A java program that demonstrates this key exchange protocol. Diffie–Hellman key exchange establishes a shared secret between two parties that can be used for secret communication for exchanging data over a public network. The following is the simplest implementation of the protocol.
Alice and Bob wish to communicate secretly over a public network. The following is how they do it.
- They publicly agree to use a modulus
p = 23(a prime number) and a baseg = 5(which is a primitive root modulo 23). - Alice chooses a secret integer
a = 4, then sends Bobgᵃ mod p.A = 5⁴ mod 23 = 4
- Bob chooses a secret integer
b = 3, then sends Alicegᵇ mod p.B = 5³ mod 23 = 10
- Alice computes
s = Bᵃ mod p.s = 10⁴ mod 23 = 18
- Bob computes
s = Aᵇ mod p.s = 4³ mod 23 = 18
- Alice and Bob now share a secret key (18).
Alice computed (gᵃ mod p)ᵇ mod p and Bob computed (gᵇ mod p)ᵃ mod p which are equivalent.
The encryption relies on the fact that the private numbers (a or b) can not be computed quickly, given only g and p, even by the fastest modern computers. Such a problem is called the discrete logarithm problem.
To make the given example more secure, larger values (600+ digits) of a, b, and p need to be chosen.
Here is a list of prime numbers up to 1000 billion. for you to try.