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Questions tagged [np]

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2 votes
1 answer
157 views

probabilistic polynomial-time Turing machine with one-way function

Suppose that there exists a function $𝑓:\{0,1\}^𝑛 β†’ \{0,1\}^𝑛$ such that, 𝑓 is computable in polynomial time; and the following task cannot be computed in polynomial time (that is, there are $π‘₯ ∈ ...
Xoxoxo's user avatar
  • 45
2 votes
2 answers
190 views

How to prove that $𝐿$ is in $\mathsf{NP} \setminus \mathsf{P}?$

Suppose that there exists a function $𝑓:\{0,1\}^𝑛 β†’ \{0,1\}^𝑛$ such that, 𝑓 is computable in polynomial time; and the following task cannot be computed in polynomial time (that is, there are $π‘₯ ∈ ...
Xoxoxo's user avatar
  • 45
1 vote
3 answers
494 views

P versus semi-NP?

I am not sure to fully understand the interest of the P versus NP problem for cryptography. I get that it is important to have a problem which is hard to solve but easy to check. But it seems to me ...
Marc Dinh's user avatar
  • 113
2 votes
1 answer
77 views

3-Coloring Zero-Knowledge Proof: rational verifier?

I'm studying the application of Zero-Knowledge Proofs (ZKP) to graph 3-colorability. I haven't fully understood the need for randomness in the verifier's choice of the edge to challenge the prover ...
Tom_tomato's user avatar
0 votes
0 answers
49 views

One-way function constructed by multivariable polynomials

Although the conjecture regarding the existence of one-way functions remained open, there are numerous NP-based methods for constructing diverse one-way functions, including DL, lattice, and subset ...
X.H. Yue's user avatar
  • 456