So I am a computer science student and have some problems reading cryptographic mathematics notations, so I need help from mathematicians. I was reading a 2018 IEEE journal about identity-based data integrity checking, and was met with this:
...Assume the user's identity is l-bit, which is described as
$ID = (ID_1, ID_2, ID_3, ..., ID_l) \in \{0,1\}^l$
...
I searched about sets with powers, sets of elements with powers, but garnered no useful results. I remembered about this in automata course, which more or less translates that to this:
On a set of l amount of ID, each ID is constructed with l digits of 0s and 1s.
But I'm still skeptical about that, am I wrong?
Thank you!
It is the number of copies of the set. For example, $$ A^3= A \times A \times A= \{(a_1,a_2,a_3) \colon a_1,a_2,a_3 \in A\} $$ The notation was chosen to resemble ordinary powers: $x \cdot x \cdot x= x^3$. As another example, $$ \{0,1\}^3= \{(0,0,0),(0,0,1),(0,1,0),(0,1,1),(1,0,0),(1,0,1),(1,1,0),(1,1,1)\} $$ The 'exponent' is the number of copies of the set that you have. You can even used cardinal powers for infinite (or 'more than infinite') copies.