Where does “sysame” come from?

sysame (Middle English) comes from Latin sisami, from Latin sisamum, from Latin sesama, from Ancient Greek σήσαμον, from Aramaic שושמא, from Aramaic שומשומא, from Akkadian šamaššammum, from Akkadian šamnum — fat (foodstuff).

Ancestry of “sysame”, step by step

Step	Language	Word	Meaning
1	Latin	sisami	—
2	Latin	sisamum	—
3	Latin	sesama	—
4	Ancient Greek	σήσαμον	sesame
5	Aramaic	שושמא	—
6	Aramaic	שומשומא	—
7	Akkadian	šamaššammum	an oil-producing plant and its seeds, probably sesame
8	Akkadian	šamnum	oil, fat, cream
9	Proto-Semitic	*šamn-	fat (foodstuff)

Every word from Proto-Semitic *šamn- →Every word from Akkadian šamnum →Every word from Akkadian šamaššammum →