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Hello for my thesis I am making research about SSS computational time.

Based on (K,N) threshold scheme Where K is the minimum number of shares to rebuild the secret and N is the number of shares in which the secret will be divided

Which value affects more the computational time? K or N

I think K is it right?

Hope someone can help me.

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    $\begingroup$ If this is a thesis (that is, you're turning it in as a part of an academic degree), you might want to try doing a bit of research, say, by reading the wikipedia article on SSS, and looking through the equations... $\endgroup$ – poncho Mar 14 '18 at 13:21
  • $\begingroup$ You think it is K. Why do you think that? Can you clearly describe to us why you think that is the answer? $\endgroup$ – mikeazo Mar 14 '18 at 13:24
  • $\begingroup$ You might also want to consider "the computational time of what?". SSS consists of two parts (generating the $N$ shares, and then recombining $K$ of them); which of the two operations are you considering (or is it both)? $\endgroup$ – poncho Mar 14 '18 at 13:30
  • $\begingroup$ Sorry I Didn't explain very well my problem. Let me restart from the beginning.. I am implementing the sss for generate a random number into a p2p network. for computational time I mean the time that each node of the network will spend for generate the secret and for rebuild it. After looking the equation I realize that K is value the most effect the rebuild because with high k I will have a longer polynomial I think now I undestand the situation... $\endgroup$ – emanuele Mar 14 '18 at 13:52
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To find out how the computational time differs between the variables K and N, I suggest you analyze your implementation of the algorithm. Different algorithms can have different computational times for variables.

An easy example is by looking at the computational time for the variable n in sorting algorithms, in which n is the size of the list of numbers you wish to sort (in either ascending or descending order). A multitude of algorithms have been developed to sort a list of n random numbers and the computational time depends on the implementation of the algorithm. Using the BubbleSort algorithm gives a computational time of $O(n^2)$, while the HeapSort algorithm has a computational time of $O(n \times log(n))$.

After implementing the secret sharing scheme, you can analyze how the computational load changes by increasing either K or N and figure out the computational time.

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