updated IS codes

IS/Lab/Lab6/elgamal_schnorr.py

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+import os
+import random
+from typing import Tuple
+
+from Crypto.Hash import SHA256
+from Crypto.Util.number import getPrime
+
+
+def elgamal_keygen(bits: int = 512) -> Tuple[Tuple[int, int, int], int]:
+    p = getPrime(bits)
+    g = random.randrange(2, p - 1)
+    x = random.randrange(1, p - 1)
+    h = pow(g, x, p)
+    return (p, g, h), x
+
+
+def elgamal_encrypt(message: bytes, pub_key: Tuple[int, int, int]) -> Tuple[int, int]:
+    p, g, h = pub_key
+    m = int.from_bytes(message, "big")
+    if m >= p:
+        raise ValueError("Message too large for key size")
+    k = random.randrange(1, p - 1)
+    c1 = pow(g, k, p)
+    s = pow(h, k, p)
+    c2 = (m * s) % p
+    return c1, c2
+
+
+def elgamal_decrypt(ciphertext: Tuple[int, int], priv_key: int, pub_key: Tuple[int, int, int]) -> bytes:
+    c1, c2 = ciphertext
+    p, _, _ = pub_key
+    s = pow(c1, priv_key, p)
+    s_inv = pow(s, p - 2, p)
+    m = (c2 * s_inv) % p
+    if m == 0:
+        return b""
+    m_len = (m.bit_length() + 7) // 8
+    return m.to_bytes(m_len, "big")
+
+
+def schnorr_keygen(bits: int = 512) -> Tuple[Tuple[int, int, int], int]:
+    # Use same style group as ElGamal demo for simplicity
+    p = getPrime(bits)
+    g = random.randrange(2, p - 1)
+    x = random.randrange(1, p - 1)
+    y = pow(g, x, p)
+    return (p, g, y), x
+
+
+def schnorr_sign(message: bytes, priv_key: int, params: Tuple[int, int, int]) -> Tuple[int, int]:
+    p, g, _ = params
+    k = random.randrange(1, p - 1)
+    r = pow(g, k, p)
+    h = SHA256.new()
+    h.update(r.to_bytes((r.bit_length() + 7) // 8 or 1, "big") + message)
+    e = int.from_bytes(h.digest(), "big") % (p - 1)
+    s = (k + e * priv_key) % (p - 1)
+    return e, s
+
+
+def schnorr_verify(message: bytes, signature: Tuple[int, int], params: Tuple[int, int, int]) -> bool:
+    p, g, y = params
+    e, s = signature
+    # Compute r' = g^s * y^{-e} mod p
+    y_inv_e = pow(y, (p - 1 - e) % (p - 1), p)
+    r_prime = (pow(g, s, p) * y_inv_e) % p
+    h = SHA256.new()
+    h.update(r_prime.to_bytes((r_prime.bit_length() + 7) // 8 or 1, "big") + message)
+    e_prime = int.from_bytes(h.digest(), "big") % (p - 1)
+    return e_prime == e
+
+
+def demo() -> None:
+    print("Lab6: ElGamal (encrypt/decrypt) and Schnorr (sign/verify) demo")
+    default_msg = os.environ.get("LAB6_MESSAGE", "Test message for Lab6")
+    try:
+        user_msg = input(f"Enter plaintext [{default_msg}]: ").strip()
+    except EOFError:
+        user_msg = ""
+    message = (user_msg or default_msg).encode()
+
+    # ElGamal
+    pub_e, priv_e = elgamal_keygen(512)
+    c1, c2 = elgamal_encrypt(message, pub_e)
+    recovered = elgamal_decrypt((c1, c2), priv_e, pub_e)
+    print("\nElGamal:")
+    print(f"- Public: p({pub_e[0].bit_length()} bits), g, h")
+    print(f"- Ciphertext c1={hex(c1)[:18]}..., c2={hex(c2)[:18]}...")
+    print(f"- Decrypt OK: {recovered == message}")
+
+    # Schnorr
+    pub_s, priv_s = schnorr_keygen(512)
+    sig = schnorr_sign(message, priv_s, pub_s)
+    ok = schnorr_verify(message, sig, pub_s)
+    print("\nSchnorr:")
+    print(f"- Public: p({pub_s[0].bit_length()} bits), g, y")
+    print(f"- Signature e={sig[0]}, s={sig[1]}")
+    print(f"- Verify OK: {ok}")
+
+
+if __name__ == "__main__":
+    demo()
+
+