+ return v1==v2
+
+
+q,alpha=readFile();
+Xa=generate_private_key(q);
+Ya=generate_public_key(q,alpha);
+M="hello"
+m=hash_message(M)
+m = m % q
+# m=14
+s1,s2=sign(m,q,alpha,Xa)
+result=verify(alpha,m,q,Ya,s1,s2)
+# print(" q ",q," alpha ",alpha," Xa ",Xa," Ya ",Ya," s1 ",s1," s2 ",s2," result ",v1,v2)
+print("result ",result)
+

publickeys.txt

@@ -1 +1 @@
-7 5
+19 10