P不等于NP的证明（一种新的对称加密算法，对抗任何线性攻击和差分攻击）
A proof of P != NP (New symmetric encryption algorithm against any linear attacks and differential attacks)
AI总结：
本文提出一种新的对称加密算法，能够在线性时间内完成加密和解密，证明了密钥破解的计算复杂度为指数级，从而证明P≠NP。
摘要：
P vs NP问题是计算复杂性领域中最重要未解决的问题。其影响已渗透到算法设计的所有方面，尤其是在密码学领域。基于短密钥的密码算法安全性的核心在于P是否等于NP。事实上，密码密钥的安全性要求比P≠NP更为严格，密钥的安全性不仅需要足够的计算复杂度来破解，还必须考虑每个密钥位的安全性，并完全避免各种攻击方法的有效性。本文创新性地提出了一种新的编码机制，并开发了一种新的分组对称加密算法，其加密和解密可以在线性时间内完成。对于攻击者而言，在只知道明文-密文对应关系的情况下，破解密钥的问题等同于求解包含至少一个无法消除变量的方程组，且每个变量的可能取值数与密钥长度呈指数关系。为了解这个方程组，必须至少穷举一个变量，从而证明破解密钥的计算复杂度是指数级的。因此，解密是一个单向函数，根据“单向函数的存在意味着P≠NP”，从而解决了P vs NP问题。此外，本文还深入探讨了这种新编码机制的底层数学规律，并开发了二进制的右乘法运算。基于此右乘法运算，我们进一步构建了非线性运算，并设计了另一种对所有形式的线性和差分攻击具有抵抗力的分组对称加密算法。
英文摘要：
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, whose encryption and decryption can be completed in linear time. The key consists of 12 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 12 unknown variables $(w_{1}, w_{2}, ..., w_{11}, w_{12})$ together with some implicit variables which are generated by the encryption process. In this paper, we will prove that there is no universal algorithm without brute-force searching at least one variable during the process of verifying five variables $(w_{1}$, $w_{2}$, $w_{3}$, $w_{4}$, $w_{9})$ whose computational complexity is not greater than solving the 12 variables......
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
