Firstly, the initial C in Cirth is pronounced as a K, never as an S.
With that out of the way, let’s move on…
There are 3 common types of Cirth, one that was used by elves long ago, “Certhas Daeron”, which was the basis for the Cirth used by Dwarves. During the First Age, Elvish craftsmen in Beleriand began developing an informal alphabet for use with their Sindarin language. This alphabet became known as the Cirth (meaning: “runes”). The Cirth letters were almost entirely made from straight lines that could be easily engraved onto hard surfaces. The Elves used the Cirth exclusively for carved inscriptions.
Dwarves use two types of Cirth, the first is likely the most widely used, known as “Angerthas Moria” (which is the Elvish name, in Khuzdul it would be: Kirth Khazâddûmu). During the beginning of the Second Age in Eregion, Dwarves first came to know the Elvish runes of the Noldor. They modified the runes to suit the specific needs of their language, Khuzdul. The Dwarves spread their revised alphabet to Moria, where it came to be known as Angerthas Moria (meaning: “The Long Rune-rows of Moria”) . The Dwarves used the runes extensively, and developed both carved and pen-written forms. They spread their alphabet whereever they went through out Middle-earth. Variations of Angerthas Moria were also used by other races for their languages, such as the Mannish tongue Westron.
The second system of writing, called “Angerthas Erebor” (Kirth Zesulu) is much more recent. At the beginning of the Third Age, the Dwarves were driven out of Moria. Some migrated to the Grey Mountains, some to the Iron Hills, and some came to Lonely Mountain (or Erebor). The Dwarves in Erebor modified the Cirth even more. Several letters reverted back to the original Angerthas Daeron phonetic value. They also added a number of extra characters.
Both Dwarrow writing systems are in use today. You will find the Moria Cirth style more common still in Middle-Earth and considered the standard style. The Erebor Cirth style still has many users in the North-Eastern mountain ranges, though fewer in the West (Ered Luin) and almost none in Khazâd-dûm.
Strangely enough in the LoTR movies both Erebor and Moria style are used on Balin’s tomb. For our Khuzdul lessons I’ve researched about a dozen different documents on Cirth that can be found on the web, and they all have differences between them. So I reverted to the source and read the “The History of Middle-earth” edited by Christopher Tolkien – Volume VII, “The Treason of Isengard”, Appendix on Runes, amongst other original works. On the internet there is one source that comes very close to being exactly correct, which is: HERE. Again note, that there are two minor mistakes in the Moria style cirth table listed (HERE). It is very close to being accurate however. I have put all my findings in the tools that accompany the lessons – which allow the user to type the word in latin characters and get it converted into both dwarven Cirth versions.