[Beldin]

> when can you claim something as secure?

Typically: don't do that.

Nevertheless, if you insist: you can claim a certain abstraction of a system guarantees certain mathematically expressed requirements cannot be violated by a certain attacker model once you've formally proved that.

Of course, all implementations have implementation details which violate the abstraction, your mathematically expressed requirements may not fully capture your intentions, and in practice, an attacker may have additional options that your model doesn't consider. But hey, now you can truthfully claim that "the system" is "secure" - for some values of "system" and "secure".