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Krijn avatar Crypto

Variant of Decisional Diffie Hellman

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Krijn

Given a cryptographic prime $p$ and a generator $g$ of $\mathbb{F}_p$, the Decisional Diffie Hellman problem asks us to distinguish $(g^a, g^b, g^{ab})$ from $(g^a, g^b, g^z)$ for random $a, b, z$. This is an easy problem, because the generator has Legendre symbol -1, which allows us to differentiate between such triples.

But the distribution of the Legendre symbol for $g^{ab}$ and $g^z$ for random $a, b, z$ is already different, and so we don't even need $g^a$ and $g^b$ to differentiate between "real" shared secrets and random values in this Diffie Hellman setup. Is there a name for this variant of DDH?

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