The Diffie-Hellman key exchange
Chooses the secret value:
Computes the public value:
Receives \( B \)
Computes the shared secret key:
Before Alice and Bob can compute the shared secret key they need two parameters: a prime number \( p \) and a generator \( g \) of the group \( \mathbb{Z}_{p}^{*} \), which are public and chosen by a trusted third party:
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Alice and Bob receives the prime number \( p \) and the generator \( g \) of the group \( \mathbb{Z}_{p}^{*} \).
Alice then chooses the secret value \( a \) and Bob chooses the secret value \( b \) which both are integers between \( 1 \) and \( p-1 \).
First Alice computes her public value \( A \) and sends it to Bob.
Then Bob computes his public value \( B \) and sends it to Alice.
With their secret values \( a \) and \( b \) and their received public values \( A \) and \( B \) Alice and Bob computes the shared secret key, which is only known by them.
Receives \( A \)