Question

Number Theory (Network Security)

2.5 What is Euler's totient function?

2.8 What is the diffrerence between an index and a discrete logarithm?

Answer 1

2.5 The totient function , also called Euler's totient function ,

This function for an input n counts the number relatively prime to n in {1,2,3,4....,n} ,i.e., the numbers whose GCD (Greatest Common Divisor) with n is 1.

for example,

let consider n = 24,

then numbers from 1 to 24 ,i.e., {1,2,3,....,24} whose gcd with '24' is '1'

those numbers are (1, 5, 7, 11, 13, 17, 19, 23) , then .

because gcd(1, 24) = 1, gcd(5, 24) = 1, gcd(7, 24) = 1, gcd(11, 24) = 1, gcd(13, 24) = 1, gcd(17, 24) = 1, gcd(19, 24) = 1, gcd(23, 24) = 1, hence total 8.