Artificial intelligent assistant

Notation: Meaning of brackets with subscript? I came across the following expression: $[m + 2r + 2\sum_{i \in S}{x_i}]_{x_0}$. What does the subscripted bracket notation mean? Context: Found in this paper < Page 6, Section 3.1, in description of "Encrypt" function.

In section 2, the paper gives this definition:

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