cipher - The Writing's on the Wall

In the course of your travels, you stumble onto a cryptic message:

You lament that the three bottom lines are badly degraded and nearly unreadable. You're certain that the information they contain is necessary to decode the message.

The smaller squares scattered throughout the message intrigue you. You're positive they're not punctuation. They remind you of something else from your college days.

It also occurs to you that the symbols' square shape is somehow significant.

After contemplating the problem for a while, inspiration strikes and you're able to decode the message into a short phrase. In light of your circumstances, the phrase deeply depresses you. You carry on with your journey anyway, your heart heavy.

What is the decoded message?

Answer

Taking the lines with squares on them, we get this message:

$(K(AK^T)^{-1}+E^TH^T(HKO((AO)^{-1}C^T+O^{-1}K^{-1}L^T)+T^T))^T+S$

Superscript T has a specific meaning: it's the transpose of a matrix. Assuming letters represent matrices, the bottom three lines can be guessed:

• $K$ is [symme]tric



• $H$ an[d] $A$ a[r]e [orthog]onal


• $I$ i[s the] identi[ty]

This means that $K=K^T$, $A^{-1}=A^T$, and $H^{-1}=H^T$. Also, $I$ can be multiplied anywhere without changing the result. Now we can evaluate the expression using matrix mathematics:

$(K(AK^T)^{-1}+E^TH^T(HKO((AO)^{-1}C^T+O^{-1}K^{-1}L^T)+T^T))^T+S\\ =(K(AK)^{-1}+E^TH^T(HKO(O^{-1}A^{-1}C^T+O^{-1}K^{-1}L^T)+T^T))^T+S\\ =(KK^{-1}A^{-1}+E^TH^T(HK(OO^{-1}A^{-1}C^T+OO^{-1}K^{-1}L^T)+T^T))^T+S\\ =(A^{-1}+E^TH^THK(A^{-1}C^T+K^{-1}L^T)+E^TH^TT^T)^T+S\\ =(A^T+E^TKA^{-1}C^T+E^TKK^{-1}L^T+E^TH^TT^T)^T+S\\ =(A^T+E^TK^TA^TC^T+E^TL^T+E^TH^TT^T)^T+S\\ =(A^T)^T+(E^TK^TA^TC^T)^T+(E^TL^T)^T+(E^TH^TT^T)^T+S\\ =A+CAKE+LE+THE+S\\ =THE+CAKE+IS+A+LIE$

So the message is "The cake is a lie."