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How to design a secret sharing scheme where when participants are positioned as a matrix, the minimum group people who can reconstruct the secret are the ones that are in same row or in same column?

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    $\begingroup$ Could you please provide some motivation for the question? Currently it looks like an assignment. Please check our FAQ particularly the section tips about writing better questions. $\endgroup$ – Kaveh Nov 6 '12 at 3:34
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For an m x n matrix, you can simply create m+n independent sharings (using any n-out-of-n or m-out-of-m secret sharing scheme, such as the XOR scheme), one for each row and for each column.

Each participant will get tow shares, one for his row and one for his column. His total share size is 2s, where s is the length of the secret. Since you can't get share size less than s, this simple scheme is within a factor of 2 of the optimum.

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