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. For the attacker, in the case where only the plaintext-ciphertext correspondence is known, the problem of cracking the key is equivalent to solving a system of equations which contains at least one variable that cannot be eliminated, and the number of possible values for each 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 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. In addition, this paper delves into the underlying mathematical laws of this new encoding mechanism, and develops a right multiplication operation to binary. Based on this right multiplication operation, we further constructed a nonlinear operation and designed another block symmetric encryption algorithm that is resistant to all forms of linear and differential attacks.

翻译：P vs NP问题是计算复杂性领域尚未解决的最重要问题，其影响已渗透至算法设计的各个层面，尤其在密码学领域。基于短密钥的密码算法安全性取决于P是否等于NP。实际上，密码密钥的安全要求远比P≠NP严格，密钥安全性不仅需要确保破解具有足够高的计算复杂度，还需考虑密钥每个比特的安全性，同时充分规避各类攻击方法的有效性。本文创新性地提出一种新型编码机制，并开发了一种新型分组对称加密算法，其加密与解密可在线性时间内完成。对于攻击者而言，在仅知明文-密文对应关系的情况下，破解密钥问题等价于求解一个至少包含一个不可消去变量的方程组，且每个变量的可能取值数量与密钥长度呈指数关系。求解该方程组需至少对一个变量进行穷举搜索，从而证明破解密钥的计算复杂度为指数级。因此，解密过程是一个单向函数，根据“存在单向函数意味着P≠NP”，进而解决了P vs NP这一未解决问题。此外，本文深入探究了这种新型编码机制的内在数学规律，并建立了二进制的右乘运算。基于该右乘运算，我们进一步构造了非线性运算，并设计了另一个能够抵御所有形式线性攻击与差分攻击的分组对称加密算法。