I'll try to answer what I believe to be what you are asking, namely:
If $P = NP$, can one "fix" cryptography by replacing constructions with interactive protocols?
This is a natural enough question, but has a well-known (negative) answer.
Specifically, any interactive protocol that requires a fixed (finite) number of rounds of interaction is said to live in a complexity class called the polynomial hierarchy $PH$. It is a priori possible that $P = NP$, but $P \subsetneq PH$.
In this setting the answer to the above question is "yes, in principle" (although I know of no constructions).
Unfortunately, one of the basic results about $PH$ is that this is false, meaning $P = NP\implies P= PH$, so basing cryptography (in a world where $P = NP$) on solely a finite number of rounds of interactivity is not possible.
There are some caveats here with protocols that have $\omega(1)$ rounds (these are in a complexity class called IP), but those would be so unbelievably slow (due to each round incurring an unavoidable latency from the speed of light) that they are not particularly interesting.
There are a few other potential ways to get (something like) cryptography in a world where $P = NP$ though, namely:
- Using "noisy channel" assumptions, for example the wiretap channel, and
- Using quantum channels
Both have significant downsides compared to complexity-theoretic cryptography (which I will not attempt to summarize here), but their validity is not threatened by $P = NP$, and are probably good things to look up if you are interested in the possibility of secure communication in a world where $P = NP$.
That all being said, authenticating yourself to computers would be much more difficult overall.
Another "solution" would be to rely on in-person authentication.
Of course, one can behave fraudulently here, but it is somewhat more difficult to do at scale.
