Cryptography thing 52
6th knowledge: how do we explain the NP problem into a set of propositions can be proved in polynomial.
This is a matter of cryptography sixth chapter 52, we went on to explain complexity theory, this we have another definition of NP problems. (Note: That this section, we have "if the problem is NP" Converting to another set of theorems can be determined in polynomial time).
This question is followed by last week's issue. Last week we answered what is the complexity class NP problem. This week we answer a question related to how the NP --- we interpret as a set of propositions that can be checked in polynomial time.
Now we see on a hunch "of a problem is NP" What does that mean? He is not only an intuitive definition, it is clear explanation why these complex issues so important to cryptography and other problems of the world . Now before we discuss how to use, let's give the definition:
NP is a class of problems can be identified in polynomial time
This in the end do you mean? First, we have an element \ (the X-\) , we want to know if \ (the X-\ in L \) ( \ (L \) is NP language). We have a proven \ (P \) to \ (x \) output a proof \ (w \) , which may need to give a polynomial time in a given \ (x \) to find \ (w \) . Then if we give \ (X \) and \ (W \) to our verifier \ (V \) , \ (V \) can output in polynomial time if the \ (X \ in L \) .
This is not a reference !!! but some explanation, in fact, to my knowledge I do not understand a bit of time in here to see.
Here it is an interactive proof systems, limiting the time complexity of the interaction. Why have to give a V, then gives it a P. This is part of an interactive proof systems defined. In this calculation model (interactive proof system), limit it to calculate time, you can give the definition of NP problems.
I highly recommend reading here under this section's Sipser Introduction to at The Theory of Computation , Section 7.3.
This definition seems to be different and given last week, but in fact they are equivalent. (Sipser book precise definition). Speaking informally, their equivalence is because \ (w \) may be a sequence of decisions made NDT at each branch node, thus determining the non-degradation of the automaton to determine. (Above that section also gives a precise proof),
So why is this issue so useful in cryptography it? Essentially, we have a class that reason, if you do not witness(credentials? Key?) Can be exponential time to check, but if you have this witnessthen you can use polynomial time to complete. This is a lot of cryptographic algorithms feel. (23333). If you do not know the key so it is hard to decrypt the message if you know the key then you will soon be able to decrypt the message.
A warning: While the use of cryptography NP problem seems like a good approach. But it may not be so simple. NP problem because the language is based on the worst time. However cryptography algorithm is based on the average time. For example, we have a NP language, an element needs exponential time to solve other elements very quickly. This is not a good encryption scheme. We hope that all messages are safe. Instead of just one.
Now we know that integer factorization do not know whether NP-complete, do not know whether P class of problems. But it is a case in point. Questions about the careful selection NP instance I wanted to say. In general, a number of factors to find easily. Half divisible by 2. But if we choose a particular we will be hard to break down. Let us focus on ideas in the form \ (N = p * q \ ) to \ (p, q \) primes. Now if these two figures have a very small, so it is easy to break down, and we hope the same as the size of these two numbers. From this we can build this encryption scheme (RSA).