El Camel

elgamal.py

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+import math
+
+
+class Elgamal:
+    def __init__(self, p: int, alpha: int, d: int) -> None:
+        "contract: p is prime, and"
+        if not 0 <= alpha < p or math.gcd(alpha, p) != 1:
+            # set Z*_n is all i [0, n) st gcd(i, n) = 1, if n is prime thats jus the whole thing
+            raise ValueError()
+        if not 2 <= d <= p - 2:
+            raise ValueError()
+        self.p, self.alpha, self.d = p, alpha, d
+        self.beta = pow(alpha, d, p)
+
+    @property
+    def pubkey(self):
+        return (self.p, self.alpha, self.beta)
+
+    @property
+    def privkey(self):
+        return self.d
+
+    def sig_gen(self, x: int, ke: int) -> tuple[int, int]:
+        if not 2 <= ke <= self.p - 2 or math.gcd(ke, self.p - 1) != 1:
+            raise ValueError()
+        r = pow(self.alpha, ke, self.p)
+        kei = pow(ke, -1, self.p - 1) # mod p - 1 
+        s = ((x - self.d * r) * kei) % (self.p - 1)
+        return r, s
+
+    @staticmethod
+    def sig_verify(x: int, rs: tuple[int, int], pab: tuple[int, int, int]) -> bool:
+        r, s = rs
+        p, alpha, beta = pab
+        t = (pow(beta, r, p) * pow(r, s, p)) % p
+        return (t - pow(alpha, x, p)) % p == 0
+
+
+def main():
+    bob = Elgamal(29, 2, 12)
+    assert bob.beta % 29 == 7
+
+    r, s = bob.sig_gen(26, 5)
+    assert r % 29 == 3, f"{r = }"
+    assert s % 28 == 26, f"{s = }"
+    assert Elgamal.sig_verify(26, (r, s), bob.pubkey)
+
+
+if __name__ == "__main__":
+    main()