diff --git a/src/ecdsa/numbertheory.py b/src/ecdsa/numbertheory.py
index e5cc888d..7b3ef892 100644
--- a/src/ecdsa/numbertheory.py
+++ b/src/ecdsa/numbertheory.py
@@ -62,8 +62,23 @@ def modular_exp(base, exponent, modulus):  # pragma: no cover
         raise NegativeExponentError(
             "Negative exponents (%d) not allowed" % exponent
         )
-    return pow(base, exponent, modulus)
-
+    if (type(exponent)==int):
+        return fast_modular_exponentiation(base, exponent, modulus)
+    else:
+        return pow(base, exponent, modulus)
+
+def fast_modular_exponentiation(base, exponent, modulas):
+
+    """Log(N) computation required to find the final Exponent"""
+    binary = bin(exponent)[-1:1:-1] 
+    l = {}
+    ans = 1
+    for i in range(len(binary)):
+        l[i] = base
+        base = (base**2)%modulas
+        if binary[i]=='1':
+            ans *= l[i]%modulas
+        return ans%modulas
 
 def polynomial_reduce_mod(poly, polymod, p):
     """Reduce poly by polymod, integer arithmetic modulo p.