@vitonsky The most famous example of suspected backdoor โ Dual_EC_DRBG โ was found. Researchers noticed it had a suspicious constant and published the concern years before Snowden confirmed it. The community caught it through exactly this kind of scrutiny. Serpent (our primary cipher) got more first-place security votes than AES from the NIST panel โ partly because its conservative design makes it easier to audit for exactly this kind of thing.
For algorithms with no known weaknesses after 20+ years of public cryptanalysis: at some point "sufficiently many smart people from adversarial countries have independently verified this" becomes a meaningful form of trust. Not infinite trust, but the same kind of trust you extend to arithmetic.
The honest limit: a math PhD is not required, but understanding why a construction is secure does require study. What you can do as a programmer without the PhD is verify test vectors from independent sources, use implementations that have been independently audited, and prefer older, more-analyzed algorithms over newer ones.
That's exactly what leviathan does. we chose Serpent partly because 25 years of cryptanalysis has failed to break it in any practical way.
The zero-trust version of this isn't "trust no spec", it's "verify outputs against independent implementations, prefer algorithms with long public track records, and read the audit trail."