Once you can answer yes to:
<snip> How can you be sure you've used a secure implementation? No idea </snip>
Then you will be able to ascertain for yourself whether your encrypted data, placed in a publicly available location, is "Safe Enough", "Secure Enough" for your needs.
It would be naive to assume that any data placed somewhere, encrypted or not, is stored with a completely invulnerable method.
That having been said, one must rise to the occasion of determining how secure something needs to be, and then availing oneself of the means to achieve that level of security.
I hope that helps, but in reality, there really isn't a cut and dried YES|NO answer - only relative levels of reasonable assurance in securing your data and communications.