Is there a secret sharing scheme where the knowledge of just one share is sufficient to find the secret, in other words a (one-out-of-n) sharing scheme ? Plz I need to know if it is possible to make such operation with secter sharing

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    $\begingroup$ I'm curious, could you give an example of when such a scheme would be of any practical use? $\endgroup$ – mikeazo Nov 1 '11 at 19:08

Just tell the whole secret to each person.

  • $\begingroup$ thank you for the answer, Let me ask the question another way, assume a group of participants (Pi) each one holds a secret Si, suppose that these secrets (Si) are the shares of a given secret "S" where S is not equal to Si and any participant is able to derive the secret S using just its share Si (without combining with secrets of other shares), is there a secret sharing scheme allowing that ? $\endgroup$ – Hamouid Nov 1 '11 at 18:49
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    $\begingroup$ Sure, tell each person the secret minus 1. (Your requirements are trivial to meet, and can be met by almost any algorithm, trivial or complex. Assuming you're not just joking, you must have requirements you're not stating. Rather than us going back and forth where you add requirements just to invalidate my solution, you should try to clearly state your actual requirements. It's not unusual for the hardest part of solving any crypto problem to be figuring out the actual requirements.) $\endgroup$ – David Schwartz Nov 1 '11 at 18:50
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    $\begingroup$ @DavidSchwartz I bet I know what you would say for $0$ out of $n$. $\endgroup$ – PyRulez Feb 13 '16 at 20:31

Assuming each participant $i$ has a key-pair $(x_i,y_i)$ for an asymmetric encryption scheme (with $x_i$ being the private and $y_i$ the public key), you can divide your secret as

$$ S_i := \operatorname{Enc}(y_i, S).$$

Then each participant can retrieve the secret as

$$ S = \operatorname{Dec}(x_i, S_i).$$

Of course, simply giving each participant $S$ fulfills the same purpose.

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    $\begingroup$ this is a Good Idea $\endgroup$ – Hamouid Nov 1 '11 at 19:22

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