"Cryptic promoter" means a promoter region (all genes have promoter regions) that is epigenetically silenced (turned off). It is turned on by other enzymes that change the epigenetics on the promoter. It is just an extra level of control for that particular gene. There is nothing sinister or strange about it, in fact it is quite common.

Many of the names given to biological things are derived from Latin. "Luciferase" (and its target Luciferin) are from the Latin word for "bringer of light" which is fitting because they bring light. Luciferase catalyzes a reaction which emits light.

Because these produce light they are commonly used in research as a reporting system (makes it easy to see if a connected function happened under a microscope). You can connect many reactions of interest to this reporting system, so it being tied to RNA research, or HIV, or Hep C, or whatever is not directly related to the Luciferase molecule itself, but in how useful of a tool it is in studying other things.

In this study (without reading further than the abstract) it appears they are looking at a specific epigenetic modification on the FLuc promoter and how it might impact the statistical results of other research that uses it as a reporter.

There is nothing sinister in this unless you are looking for something sinister. Nevertheless, given everything else I have learned about the world I never knew before, I will mark this as a data point, but nothing more damning than that.

First part of article:

Abstract

A firefly luciferase (FLuc) counts among the most popular reporters of present-day molecular and cellular biology. In this study, we report a cryptic promoter activity in the luc+ gene, which is the most frequently used version of the firefly luciferase. The FLuc coding region displays cryptic promoter activity both in mammalian and yeast cells. In human CCL13 and Huh7 cells, cryptic transcription from the luc+ gene is 10–16 times weaker in comparison to the strong immediate-early cytomegalovirus promoter. Additionally, we discuss a possible impact of the FLuc gene cryptic promoter on experimental results especially in some fields of the RNA-oriented research, for example, in analysis of translation initiation or analysis of miRNA/siRNA function. Specifically, we propose how this newly described cryptic promoter activity within the FLuc gene might contribute to the previous determination of the strength of the cryptic promoter found in the cDNA corresponding to the hepatitis C virus internal ribosome entry site. Our findings should appeal to the researchers to be more careful when designing firefly luciferase-based assays as well as open the possibility of performing some experiments with the hepatitis C virus internal ribosome entry site, which could not be considered until now