Decisional Diffie-Hellman: compute Legendre symbol of $g^{ab}$ from $g^a$ and $g^b$?
Because (I assume) $g$ is a generator, it is not a square (prove this), so its Legendre symbol is $-1$. And hence, the Legendre symbols of $g^a$ and $g^b$ leak the parities or $a$ and $b$. Hence they leak the parity of $ab$, which leaks the Legendre symbol of $g^{ab}$.