If various PKC is shown to be not NP=Hard, what happens to crypto? More importantly, what happens to crypto wallets? If it is shown that P=NP for many currently assumed to be hard problems, but finding the easy solution is itself hard, does the original problem remain NP=Hard?
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If P=NP and the polynomial complexity is not unreachable (a sufficiently high constant can still render polynomial time impractical) then all non-information-theoretically secure cryptography is impossible in principle.
The reason being is that any computationally-bound cryptography can be represented as a circuit. And solved by solving an NP problem such as boolean satisfiability.
LightTunnelEnd
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First of all, $P\neq NP$ has to do with worst-case complexity not average case, so it's really not a good basis for developing cryptosystems in the positive direction. Systems based on problems which are NP-hard were broken. You want your cryptosystem to be hard to break on average.
With regards to your question:
a method of finding factors, or the "secret" number in a mod operation takes only 5-10x the amount of computation as running the original function, would that qualify as answering the problems as being easy?
Even breaking a supposedly one-way function with a polynomial factor of extra complexity would be easy. So if the reverse direction can be computed within $f(n)\times (n)$ where $f(n)$ is a polynomial and $C_f(n)$ is the complexity of the forward computation, this would be enough to be considered a break. We want $f(n)$ to be exponential in $n$ for security.
Your other comments are unclear. What is a "direct method for factoring or DL"?
kodlu
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