In RFC5647, NIST SP 800-38D, etc., || is used to denote concatenation. How did that come to be?
In most programming languages || represents "or" and + denotes concatenation and the fact that crypto texts just kind of mixed it up seems to make for an easy gotcha.
The origin is set theory and not programming languages. In the context of cryptography, I could describe a set that is
$$x_1 \parallel x_2 \parallel \dots \parallel x_n$$
as a concatenation of the series described by
$$\parallel_{i=1}^n x_i.$$
Furthermore, it's worth noting that + to a mathematician would suggest that it is a commutative, which might not be true depending on the set (as we could have a set of functions).
Some languages like PL/I and Oracle Database SQL indeed use || for string concatenation.
One reason is maybe that + might be confusing when talking about fundamental cryptography, since there is a lot of math involved. The mathematical notation for 'OR' would be reversed caret $\lor$ and the exclusive 'OR', better known as 'XOR' is a circled plus $\oplus$.
But I don't think that there is a specific reason for using || for a string concatenation. If anything then I would presume that someone used it once early and then it has become accustomed until it has become a standard for cryptography.
