feat: add evaluate_polynomial method

pactus/utils/utils.py

@@ -17,3 +17,29 @@ def encode_from_base256_with_type(hrp: str, typ: str, data: bytes) -> str:
     converted = bech32m.convertbits(list(data), 8, 5, pad=True)
     converted = [typ, *converted]
     return bech32m.bech32_encode(hrp, converted, bech32m.Encoding.BECH32M)
+
+
+def evaluate_polynomial(c: list[int], x: int, mod: int) -> int | None:
+    """
+    Evaluate the polynomial f(x) = c[0] + c[1] * x + c[2] * x^2 + ... + c[n-1] * x^(n-1).
+
+    Args:
+        c: List of polynomial coefficients (c[0] is the constant term)
+        x: The value at which to evaluate the polynomial
+        mod: The modulus to use for the evaluation
+
+    Returns:
+        The computed value f(x) if success, None otherwise
+
+    """
+    if not c:
+        return None
+
+    if len(c) == 1:
+        return c[0]
+
+    y = c[-1]
+    for i in range(len(c) - 2, -1, -1):
+        y = (y * x + c[i]) % mod
+
+    return y

tests/test_utils.py

@@ -0,0 +1,63 @@
+import unittest
+from pactus.utils import utils
+
+
+class TestEvaluatePolynomial(unittest.TestCase):
+    def test_empty_coefficients(self):
+        self.assertIsNone(utils.evaluate_polynomial([], 2, 7))
+
+    def test_single_coefficient(self):
+        self.assertEqual(utils.evaluate_polynomial([5], 10, 7), 5)
+
+    def test_x_zero(self):
+        # f(0) = c[0] % mod
+        self.assertEqual(utils.evaluate_polynomial([3, 2, 1], 0, 5), 3 % 5)
+
+    def test_x_one(self):
+        # f(1) = sum(c) % mod
+        self.assertEqual(utils.evaluate_polynomial([1, 2, 3], 1, 7), (1 + 2 + 3) % 7)
+
+    def test_multiple_coefficients(self):
+        # f(2) = 1 + 2*2 + 3*2^2 = 1 + 4 + 12 = 17 % 5 = 2
+        self.assertEqual(utils.evaluate_polynomial([1, 2, 3], 2, 5), 2)
+
+    def test_negative_coefficients(self):
+        # f(2) = -1 + 2*2 + (-3)*2^2 = -1 + 4 - 12 = -9 % 7 = 5
+        self.assertEqual(utils.evaluate_polynomial([-1, 2, -3], 2, 7), 5)
+
+    def test_negative_x(self):
+        # f(-1) = 2 + 3*(-1) + 4*(-1)^2 = 2 - 3 + 4 = 3 % 6 = 3
+        self.assertEqual(utils.evaluate_polynomial([2, 3, 4], -1, 6), 3)
+
+    def test_large_modulus(self):
+        # f(3) = 2 + 4*3 + 5*9 = 2 + 12 + 45 = 59 % 1000 = 59
+        self.assertEqual(utils.evaluate_polynomial([2, 4, 5], 3, 1000), 59)
+
+    def test_modulus_one(self):
+        # Any value mod 1 is 0
+        self.assertEqual(utils.evaluate_polynomial([1, 2, 3], 5, 1), 0)
+
+    def test_wikipedia_example(self):
+        # https://en.wikipedia.org/wiki/Shamir%27s_secret_sharing
+        self.assertEqual(
+            utils.evaluate_polynomial([1234, 166, 94], 1, 2**127 - 1), 1494
+        )
+        self.assertEqual(
+            utils.evaluate_polynomial([1234, 166, 94], 2, 2**127 - 1), 1942
+        )
+        self.assertEqual(
+            utils.evaluate_polynomial([1234, 166, 94], 3, 2**127 - 1), 2578
+        )
+        self.assertEqual(
+            utils.evaluate_polynomial([1234, 166, 94], 4, 2**127 - 1), 3402
+        )
+        self.assertEqual(
+            utils.evaluate_polynomial([1234, 166, 94], 5, 2**127 - 1), 4414
+        )
+        self.assertEqual(
+            utils.evaluate_polynomial([1234, 166, 94], 6, 2**127 - 1), 5614
+        )
+
+
+if __name__ == "__main__":
+    unittest.main()