I am unaware of the origin and function of the Sator Square. The nature of the word Sator resembles the planet Saturn. Sator in the square can be rearranged into various anagrams pertaining Satan for one, and other meanings that is adaptable to the users of the Sator.
SATOR: (nominative or vocative noun; from serere, 'to sow') sower, planter, founder, progenitor, originator; literally 'seeder'.
There are stories about the Sator Square manifested during the beginning of Christianity. Perhaps this was Pagan Priests or something, trying to preserve and communicate occult and spiritual knowledge to each other, without the risk of persecution, destruction and extermination.
Though, as with anything else, the Jews comes in and alter whatever they can get their hands on, in order to benefit their Global Agenda. The Jews have likely corrupted the true meaning behind this Square, if it ever had any significance or was in use of Pagans.
"It has instead been argued that the square was created in its ROTAS-form as a Jewish symbol, embedded with cryptic religious symbolism, which was later adopted in its SATOR-form by Christians." [1]
However, the Sator Square do seem to contain hidden messages and multiple levels of functions and secrets:
"There are many other less-supported academic origin theories, such as: a Pythagorean or Stoic puzzle, a Gnostic or Orphic or Italian pagan amulet, a cryptic Mithraic or Semitic numerology charm, or that it was simply a device for working out wind directions." [1]
Remember that the true origin of the Kabbalistic Squares are astronomical with the purpose of uplifting us. Based upon the Square and its relation to Witchcraft, it seems that the Square is based upon astrology or astronomical mathematical measurement:
Tenet is the name of the organization that the Protagonist himself created to keep the earth's timeline flowing correctly. It's also an interlocking hand gesture that indicates the flowing of time backward and forward, and a palindrome that's spelled the same way in either direction. [2]
Apparently, the letters of the SATOR square themselves can be rearranged to form an anagram reading PATER NOSTER A O (which is Latin for “Our Father… and then the letters, Alpha and Omega, i.e. the beginning and end). The letters can also be rearranged into what seems to be Satanic prayers:
Oro te, pater, Oro te, pater, sanas. (“I pray thee Father, I pray thee Father, heal me.”)
O pater, ores pro aetate nostra. (“O Father, speak for our age.”)
Retro, Satana, toto apere osper. (“Back, Satan, open the whole party.”)
Satan, oro te pro arte, a te spero. (“Satan, I pray thee for art, I hope from thee.”)
Satan, ter oro te, opera praesto. (“Satan, I beseech thee thrice, work is available.”)
Source:
1. https://en.wikipedia.org/wiki/Sator_Square
2. https://www.gq.com/story/tenet-explained
3. The arrangement of the letters: https://www.houseofgoodfortune.org/bonheur-blog/magic-squares-amp-sator-square