test: remove modinv python util helper function

test/functional/test_framework/key.py

@@ -13,8 +13,6 @@ import os
 import random
 import unittest
 
-from .util import modinv
-
 # Point with no known discrete log.
 H_POINT = "50929b74c1a04954b78b4b6035e97a5e078a5a0f28ec96d547bfee9ace803ac0"
 
@@ -78,7 +76,7 @@ class EllipticCurve:
         x1, y1, z1 = p1
         if z1 == 0:
             return None
-        inv = modinv(z1, self.p)
+        inv = pow(z1, -1, self.p)
         inv_2 = (inv**2) % self.p
         inv_3 = (inv_2 * inv) % self.p
         return ((inv_2 * x1) % self.p, (inv_3 * y1) % self.p, 1)
@@ -319,7 +317,7 @@ class ECPubKey():
         z = int.from_bytes(msg, 'big')
 
         # Run verifier algorithm on r, s
-        w = modinv(s, SECP256K1_ORDER)
+        w = pow(s, -1, SECP256K1_ORDER)
         u1 = z*w % SECP256K1_ORDER
         u2 = r*w % SECP256K1_ORDER
         R = SECP256K1.affine(SECP256K1.mul([(SECP256K1_G, u1), (self.p, u2)]))
@@ -397,7 +395,7 @@ class ECKey():
             k = random.randrange(1, SECP256K1_ORDER)
         R = SECP256K1.affine(SECP256K1.mul([(SECP256K1_G, k)]))
         r = R[0] % SECP256K1_ORDER
-        s = (modinv(k, SECP256K1_ORDER) * (z + self.secret * r)) % SECP256K1_ORDER
+        s = (pow(k, -1, SECP256K1_ORDER) * (z + self.secret * r)) % SECP256K1_ORDER
         if low_s and s > SECP256K1_ORDER_HALF:
             s = SECP256K1_ORDER - s
         # Represent in DER format. The byte representations of r and s have

test/functional/test_framework/muhash.py

@@ -6,8 +6,6 @@
 import hashlib
 import unittest
 
-from .util import modinv
-
 def rot32(v, bits):
     """Rotate the 32-bit value v left by bits bits."""
     bits %= 32  # Make sure the term below does not throw an exception
@@ -88,7 +86,7 @@ class MuHash3072:
 
     def digest(self):
         """Extract the final hash. Does not modify this object."""
-        val = (self.numerator * modinv(self.denominator, self.MODULUS)) % self.MODULUS
+        val = (self.numerator * pow(self.denominator, -1, self.MODULUS)) % self.MODULUS
         bytes384 = val.to_bytes(384, 'little')
         return hashlib.sha256(bytes384).digest()
 

test/functional/test_framework/util.py

@@ -15,7 +15,6 @@ import os
 import random
 import re
 import time
-import unittest
 
 from . import coverage
 from .authproxy import AuthServiceProxy, JSONRPCException
@@ -537,22 +536,3 @@ def find_vout_for_address(node, txid, addr):
         if addr == tx["vout"][i]["scriptPubKey"]["address"]:
             return i
     raise RuntimeError("Vout not found for address: txid=%s, addr=%s" % (txid, addr))
-
-def modinv(a, n):
-    """Compute the modular inverse of a modulo n using the extended Euclidean
-    Algorithm. See https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Modular_integers.
-    """
-    return pow(a, -1, n)
-
-class TestFrameworkUtil(unittest.TestCase):
-    def test_modinv(self):
-        test_vectors = [
-            [7, 11],
-            [11, 29],
-            [90, 13],
-            [1891, 3797],
-            [6003722857, 77695236973],
-        ]
-
-        for a, n in test_vectors:
-            self.assertEqual(modinv(a, n), pow(a, n-2, n))