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5

In order for Diffie-Hellman to be extra secure we must use a safe prime which is (p – 1) / 2 will also be a prime. We don't have to; there are other options which achieve the same effect. However, it works. so my question is what extra benefit of using such a prime, what's new does it bring to the table. Well, a lot of the security of DH depends on the ...

1

The Decisional Diffie-Hellman assumption, on which the key-exchange would be based on does not hold in $\mathbb{Z}_q^*$. The reason is that the Jacobi symbol "leaks" information about the shared key. Therefore one, instead, works with the subgroup of $\mathbb{Z}_q^*$ of order $p$, which is intuitively obtained by "quotienting out" this ...

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