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there should be more whitespace in the first version (this might be more or less pronounced on your screen, and also depends on the characters within the identifier).

• \{ 0, 1 \} gives the two-elements set $\{ 0, 1 \}$
• \emptyset gives the empty set $\emptyset$
• A \cup B and A \cap B give $A \cup B$ (union) and $A \cap B$ (intersection)
• a \in A gives $a \in A$, while b \not\in A gives $b \not\in A$
• A \subset B or A \subseteq B give $A \subset B$ or $A \subseteq B$
• Standard sets, usually written in blackboard bold with \mathbb or \Bbb:
  • $\Bbb N$ \Bbb N is some set of natural numbers with ambiguity over whether zero is included or not, so avoid this notation
  • $\Bbb N^0, \Bbb N_0$ \Bbb N^0, \Bbb N_0 is the set of natural numbers starting at zero
  • $\Bbb N^1, \Bbb N_1, \Bbb N^+$ \Bbb N^1, \Bbb N_1, \Bbb N^+ is the set of natural numbers starting at one
  • $\Bbb Z$ \Bbb Z is the ring of integers (from German Zahl)
  • $\Bbb Z^-, \Bbb Z^+, \Bbb Z \setminus \{0\}$ \Bbb Z^-, \Bbb Z^+, \Bbb Z \setminus \{0\} are the sets of negative, positive, and nonzero integers
  • $\Bbb Q$ Bbb Q is the field of rational numbers; similarly, $\Bbb Q^-, \Bbb Q^+, \Bbb Q \setminus \{0\}$ \Bbb Q^-, \Bbb Q^+, \Bbb Q \setminus \{0\} for negative, positive, and nonzero
  • $\Bbb R$ \Bbb R is the field of real numbers; similarly, $\Bbb R^-, \Bbb R^+, \Bbb R \setminus \{0\}$ \Bbb R^-, \Bbb R^+, \Bbb R \setminus \{0\} for negative, positive, and nonzero
  • $\Bbb C$ \Bbb C is the field of complex numbers
  • the ring of integers modplo $p$ is alternately written $\Bbb Z/p\Bbb Z$\Bbb Z/p\Bbb z or $\Bbb Z_p$ \Bbb Z_p, but beware $\Bbb Z_p$ also means the $p$-adic integers
  • the multiplicative group of integers modulo $n$ is alternately written $(\Bbb Z/n\Bbb Z)^\times$(\Bbb Z/n\Bbb Z)^\times, $(\Bbb Z/n\Bbb Z)^*$ (\Bbb Z/n\Bbb Z)^*, $\Bbb Z_n^*$ (\Bbb Z/n\Bbb Z)^*, etc.
  • $\operatorname{GF}(p^n), \Bbb F_{p^n}$ \operatorname{GF}(p^n), \Bbb F_{p^n} is the finite field of characteristic $p$ with $p^n$ elements

\begin{gather}
  M :\quad y^2 = x^3 + 486662 x^2 + x, \\
  E\colon -x^2 + y^2 = 1 - \frac{121665}{121666} x^2 y^2.
\end{gather}

