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It doesn't really matter how many values turn out to be exactly x pixels across given the type settings, you still have to do an exhaustive search on different numbers of characters to find them. That problem is simplified by a fixed width font.

In general, though, a proportional face will give a larger number of possible widths, meaning more information to work with (fewer possible strings will map to any particular width).

Additionally, depending on the type of information you are trying to recover, you may already know the number of characters (for example, a US SSN), in which case fixed-width typefaces mean you get no information you didn't already have, whereas a proportional one would at least give you a little bit of info. But on the other hard I would also guess fixed-length strings such as an SSN are more likely to appear in a more "table"-like part of a document than in the middle of a paragraph of text.

I suspect it'd still be a bloody hard analysis either way, but at least according to this back-of-the-envelope theory a proportional typeface should preserve more information.

Oh yeah, in the case where you already know the number of characters, a proportional case font definitely gives you more information. That's a good point. I was thinking more of the general case where any number of characters might be redacted from a document.

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