feat: split secret for BLS

README.md

@@ -30,7 +30,7 @@ Explore the `examples` folder for more detailed usage scenarios.
 For local development, you can install the package in editable mode, which allows you to make changes and test them immediately:
 
 ```bash
-python3 -m pip install .
+python3 -m pip install -e .
 ```
 
 After making changes, it's important to ensure all tests pass by running:

examples/example_bls_threshold.py

@@ -0,0 +1,27 @@
+from pactus.crypto.bls.private_key import PrivateKey
+
+
+# Example of BLS threshold signature aggregation using Shamir's Secret Sharing
+# This example demonstrates how to create a threshold signature scheme
+# where a subset of signers can create a valid signature.
+
+
+def main() -> None:
+    # msg = "some message".encode()
+    N = 3  # Number of signers
+    T = 2  # Threshold for aggregation
+
+    msk = PrivateKey.random()  # Master Secret Key
+    mpk = msk.public_key()
+
+    print(f"Master Secret Key: {msk.raw_bytes().hex()}")
+    print(f"Master Public Key: {mpk.string()}")
+
+    shares = msk.split(N, T)
+
+    for i, sk in enumerate(shares):
+        print(f"Private Key Share {i + 1}: {sk.raw_bytes().hex()}")
+
+
+if __name__ == "__main__":
+    main()

pactus/crypto/bls/private_key.py

@@ -79,3 +79,30 @@ def public_key(self) -> PublicKey:
     def sign(self, msg: bytes) -> Signature:
         point_g1 = sign(self.scalar, msg, ciphersuite=DST)
         return Signature(point_g1)
+
+    def split(self, n: int, t: int) -> list[PrivateKey]:
+        if n < t:
+            msg = f"n must be greater than t: n={n}, t={t}"
+            raise ValueError(msg)
+
+        if n < 1:
+            msg = f"n must be greater than 1: n={n}"
+            raise ValueError(msg)
+
+        # Create the coefficients for the polynomial: c[0] = secret, c[1..t-1] = random private keys
+        coeffs = [self.scalar]
+        for _ in range(1, t):
+            rand_priv = PrivateKey.random()
+            coeffs.append(rand_priv.scalar)
+
+        # Generate n shares by evaluating the polynomial at x = 1..n
+        shares = []
+        for i in range(1, n + 1):
+            share_scalar = utils.evaluate_polynomial(coeffs, i, curve_order)
+            if share_scalar is None:
+                msg = f"Failed to evaluate polynomial at x={i}"
+                raise ValueError(msg)
+
+            shares.append(PrivateKey(share_scalar))
+
+        return shares