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Here is a question in cryptography which is probably naive, and a reference request.

Suppose I have 3 matrices $I1$, $I2$, and $I3$ (same size) that I want to combine to to create a matrix $R$ (or 3 different matrices $R1$, $R2$, and $R3$) such that it would not be possible to recover any of $I1$, $I2$, and $I3$ from $R$ (or $R1$, $R2$, and $R3$). Also, I would be able to reconstruct $R$ (or $R1$, $R2$, and $R3$) if I am missing one of the $I$s.

Think of it this way. In secret sharing we create different shares from one secret where we can reconstruct the secret with combination of some of the shares whereas here is somehow the reverse of secret sharing. I have 3 secrets and want to find a combination(s) such that with any two of the Is, the combination can be reconstructed.

Thanks.

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    If your $I_1$, $I_2$ and $I_3$ can be arbitary _and_ you want to be able to reconstruct $R$ using only two of them, then the only possibility is to let $R$ be constant, that is, independent of all three inputs. So that probably isn't what you mean -- but it is what you have written. It doesn't seem to have much to do with cryptography either. I would advise you to rewrite your question from scratch, being careful to give all details about what you need to be able to do and what you need to prevent others from doing.2012-09-05
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    I think, now I get it. You want an easily computable function $f:(I_1, I_2, I_3)\mapsto R$ such that inverses of the form $g_1:(R, I_2, I_3)\mapsto I_1$ etc. exist, but $(R,I_1)\mapsto I_2$ should not be feasible. I sthat correct? For, as Henning said, reconstructing $R$ from two shares alone makes no sense: If $R$ can be computed from $I_1, I_2$, then the $R$ belonging to $I_1, I_2, I_3$ must be the same as for $I_1, I_2, 0$ and by symmetry also the same as for $I_1, 0, 0$ and finally $0,0,0$.2012-09-05
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    @HagenV: Thank. I am looking for the function f as you described with the condition that R should not reveal anything about Is and their combinations and G(R,I2,I3)--> T or G(R,I1,I3)--> T or G(R,I1,I2)--> T and T is the parameter that I use in my computation as a key type of thing2012-09-05

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