Cyano is one of the std alga's encountered in new tanks ... as with other algae in new aquariums it grows because the numerous micro organisms that would otherwise consume phosphate/nitrates just don't exist in sufficient numbers.
Cyano thrive on excess nutrients .. the prime nutrient is phosphate. The "cure" for cyano is to try and limit the importation of phosphates as well as try to maximize their export.
Cyano like other nuisance alga's rarely does any harm (unless its smothering your corals) and some would suggest you "grin & bear it" and let it act as an inexpensive phosphate sponge ... just let it grow and periodically siphon it out.
Phosphates are one of those basic elements and tend to be in everything .. in our tanks water and food tend to be the prime sources. As far as limiting "import" you need to make sure your using RO/DI. All food has phosphates and you need to try and select those foods that have less phosphates than others. Some flake foods are loaded with phosphates .. most frozen food has less phosphates. If your using flake consider switching to frozen .. if your using frozen make sure you thaw the frozen and then rinse the frozen food to eliminate phosphates & excess nutrients in the water (which don't feed fish but do feed algae). Also .. most aquarist overfeed their tanks so whether your using high or low phosphate food your contributing to the problem .. consider reducing the amt of food.
The best methods for exporting phosphate include .. water changes using RO/DI water, use of a phosphate binder (phosban etc), wet skimming, siphoning out the phosphate laden cyano, macro algae, dripping Kalkwasser (helps precipitate Phosphates), and probably a few more which my Alzheimer brain can't bring to light right now.
At any rate .. hope this helps - good luck.