Revisiting A Strategy For Differential Analysis

In an entry to one of my 65535sec student research blogs, I observed that one strategy for analysis is to represent the cryptogram as a matrix A. The perform a differential analysis on A x A^T and the differing A^T x A.

By mentally imagining using such a procedure against Vigenere, I infer a question. The key material of Vigenere has a periodicity. I can suppose the A x A^T vs A^T x A would also exhibit a period, but I would be surprised if it reduced to a one to one simple substitution.

As such, I suppose it would be worth asking what can usefully be said about the data for differential analysis?

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