What is the best method to compose a set of matrices into one and then unambiguously decrypt it?

I am presented with the following problem:

Given a set of matrices $M = \{A^i_{m,n} : 0 < i < 101 \}$ design a procedure to compose all of them into one encrypted matrix $E_{m,n}$ and later decompose (decrypt) it into the initial set. The procedure should be as difficult to break as possible (quantum-resistant preferably). It does not need to be fast, as the message will be sent only once (meaning the encryption process might take hours or days with the current technology). Presumably, there will exist an encryption key $k$, which should be smaller in size than the set of matrices (as small as possible, preferably). No need for dual-key systems, one is enough for this specific problem I have in mind.

One important note: all of the elements in all of the original matrices come from $Z/nZ$ with some given $n$ (therefore they are integers: $x : 0 \leq x < n$), although this fact does not need to be used in the procedure.

Bonus points if the procedure preserves ordering of the matrices (i.e. we have a sequence $S$ instead of a set $M$). Would that be even possible?

Given a set of matrices $M = \{A^i_{m,n} : 0 < i < 101 \}$ design a procedure to compose all of them into one encrypted matrix $E_{m,n}$ and later decompose (decrypt) it into the initial set.

The standard way to address this would be to divide this up into a three step process:

• Convert the sequence of matrices $M$ into a bit string $P$ (in an invertible way)

• Hand the bit string $P$ to a standard symmetric encryption process (e.g. AES-SIV), keyed by your secret $k$, resulting in a slightly longer bit string $C$

• Convert the bit string $C$ into the matrix $E_{m,n}$ (in an invertible way)

The decryption method should be obvious.

Yes, $E_{m,n}$ will take up as much space as all the matrices in $M$ (and actually slightly more; standard encryption methods do increase the length by a fixed amount); however any value-preserving method will has that property, so that's not that big of a deal. You might end up making the elements within $E_{m,n}$ elements of $\mathbb{Z}/n^{101}$ (101 rather than 100 to account for the expansion in step 2) - since we're using the elements within $M$ only as transport, that shouldn't be that big of a deal.

And, assuming your encoding method in step 1 preserves the matrix ordering, I get the bonus points as well - I wonder what I can spend them on :-)