Online RSA key generation help


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Euler's phi(n) function The Euler's phi(n) function is used to create the private key.

The Euler's phi(n) function is automatically calculated when both prime numbers p and q are available:

phi(n) = (p - 1) * (q - 1)

p = prime number p
q = prime number q
n = modulus (p * q)

The Euler's phi function is defined as follows:
phi(i) = the number of positive integers less than or equal to i that are coprime to i.

Example 1:
phi(8) = 4

Because 8 is coprime to 1, 3, 5 and 7

Example 2:
phi(15) = 8

Because 15 is coprime to 1, 2, 4, 7, 8, 11, 13 and 14

If p is a prime number, then: phi(p) = (p-1)

Example 3:
phi(7) = 6

Because 7 is coprime to 1, 2, 3, 4, 5 and 6

Example 4:
phi(13) = 12

Because 13 is coprime to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12

If p and q are different prime numbers, then phi(p*q) = (p - 1)*(q - 1)

Example 5:
p=3, q=5
phi(3*5) = (3 - 1)*(5 - 1)
phi(15) = 2*4 = 8

Because 15 is coprime to 1, 2, 4, 7, 8, 11, 13 and 14

Example 6:
p=5, q=7
phi(5*7) = (5 - 1)*(7 - 1)
phi(35) = 4*6 = 24

Because 35 is coprime to 1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 17, 18, 19, 22, 23, 24, 26, 27, 29, 31, 32, 33 and 34