Proof of the Existence of One-Way Functions and a True Random Number Generator (Solution to P versus NP problem)

Here is probably the smartest idea I'll ever have. 

First, take some time to watch this video (skip to the 15:10 mark):

Now look at this graph:

It's an asymmetric oscillation with one hump. If you iterate it, you get random numbers in the range of 100 to 200. It's a true random number generator and thus a one-way function. Furthermore, it describes a family of one-way functions. Any composite of trigonometric, logarithmic, and exponential functions will produce something similar. Of course, the initial value must be in the domain of ln(x) and produce an f(x) > 1. Else, the function approaches zero upon iteration. 

Thus, a general equation for one-way functions and random number generators is:

f(x) = a*(b*sin(c*x) + d*ln(e*x))^f

Where a, b, c, d, e, and f are real numbers. 

Note that when f(x) = r*(1-x) is iterated, chaos occurs when r = 3.759816

https://youtu.be/ovJcsL7vyrk?si=y8JO21psWtpq2TYS&t=312

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In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems.

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The existence of such one-way functions is still an open conjecture. Their existence would prove that the complexity classes P and NP are not equal, thus resolving the foremost unsolved question of theoretical computer science.[1]: ex. 2.2, page 70  The converse is not known to be true, i.e. the existence of a proof that P≠NP would not directly imply the existence of one-way functions.[2]

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Cool. I solved the P = NP problem too. You're terminated, fucker.

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Although the P versus NP problem was formally defined in 1971, there were previous inklings of the problems involved, the difficulty of proof, and the potential consequences. In 1955, mathematician John Nash wrote a letter to the NSA, in which he speculated that cracking a sufficiently complex code would require time exponential in the length of the key.[5] If proved (and Nash was suitably skeptical), this would imply what is now called P ≠ NP, since a proposed key can easily be verified in polynomial time. Another mention of the underlying problem occurred in a 1956 letter written by Kurt Gödel to John von Neumann. Gödel asked whether theorem-proving (now known to be co-NP-complete) could be solved in quadratic or linear time,[6] and pointed out one of the most important consequences—that if so, then the discovery of mathematical proofs could be automated.

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