  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, Shannon[1] strictly proved that the one-time-pad system meets
unconditional security, but because the one-time-pad system requires the length
of key to be at least the length of plaintext, how to transfer the key is a
troublesome problem that restricts the use of the one-time-pad system in
practice. Cryptography algorithms used in practice are all based on short key,
and the security of the short key mechanism is ultimately based on "one-way"
assumption, that is, it is assumed that a one-way function exists. In fact, the
existence of one-way function can directly lead to the important conclusion P
!= NP. In this paper, we originally constructed a short-key block cipher
algorithm. The core feature of this algorithm is that for any block, when a
plaintext-ciphertext pair is known, any key in the key space can satisfy the
plaintext-ciphertext pair, that is, for each block, the plaintext-ciphertext
pair and the key are independence, and the independence between blocks is also
easy to construct. This feature is completely different from all existing
short-key cipher algorithms. Based on the above feature, we construct a problem
and theoretically prove that the problem satisfies the properties of one-way
functions, thereby solving the problem of the existence of one-way functions,
that is, directly proving that P != NP.
