Firstly, we introduce a common proposition "the existence of one-way functions =>P≠NP", which is considered a fundamental theorem in general cryptography or computational complexity theory. one-way functions have two conditions:
1) calculating f(x) can be completed in polynomial time.
2) Calculating the inverse function f^{-1}(x) cannot be completed in polynomial time.
If we find a one-way function, it means that the problem validated in polynomial time cannot be solved in polynomial time, which means P≠NP.
Of course, P≠NP does not infer the existence of one-way functions (the existence of one-way functions is currently an open problem). We won't discuss this further.
In fact, we have constructed a short key block symmetric cipher algorithm that satisfies the conditions of one-way functions to crack the key given any plaintext-ciphertext pairs:
1. Verifying whether a given key is correct can be done in polynomial time (by comparing the plaintext decypted by the given key).
2. Given any plaintext-ciphertext pair, there is no effective cracking method except for exhaustive search (the key space is exponential and cannot be exhaustively searched in polynomial time). This can be discussed in two situations:
I) Given the plaintext-ciphertext pair of a single block, any key is equally probabilistic unknowable (this is different from all current encryption mechanisms, where existing encryption mechanisms theoretically have a uniquely determined key given the plaintext-ciphertext pairs of each block). In our encryption algorithm, given the plaintext-ciphertext pair of a single block, keys are indistinguishab le in combinatorial mathematical logic, so theoretically, knowing the plaintext-ciphertext pair of a single block, exhaustive search is ineffective for cracking the key.
II) When knowing the plaintext-ciphertext pairs between any two or more blocks, the random parameters that any two blocks depend on are completely independently generated and the encryption process is also independent of each other. This theoretically proves that there is no other effective method to crack keys besides exhaustive search.
In fact, throughout the entire construction process, the core is to demonstrate that for any given number of plaintext ciphertext pairs, there is no other method to crack the key except exhaustive search. As long as this characteristic is satisfied, the one-way function conditions hold, and thus P≠NP is a direct inference.
Please refer to the paper: https://arxiv.org/pdf/2203.05022
1) calculating f(x) can be completed in polynomial time.
2) Calculating the inverse function f^{-1}(x) cannot be completed in polynomial time.
If we find a one-way function, it means that the problem validated in polynomial time cannot be solved in polynomial time, which means P≠NP.
Of course, P≠NP does not infer the existence of one-way functions (the existence of one-way functions is currently an open problem). We won't discuss this further.
In fact, we have constructed a short key block symmetric cipher algorithm that satisfies the conditions of one-way functions to crack the key given any plaintext-ciphertext pairs:
1. Verifying whether a given key is correct can be done in polynomial time (by comparing the plaintext decypted by the given key).
2. Given any plaintext-ciphertext pair, there is no effective cracking method except for exhaustive search (the key space is exponential and cannot be exhaustively searched in polynomial time). This can be discussed in two situations:
I) Given the plaintext-ciphertext pair of a single block, any key is equally probabilistic unknowable (this is different from all current encryption mechanisms, where existing encryption mechanisms theoretically have a uniquely determined key given the plaintext-ciphertext pairs of each block). In our encryption algorithm, given the plaintext-ciphertext pair of a single block, keys are indistinguishab le in combinatorial mathematical logic, so theoretically, knowing the plaintext-ciphertext pair of a single block, exhaustive search is ineffective for cracking the key.
II) When knowing the plaintext-ciphertext pairs between any two or more blocks, the random parameters that any two blocks depend on are completely independently generated and the encryption process is also independent of each other. This theoretically proves that there is no other effective method to crack keys besides exhaustive search.
In fact, throughout the entire construction process, the core is to demonstrate that for any given number of plaintext ciphertext pairs, there is no other method to crack the key except exhaustive search. As long as this characteristic is satisfied, the one-way function conditions hold, and thus P≠NP is a direct inference.
Please refer to the paper: https://arxiv.org/pdf/2203.05022
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