Eagle encryption algorithm: A new approach to proving P≠NP

[gaoming094]

Firstly, we introduce a common proposition "the existence of one-way functions =>P≠NP", which is considered a fundamental theorem in general cryptography or computational complexity theory. one-way functions have two conditions:

1) calculating f(x) can be completed in polynomial time.
2) Calculating the inverse function f^{-1}(x) cannot be completed in polynomial time. If we find a one-way function, it means that the problem validated in polynomial time cannot be solved in polynomial time, which means P≠NP.

In fact, we have constructed a short key block symmetric encryption algorithm which we called eagle encryption that satisfies the conditions of one-way functions to crack the key given any plaintext-ciphertext pairs:

1. Verifying whether a given key is correct can be done in polynomial time.

2. Given any plaintext-ciphertext pair, the problem of cracking the key is equivalent to solving a system of equations which contains at least one variable that cannot be solved, and the number of possible values for one variable is exponentially to the length of the key. To solve this system of equations, it is necessary to exhaustively search for at least one variable, thus proving that the computational complexity of cracking the key is exponential.

So the decryption can be seen as an one-way function, and according to "the existence of one-way function means P≠NP", thus solving the unsolved problem of P vs NP.

Please refer to the paper: https://eprint.iacr.org/2025/445.pdf

[Ramon cold]

It looks seemingly incorrect, one variable can't be solved just means it have multiple solutions, but not hard to solve.

[klecube]

I appreciate the detailed examination of the Eagle encryption algorithm and its implications on P vs NP. As a software engineer, I've often grappled with these complexities in my projects.

[Robert V]

Wow, is this correct? has it been peer reviewed? P ≠ NP.

[gaoming094]

It looks seemingly incorrect, one variable can't be solved just means it have multiple solutions, but not hard to solve.

I think you have misunderstood the meaning. In fact, when K>6, the system of equations has only one solution. In the paper, the meaning of "at least one unknown number is unsolvable" is that the structure of the equation's constraints leads to the inevitable conclusion that one unknown variable cannot be solved from the equations and can only be obtained through exhaustive enumeration.

[gaoming094]

Wow, is this correct? has it been peer reviewed? P ≠ NP.

This paper has not been rigorous peer reviewed. Several local mathematicians have briefly reviewed it, but none of them found any obvious flaws in the paper. Given the potentially significant impact of the conclusions claimed in the paper, none of them were able to provide any substantial suggestions.

[Ramon cold]

I think you have misunderstood the meaning. In fact, when K>6, the system of equations has only one solution. In the paper, the meaning of "at least one unknown number is unsolvable" is that the structure of the equation's constraints leads to the inevitable conclusion that one unknown variable cannot be solved from the equations and can only be obtained through exhaustive enumeration.

I may still need some time to verify