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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 them some how(? do not know yet) to create a matrix called R. I need to find a way to be able to reconstruct R with any two of Is. Or I create an intermediate matrix T where I can use T and any of the Is to create R. I am looking for an approach that can be extended to more than 3. I thought of simple weighted addition or multiplication which are easy to crack and I am looking for other ways of doing it.


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This is off topic here (since it's not really a research question in mathematics), but if I understand the question right then "secret sharing" may be what you're looking for. –  Henry Cohn Sep 5 '12 at 19:55
@will: Thanks. I'll try there. @Henry: This one is something similar to the reverse of secret sharing where you want to reach one matrix from 3 not creating 3 matrix forom one. Secret sharing is not an efficient way of doing it specially for large number of elements in a big matrix. I am looking for an efficient algorithms –  Shanti Sep 5 '12 at 20:31
Oops, I misread the problem, sorry. But now it sounds impossible to me: if R can be reconstructed from any two of the I's, no matter what the third one is, then it can't depend on any of them (and must be constant). –  Henry Cohn Sep 6 '12 at 2:12
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