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.