discrete log query
- Let p be a large prime, and g a generator of Z/pZ.
Let u<p be non-zero modulo small prime q.
From g^u (mod p), is it ever possible to tell anything more about u (mod q)?
Rewording - is the simplest way of finding out any properties of u (mod q) just
to perform a discrete log, and find u itself?
I know that u==0 (mod q) is leaked due to residuacity and reciprocity,
but if I remove that case, then are all other cases indistinguishable?
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