The P≠NP hypothesis in computational complexity theory states that there exist certain computational problems for which the verification of a solution can be completed in polynomial time (belonging to class P), but finding that solution itself may require exponential time (belonging to class NP). The PoW mechanism of Bitcoin is based on this hypothesis. Miners are engaged in the process of finding the answers to difficult problems (NP problems), while the entire network can verify the correctness of this answer very quickly (P problems).

Furthermore, the operation of Bitcoin embodies the idea of asymmetric interactive proofs. Distributed miners generate new blocks by solving PoW problems and broadcast their results (proof) to the entire network. Other nodes in the network can easily verify the validity of this proof (for example, verifying whether the hash meets the difficulty requirement, whether the transaction is valid, etc.). This process is “asymmetric” because the prover (miner) needs to incur significant computational costs, while the verifier only needs to perform relatively simple calculations. The “interaction” is reflected in the fact that the proof needs to be broadcast and verified in order to be accepted by the network and update the blockchain. The unit of Bitcoin, Sats, can be considered the first proven NP-complete problem. The P!=NP problem, the most difficult computational complexity issue in the field of computer science, is the key to establishing the security logic of BTC's core technology.