How do the Tosk and Jem'Hadar's cloaks function?

Question

In Star Trek; Deep Space Nine, there are two different species that have a biological ability to render themselves invisible DS9 Ep. 1x06: Captive Pursuit has Tosk, and later seasons of DS9 have the Jem'Hadar and their Shroud throughout.

According to Memory Alpha, the script of DS9 Ep. 2x26: "The Jem'Hadar" indicates that Tosk and the Jem'Hadar do it the same way, though later episodes indicate Jem'Hadar require Ketracel White to maintain the ability. It would make sense if the Tosk had the capability naturally, and the Founders engineered it into the Jem'Hadar.

Is there any explanation for how they do it?

Answer 1

Main Canon

As far as I can tell, there isn't even a treknobabble explanation for how the shroud works. It's evidently a biological function (since in DS9: The Abandoned, we see a young Jem'Hadar warrior who learns to shroud without any external support or the implantation of any technology) but one that results in the user's clothes and and held items also becoming invisible to the naked eye. This heavily implies that they're emitting some kind of field or particles like the Suliban cloaking particles seen in Ent: The Communicator. Beyond that, we simply don't know.

EU Canon

In Worlds of Star Trek: Deep Space Nine, Volume 3 it's explicitly stated that the ability to shroud is a facet of psychic ability, one that also (theoretically) allows the user to remotely view events happening outside of their eyeline.

As Taran’atar stopped at Matheson’s order, he felt his mental grip on the image of the Founder begin to slip. Dimly aware of the door up ahead blocking the way, and of the lieutenant commander pushing a key into a slot in the bulkhead, he struggled to preserve his clear visualization of the Founder. He did not know how much longer he could sustain his efforts. Shrouding normally required a significant exertion of will, but far less, it turned out, than the task at hand. Taran’atar had never attempted what he did now, had not even known it possible until a few moments ago, having heard only unconfirmed rumors of Jem’Hadar who had utilized their shrouding capabilities for remote generation of images.

Activity up ahead penetrated his awareness. He plainly heard Matheson identify herself and request access to the defensive emplacement, distinctly felt vibrations through the decking as the door began to slide slowly into the bulkhead. Too far, he thought, intuitively understanding that his capacity to project a realistic image relied not only on his ability to concentrate, but also on his distance from the location to which he projected that image.