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The shemen ha-mish’ha was used to anoint kings and high priests. The Rosh points out that the need to anoint the high priest is from a clear passage in the Torah (see Ex 30:30), but there appears to be a prohibition to use the oil on any other person (see Ex 30:32). How was the decision made to use this oil on kings, as well?
According to the Gemara in Horayot (12a), kings were anointed by putting the oil around their head like a crown. The kohanim had the oil put on them ke-min key, or, as the Gemara explains, ke-min kaf yevani – like a Greek chi – what we would call the shape of the letter “X”. Since there is no Hebrew letter that is similar in shape to an “X,” many suggestions were made by the commentaries over the years about its appearance, given that Greek was no longer commonly used, and people did not know what the letter looked like.
This leads us to Reb Shaul Lieberman's thesis regarding the letter chi in greek and its appropriation by Christianity.