[2203.05022] A proof of P != NP (New symmetric encryption algorithm against any linear attacks and differential attacks) Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Computational Complexity arXiv:2203.05022 (cs) [Submitted on 5 Feb 2022 ( v1 ), last revised 5 Aug 2026 (this version, v12)] Title: A proof of P != NP (New symmetric encryption algorithm against any linear attacks and differential attacks) Authors: Gao Ming View a PDF of the paper titled A proof of P != NP (New symmetric encryption algorithm against any linear attacks and differential attacks), by Gao Ming View PDF HTML (experimental) Abstract: P vs NP problem is the most important unresolved problem in the field of computational complexity. Its impact has penetrated into all aspects of algorithm design, especially in the field of cryptography. The security of cryptographic algorithms based on short keys depends on whether P is equal to NP. In fact, the security requirements for cryptographic keys are much stricter than those for P $\neq$ NP, the security of the key must ensure not only a sufficiently high computational complexity to crack it, but also consider the security of each bit of the key, while fully avoiding the effectiveness of various attack methods. In this paper, we innovatively propose a new encoding mechanism and develop a novel block symmetric encryption algorithm, which be named Eagle, whose encryption and decryption can be completed in linear time. The key consists of 6 variables, for the attacker, in the case when only the plaintext-ciphertext correspondence is known, the problem of cracking the key is equivalent to solving a system of equations about six unknown variables. We prove that the computational complexity of verifying two variables should not be lower than the computational complexity of enumerating any intermediate unknown variable whose number of possible values is exponentially to the length of the key, thus proving that the computational complexity of verifying two variables can't be polynomial. Due to the computational complexity satisfying the condition of ``complexity of cracking the key = complexity of solving six variables $\geq$ complexity of solving two variables $\geq$ complexity of verifying two variables", thus the computational complexity of cracking the key can't be polynomial, So the decryption is a one-way function, and according to ``the existence of one-way function means P $\neq$ NP", thus solving the unsolved problem of P vs NP. Subjects: Computational Complexity (cs.CC) ; Information Theory (cs.IT) Cite as: arXiv:2203.05022 [cs.CC] (or arXiv:2203.05022v12 [cs.CC] for this version) https://doi.org/10.48550/arXiv.2203.05022 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Gao Ming [ view email ] [v1] Sat, 5 Feb 2022 13:11:27 UTC (303 KB) [v2] Sun, 2 Feb 2025 14:12:18 UTC (272 KB) [v3] Sun, 9 Mar 2025 02:55:33 UTC (272 KB) [v4] Sat, 10 May 2025 13:48:30 UTC (299 KB) [v5] Sat, 5 Jul 2025 02:23:33 UTC (18 KB) [v6] Mon, 2 Mar 2026 13:13:11 UTC (20 KB) [v7] Sat, 14 Mar 2026 14:48:16 UTC (22 KB) [v8] Mon, 6 Apr 2026 14:06:35 UTC (24 KB) [v9] Tue, 21 Apr 2026 03:09:07 UTC (26 KB) [v10] Thu, 30 Apr 2026 09:34:21 UTC (26 KB) [v11] Wed, 29 Jul 2026 09:48:37 UTC (30 KB) [v12] Wed, 5 Aug 2026 02:56:20 UTC (30 KB) Full-text links: Access Paper: View a PDF of the paper titled A proof of P != NP (New symmetric encryption algorithm against any linear attacks and differential attacks), by Gao Ming View PDF HTML (experimental) TeX Source view license Current browse context: cs.CC < prev | next > new | recent | 2022-03 Change to browse by: cs cs.IT math math.IT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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