# Z superscript confusion

I was practicing some questions on cryptography (newbie) and came across this question:

I know that Z26 means modulo-n arithmetic is used, but what does the superscript (3) denote? My guess is that the superscript represents the dimension of the square, key matrix. But, I would like it if someone confirms it for me or corrects my understanding.

Usually $$\mathbb{Z}^3$$ denotes the triple cartesian product (triplets) of the set of integers, so it is a set consisting of all triplets $$(a,b,c)$$ where $$a,b,c \in \mathbb{Z}$$
• Yes. My reading is that the authors write $Z_{26}$ for $\mathbb Z/26\mathbb Z$ (also noted $\mathbb Z_{26}$ in some circles), and $Z_{26}^3$ when they could have written ${Z_{26}}^3$ or $Z_{26}\times Z_{26}\times Z_{26}$, meaning the set of triplets of elements of $Z_{26}$.