what is meaning of operator " := " in cryptography? I've seen := used in several cryptography papers where the this symbol has been used instead of assignment operator ($  \leftarrow $ ) or equal sign (=), but never with an accompanying explanation. It's not exactly possible to search the precise meaning of operator ":= ". What is the exact meaning of this symbol in terms of mathematics in  cryptography is concerned.
Lindell and Katz, in their book Introduction to Modern Cryptography, use;

$\leftarrow$ as possibly probabilistic process assignment.
Some others use $\stackrel{r}{\gets}$, $\stackrel{\\\$}{\gets}$, $\gets_{R}$, and $\gets_{\\\$} $
Actually, the $\gets_{\\\$}$ fairly common.

$:=$ for the deterministic process assignment.
In some context, the $\leftarrow$ can be the same as Lindell and Katz 's $:=$. This former is more common. In some contexts, it is $=$

$=$ for equality




$\stackrel{def}{=}$ for defining a variable.


More on $\leftarrow$ and variants

When $X$ is a value, the $x \leftarrow X$ is used for  deterministic assignment, and

When $X$ is a probability distribution, the $x \leftarrow X$ is used for sampling.

When $X$ is a set, the  $x \leftarrow_R X$  is used to denote sampling from the uniform distribution over the set $X$.



Note:

In reading books, one needs to check the existence of the notation page(s) or the notation section. Many good books have a section like L&amp;K's Index of Common Notation section (page #533 in the second edition).
In the articles, the authors usually define them where they first occur, therefore, look for the first occurrence of the symbol.