7.4 Security of Diffie-Hellman key exchange
The security of the Diffie-Hellman protocol relies on the following three assumptions:
The discrete logarithm problem is hard in the chosen group š¯”¾
The Diffie-Hellman problem is hard in the chosen group š¯”¾
The public keys of Alice and Bob are authentic
We will discuss each of these assumptions in turn.
7.4.1 Discrete logarithm problem
If Eve is passively eavesdropping on the protocol exchange shown in FigureĀ 7.1, she sees the generator g and the public key values A and B coming from Alice and Bob, respectively. This means if Eve could efficiently solve the discrete logarithm problem in group š¯”¾, she could recover both private keys Ī± and Ī². Armed with this knowledge, she could also compute the shared secret of Alice and Bob.
As discussed previously, we must ensure that the discrete logarithm problem is hard in š¯”¾, so that an attacker cannot derive the private keys or the shared secret. For š¯”½...
