@@ 111,13 111,13 @@ As such, whenever you see a ZK CTF challenge, always look for what is
To quickly touch on some other big ideas on modern ZK schemes, first
consider trying to *compactly* prove that a bunch of things are
-simultaneously zero, i.e. \[\forall i, a_i = 0.\]
+simultaneously zero, i.e. $$\forall i: a_i = 0.$$
A first idea might be to just sum everything together, and that should
still be zero, but of course, that structure is entirely predictable
and far too easy to cheat.
Instead, we'll take a *random linear combination*, where the random
coefficients are obtained as a challenge from the verifier.
-Now we get \[\sum_i c_i \cdot a_i = 0,\] which satisfies both our ask
+Now we get $$\sum_i c_i \cdot a_i = 0,$$ which satisfies both our ask
for compactness and being hard to cheat on.
As long as we still cannot predict the $c_i$, that is.
In a similar fashion, these protocols often squash multiple things