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**2023/937**

**Title:**

WESP: An encryption method that is proven to require an exponentially growing time to break it

**Authors:**
Sam Widlund

**Abstract:**

First, the WESP encryption algorithm is defined. Encryptions are created by a system of equations in which the equations are generated using the values of tables that act as the encryption key. Next, it is shown that if the encryption tables are not known, the equations in the system of equations cannot be known, and it is demonstrated that the system of equations cannot be solved if the equations are not known, and thus the encryption cannot be broken in a closed form.

Then, we calculate for all symbols used in the algorithm, the minimum amount of trials needed, in order to be able to verity the trials. Since the algorithm is constantly updating key values the verifying becomes impossible if equations are not evaluated in order. The calculation shows that the minimum number of trials required is such that the number of trials, i.e., the time required to break the encryption, increases exponentially as the key size grows. Since there is no upper limit on the key size there is neither any upper limit on the time it requires to break the encryption.

It is also shown that the well-known mathematical “P vs NP” problem is solved by the presented proof. Since there is at least one algorithm (WESP) that is NP (verifiable in polynomial time) but not P (solvable in polynomial time), P cannot be the same set as NP.

**ePrint:**
https://eprint.iacr.org/2023/937

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