• \{ 0, 1 \} gives the two-elements set $\{ 0, 1 \}$
• \emptyset gives the empty set $\emptyset$
• A \cup B and A \cap B give $A \cup B$ (union) and $A \cap B$ (intersection)
• a \in A gives $a \in A$, while b \not\in A gives $b \not\in A$
• A \subset B or A \subseteq B give $A \subset B$ or $A \subseteq B$
• Standard sets, usually written in blackboard bold with \mathbb or \Bbb:
  • $\Bbb N$ \Bbb N is some set of natural numbers with ambiguity over whether zero is included or not, so avoid this notation
  • $\Bbb N^0, \Bbb N_0$ \Bbb N^0, \Bbb N_0 is the set of natural numbers starting at zero
  • $\Bbb N^1, \Bbb N_1, \Bbb N^+$ \Bbb N^1, \Bbb N_1, \Bbb N^+ is the set of natural numbers starting at one
  • $\Bbb Z$ \Bbb Z is the ring of integers (from German Zahl)
  • $\Bbb Z^-, \Bbb Z^+, \Bbb Z \setminus \{0\}$ \Bbb Z^-, \Bbb Z^+, \Bbb Z \setminus \{0\} are the sets of negative, positive, and nonzero integers
  • $\Bbb Q$ \Bbb Q is the field of rational numbers; similarly, $\Bbb Q^-, \Bbb Q^+, \Bbb Q \setminus \{0\}$ \Bbb Q^-, \Bbb Q^+, \Bbb Q \setminus \{0\} for negative, positive, and nonzero
  • $\Bbb R$ \Bbb R is the field of real numbers; similarly, $\Bbb R^-, \Bbb R^+, \Bbb R \setminus \{0\}$ \Bbb R^-, \Bbb R^+, \Bbb R \setminus \{0\} for negative, positive, and nonzero
  • $\Bbb C$ \Bbb C is the field of complex numbers
  • the ring of integers modplo $p$ is alternately written $\Bbb Z/p\Bbb Z$\Bbb Z/p\Bbb z or $\Bbb Z_p$ \Bbb Z_p, but beware $\Bbb Z_p$ also means the $p$-adic integers
  • the multiplicative group of integers modulo $n$ is alternately written $(\Bbb Z/n\Bbb Z)^\times$(\Bbb Z/n\Bbb Z)^\times, $(\Bbb Z/n\Bbb Z)^*$ (\Bbb Z/n\Bbb Z)^*, $\Bbb Z_n^*$ (\Bbb Z/n\Bbb Z)^*, etc.
  • $\operatorname{GF}(p^n), \Bbb F_{p^n}$ \operatorname{GF}(p^n), \Bbb F_{p^n} is the finite field of characteristic $p$ with $p^n$ elements

\begin{gather}
  M\colon y^2 = x^3 + 486662 x^2 + x, \\
  E\colon -x^2 + y^2 = 1 - \frac{121665}{121666} x^2 y^2.
\end{gather}

Braces / curly brackets {} are used to group expressions / symbols together within $\TeX$. You need to use the backslash \ escape character to use one within an expression: \{\} gives you $\{\}$. Parentheses () and (square) brackets can be used as-is, for instance in a range $[0, 10)$ is just [0, 10).

The following sections will show common contents of math blocks. There are however other ways of finding out how to use $\TeX$:

• right-click any formula, select "Show Math As" and then "TeX Commands";
• use Detexify to find symbols (also available as App);
• the Math site predictably uses a lot of $\TeX$ and has an excellent tutorial on their Meta;
• search or post a question on the $\TeX$ sister site (MathJax questions are off topic there, $\TeX$ formulas only please);
• ask cryptography specific questions here on Meta or in the Side Channel chat room.
• MathJax (embedding) related questions can be asked using the MathJax tag on StackOverflow.

Most cryptographic functions are undefined in the $\TeX$ packages; it is however important to make sure they are not confused with identifiers.

Braces / curly brackets {} are used to group expressions / symbols together within $\mathrm\TeX$. You need to use the backslash \ escape character to use one within an expression: \{\} gives you $\{\}$. Parentheses () and (square) brackets can be used as-is, for instance in a range $[0, 10)$ is just [0, 10).

The following sections will show common contents of math blocks. There are however other ways of finding out how to use $\mathrm\TeX$:

• right-click any formula, select "Show Math As" and then "TeX Commands";
• use Detexify to find symbols (also available as App);
• the Math site predictably uses a lot of $\mathrm\TeX$ and has an excellent tutorial on their Meta;
• search or post a question on the $\mathrm\TeX$ sister site (MathJax questions are off topic there, $\mathrm\TeX$ formulas only please);
• ask cryptography specific questions here on Meta or in the Side Channel chat room.
• MathJax (embedding) related questions can be asked using the MathJax tag on StackOverflow.

Most cryptographic functions are undefined in the $\mathrm\TeX$ packages; it is however important to make sure they are not confused with identifiers.