This is a submission for DEV Computer Science Challenge v24.06.12: One Byte Explainer.
Explainer
A fundamental question in computer science asking if every problem whose solution can be quickly verified (NP) can also be quickly solved (P). Solving this would revolutionize fields like cryptography, optimization, and more.
Additional Context
The P vs NP Problem is one of the seven Millennium Prize Problems with a $1 million reward for a correct solution, highlighting its significance in theoretical computer science and practical applications.
Top comments (1)
Here we introduce a completely innovative block cipher algorithm, which we will name Eagle Encryption Algorithm. Through it, we can prove that P≠NP.
For traditional block cipher, for any known plaintext-ciphertext pair, the key is uniquely determined, and the security depends on the computational complexity of cracking the key and the assumption of the existence of a one-way function.
For the Eagle encryption algorithm, the key cannot be uniquely determined for any known plaintext-ciphertext pair, and even all keys in the entire key space can match a given plaintext-ciphertext pair. This may seem contrary to some common sense, but in fact Eagle has achieved it. We will briefly introduce its implementation principle later.
Because the key cannot be determined for each block, traditional attack methods are ineffective such as linear attacks, differential attacks, side channel attacks, etc. Furthermore, because all keys can match a given plaintext-ciphertext pair, any key cracking for a single block or multiple groups is impossible. The only way to attack is through brute force cracking. For short key block encryption algorithms, this satisfies the condition of a one-way function. According to the statement 'the existence of one-way functions=>P ≠ NP', it is equivalent to proving the open problem of P ≠ NP.
Returning to the core feature of the Eagle algorithm, for blocked plaintexts (keys) that meet the length of 2 ^ u, there is a completely independent and randomly generated hidden variable. The other hidden variable generated after completing Eagle encoding is only related to the blocked plaintexts, that is, the hidden variables before encoding and after encoding are independent of each other, have no relationship, and can be randomly generated separately. That is to say, ciphertext is only related to the hidden variables before encoding, while plaintext is only related to the hidden variables after encoding. Only plaintext and ciphertext are retained before and after encoding, and all hidden variables are directly deleted on the encrypted party after encoding is completed. This feature has been rigorously mathematically proven in the paper, and after being tested through programming code, it fully meets the expected results.
Paper：arxiv.org/abs/2203.05022
Open Source：github.com/NP-gaoming/Eagle-Encrypt
Email: 20070602094@alu.cqu.edu.cn
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