Place the egg whites in a mixer bowl fitted with the flat paddle or scraper paddle attachment. Turn the mixer on high speed for 10 seconds to break up the egg whites.
Turn the mixer to the lowest speed; slowly add the 725 grams of powdered sugar to make a soft consistency royal icing.
Scrape those sides!
Turn up the speed to setting 3 or 4 for about two minutes.
Make sure the mixture is at the soft-peak stage. It should look shiny, like meringue, and the peaks should fall over.
** (If coloring the entire batch, add the paste, gel or liquid color at this stage, making it a shade darker than desired.) White gel color can be added to make whiter gum paste.
Turn the mixer to the slow setting and sprinkle the tylose in over a five second time period. Turn the speed up to the high setting for a few seconds. This will thicken the mixture. It should feel a little spongy, and when you press you finger in it shouldn't stick.
Scrape the mixture out of the bowl onto a work surface that has been sprinkled with some of the reserved 100 grams of powdered sugar. Place shortening on your hands and knead the paste, adding enough powdered sugar to form a soft but not sticky dough.
You can check by pinching with your fingers; they should come away clean.
Place the finished paste in a zip-top bag, then place the bagged paste in a second bag and seal well. Mature in the fridge for 24 hours, if possible, before use.