# Problem with Fiat-shamir on poly-round interactive protocol?

I have read in many places that Fiat Shamir technique is used to convert constant round interactive protocols to non-interactive arguments. What would be the problem in applying Fiat Shamir to poly-round protocols?

One simple counter-example is to consider the sequential composition, say $$n$$ times, of a constant-round protocol that has constant soundness error. By amplification theorem, the resultant protocol has negligible soundness error --- inverse-exponential in $$n$$ to be precise --- but the Fiat-Shamir transformed protocol is totally insecure as argued next. Since the soundness error is constant a malicious prover can basically sample (in constant-many attempts in expectation) "favourable" messages for each round and with high probability come up with a cheating proof: see this lecture (around 11 minutes) by Ron Rothblum for more details.