Implementing-cryptography-using-python

Chapter 4 ■ Cryptographic Math and Frequency Analysis 113
Φ(2) = 1
gcd (1, 2) is 1, but gcd (2, 2) is 2
Φ (3) = 2
gcd (1, 3) is 1 and gcd (2, 3) is 1
Φ (4) = 2
gcd (1, 4) is 1 and gcd (3, 4) is 1
Φ (5) = 4
gcd (1, 5) is 1, gcd (2, 5) is 1,
gcd (3, 5) is 1, and gcd (4, 5) is 1
Φ (6) = 2
gcd (1, 6) is 1 and gcd (5, 6) is 1
Use the following Python to test Euler’s totient function on integers 1 through
20. The output should resemble Figure 4.3.
import math
def phi(n):
amount = 0
for k in range(1, n + 1):
if math.gcd(n, k) == 1:
amount += 1
return amount
for n in range(1,20) :
print("Φ(",n,") = ",phi(n))
To add a little pizzazz to your Python program, you can use the matplotlib
library and create a graph, as shown here:
import math
import numpy as np
from matplotlib import pyplot as plt
def phi(n):
amount = 0
for k in range(1, n + 1):
if math.gcd(n, k) == 1:
amount += 1
return amount