A bijection (or a bijective function) is a function $f$ from a set $X$ to a set $Y$ with the property that, for every $y$ in $Y$, there is exactly one $x$ in $X$ such that $f(x) = y$. It follows from this definition that no unmapped element exists in either $X$ or $Y$.
EDIT: Fixed for clarity of intention I was reading "The FFX Mode of Operation for Format-Preserving Encryption" when I came across Figure 1 (see below). It's obvious why it's reversible (top-down ...
for my hobby tinkering project, I need a mixing function that takes 32-bit input and has 32-bit output (and will, most likely, run in a 32-bit C environment) and the following property (independent of ...
I'm trying to find a bijective function $y=F(x)$ which should be easy to compute in one direction but hard to compute in the other, where the one-way property is not based on a number theoretic ...
How would one go about selecting an appropriate bijective function for introducing permutations into a cipher or hash? For example, $f(x) = x+1 \space mod \space n$ is a bijective function, but isn't ...