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P vs NP and its application to zero knowledge proofs

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The P = NP problem asks: “If we can quickly verify a solution to a problem is correct, can we also quickly compute the solution?” Most researchers believe the answer is no, i.e., P ≠ NP. By understanding the P vs NP problem, we can see how Zero Knowledge Proofs (ZKPs) fit into the larger field of computer science and comprehend what ZKPs can and cannot do. It is far easier to “get” Zero Knowledge Proofs by relating them to the P vs NP problem. This tutorial has three parts: P vs NP Expressing problems and solutions as a Boolean formula P vs NP and ZKP We assume the reader is familiar with time complexity and big O notation. We say an algorithm takes polynomial time if it runs in 𝒪(nᶜ) time or better, where n is the size of the input and c is a constant. We may refer to algorithms that run in polynomial time or faster as efficient algorithms because their running time doesn't grow too quickly with the input size. We say an algorithm takes exponential time or is expensive if it runs in

The P = NP problem asks: “If we can quickly verify a solution to a problem is correct, can we also quickly compute the solution?” Most researchers believe the answer is no, i.e., P ≠ NP. By understanding the P vs NP problem, we can see how Zero Knowledge Proofs (ZKPs) fit into the larger field of computer science and comprehend what ZKPs can and cannot do. It is far easier to “get” Zero Knowledge Proofs by relating them to the P vs NP problem. This tutorial has three parts: Explaining the P vs NP problem Expressing problems and solutions as a Boolean formula P vs NP and how they relate to Zero

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