Mod exp

notebooks/Modular_Exponentiation_Problems/modular_exponentiation.py

@@ -0,0 +1,67 @@
+import time 
+def modular_exponentiation(base, exponent, modulus):
+    result = 1
+    base = base % modulus  # Handle base greater than modulus
+
+    while exponent > 0:
+        # If exponent is odd, multiply the current base with result
+        if exponent % 2 == 1:
+            result = (result * base) % modulus
+
+        # Now exponent must be even, square the base and halve the exponent
+        exponent = exponent // 2
+        base = (base * base) % modulus
+
+    return result
+def modular_exponentiation1(base,exponent,modulus):
+    print(f"To calculate the {base}^{exponent} mod {modulus}")
+    starting_time= time.time()
+    Direct_calculation_result = (base ** exponent)%modulus
+    Terminating_time=  time.time()
+    Direct_time_estimate = Terminating_time - starting_time
+    print(f"Time it took for direct calculation:Output={Direct_calculation_result}, Time={Direct_time_estimate:.6f} seconds") 
+    #Modular time calculation when function was used
+    starting_time= time.time()
+    Modular_calculation_result = modular_exponentiation(base,exponent,modulus)
+    Terminating_time=  time.time()
+    Modular_time_estimate = Terminating_time - starting_time
+    print(f"Time it took for Modular exponentiation function calculation:Output ={Modular_calculation_result}, Time={Modular_time_estimate:.6f} seconds")
+    #Using pythons built in %  function
+    starting_time= time.time()
+    Python_calculation_result = pow(base,exponent,modulus)
+    Terminating_time=  time.time()
+    Python_time_estimate = Terminating_time - starting_time
+    print(f"Time it took for Modular exponentiation function calculation:Output ={Python_calculation_result}, Time={Python_time_estimate:.6f} seconds")
+    return Direct_calculation_result,Modular_calculation_result,Python_calculation_result,Direct_time_estimate,Modular_time_estimate,Python_time_estimate
+
+# Test the function for 3^644 mod 645
+base = 3
+exponent = 644
+modulus = 645
+
+result = modular_exponentiation(base, exponent, modulus)
+print(f"3^644 mod 645 = {result}")
+# Example for 7^121 mod 13
+base = 7
+exponent = 121
+modulus =13
+Direct_calculation_result,Modular_calculation_result,Python_calculation_result,Direct_time_estimate,Modular_time_estimate,Python_time_estimate = modular_exponentiation1(base,exponent,modulus)
+# Checking to see if they all return the same answer
+assert Direct_calculation_result == Modular_calculation_result == Python_calculation_result
+
+#Displaying the speed of each of them
+print("Speed:")
+print(f"Direct_calculation:{Direct_time_estimate:6.f} seconds")
+print(f"Modular_calculation:{Modular_time_estimate:6.f} seconds")
+print(f"Python_calculation:{Python_time_estimate:6.f} seconds")
+# Trying to figure out the slowest or greatest speed
+if Direct_time_estimate > Modular_time_estimate and Python_time_estimate < Direct_time_estimate:
+    print("Direct calulation is the slowest")
+elif Modular_time_estimate > Python_time_estimate and Direct_time_estimate<Modular_time_estimate:
+    print("Modular exponentiation formular is the slowest, hence its best to use that")
+elif Python_time_estimate > Direct_time_estimate and Modular_time_estimate:
+    print("Python built in % modular is most efficient since it is the slowest ")
+else:
+    print ("All are efficient, Since the time it takes is the same for all three methods")
+
+