The corresponding part of Matrix is called Olm (for two-party conversations) and Megolm (for groups). Why (a Matrix mapping of) MLS and not those then? The Matrix people, who did have a hand in MLS, say[1] it performs better than Megolm, and IIRC Megolm is indeed something of a hack on top of plain Olm, because E2EE on Matrix has been built up gradually starting from the simpler two-party case. Unfortunately, it looks like MLS as specified is insufficient for Matrix, because it relies on a global clock—which you can’t get in a partition-tolerant federation—but they think that should eventually be solvable[2].
[1] https://matrix.org/blog/2023/07/a-giant-leap-with-mls/
[2] https://gitlab.matrix.org/matrix-org/mls-ts/-/blob/decentral...
(Equivalently, a supply of totally ordered gremlins with the ability to obtain a gremlin greater than any you’ve seen, and things blow up if any of them are ever actually incomparable.)
It’s possible to build this atop a GNSS[1], but it’s quite expensive.
[1] https://www.usenix.org/conference/osdi-06/chubby-lock-servic...
> Secure messaging protocols in use today were designed as one-to-one protocols [...] In contrast, MLS typically has costs of O(log n) for the same scenario, making it well-suited even for large groups.