Key Mathematical Notation Explained

• $\mathbb{Z}$: The set of all in­te­gers. Pro­nounced "zee" or "zed".
• $\mathbb{Z}_n$: The set of in­te­gers modulo $n$, with el­e­ments $\{0, 1, \ldots, n-1\}$.
• $\gcd(a, b)$: Great­est common di­vi­sor of $a$ and $b$. Pro­nounced "gee-cee-dee".
• $k$: An in­te­ger, often used as a can­di­date for a gen­er­a­tor.
• $p$: A prime number.
• $\phi(n)$: Euler's to­tient func­tion (pro­nounced "fee"), which counts how many num­bers less than $n$ are co­prime to $n$.

Here, the ver­ti­cal bars $| \cdot |$ denote the size of the set, that is, the number of el­e­ments it con­tains.

• $\exp(x)$: The ex­po­nen­tial func­tion, $e^x$.
• $i$: The imag­i­nary unit, sat­is­fy­ing $i^2 = -1$.
• $\theta$: An angle in ra­di­ans.