The security of RLWE is "believed" to be strong (meaning there has not been a proof of the opposite yet). It is based on the Lattice problem which is likely to be resistant even to quantum computers.
For a more formal and complete explanation, the paper "A Decade of Lattice Cryptography" was very instructive. https://eprint.iacr.org/2015/939.pdf
It's based on the "Learning With Errors" problem and it's relative, "Ring Learning With Errors", both of which have reductions to lattice crypto problems, the same sort that are in the new NIST proposals for post quantum cryptography. See this article for some more info about how security is evaluated: https://jeremykun.com/2022/12/28/estimating-the-security-of-...
That said, the compiler itself doesn't use any crypto. It generates code for a backend API, and the backend implements the FHE scheme
I'm hoping something of the like of "this is secure if AES is secure"