In the lecture on Discrete Logarithm $($DL$)$ cryptosystems we saw that

leaking the DL parity through the Legendre symbol can allow construction

efficient splitter for Diffie$-$Hellman triples and consequently solving the DDH problem in Z

$$

p

$.$ Could this particular leak lead to the revelation of the whole thing?

of the discrete logarithm in Z

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p

Justify your answer.