# Shamir's Secret Sharing Computation time

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.

• 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... – poncho Mar 14 '18 at 13:21
• You think it is K. Why do you think that? Can you clearly describe to us why you think that is the answer? – mikeazo Mar 14 '18 at 13:24
• 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)? – poncho Mar 14 '18 at 13:30
• 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... – emanuele Mar 14 '18 at 13:52

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 $O(n \times log(n))$.