Diffie-Hellman Example

Here is an example of Diffie-Hellman using small numbers.
- The eavesdropper monitors what is sent between the sender and the recipient, but does not alter the contents of their communications.
  
  a = sender's private key a = 3
  
  b = recipient's private key b = 4
  
  g = public base g = 1
  
  p = public (prime) number p = 5
  
  s = shared secret key s = 1

Sender
knows	does not know
p = 5	b = 4
base g = 2
a = 3
2³ mod 5 = 3
2^b mod 5 = 1
1³ mod 5 = 1
3^b mod 5 = 1
1³ mod 5 = 3^b mod 5
s = 1

Recipient
knows	does not know
p = 5	a = 3
base g = 2
b = 4
2⁴ mod 5 = 1
2^a mod 5 = 3
3⁴ mod 5 = 1
1^a mod 5 = 1
3⁴ mod 5 = 1^a mod 5
s = 1

Eavesdropper
knows	does not know
p = 5	a = 3
base g = 2	b = 4
	s = 1
2^a mod 5 = 3
2^b mod 5 = 1
1^a mod 5 = s
3^b mod 5 = s
1^a mod 5 = 3^b mod 5

What is RSA encryption?

© 2006 John Michael Pierobon

Notes