First of all, there's a lot of recent (and not so recent) work in Local Differential Privacy [1], which uses the "untrusted curator" model. Although this software doesn't use it, the article mentions RAPPOR, which is a good example.
Second of all, encryption protects your _data_, but not your _privacy_; that is, assuming your data gets used in any way, you have no guarantees about whether the result reveals anything you'd rather keep secret. Of course, if you're talking about normal encryption, your data _can't_ be used, but then you're not really sharing it at all, as much as storing it there (like Dropbox). But once you start talking about things like homomorphic encryption or secure multiparty computation, it's important to keep in mind that they are complements to differential privacy, not replacements.
First of all, there's a lot of recent (and not so recent) work in Local Differential Privacy [1], which uses the "untrusted curator" model. Although this software doesn't use it, the article mentions RAPPOR, which is a good example.
Second of all, encryption protects your _data_, but not your _privacy_; that is, assuming your data gets used in any way, you have no guarantees about whether the result reveals anything you'd rather keep secret. Of course, if you're talking about normal encryption, your data _can't_ be used, but then you're not really sharing it at all, as much as storing it there (like Dropbox). But once you start talking about things like homomorphic encryption or secure multiparty computation, it's important to keep in mind that they are complements to differential privacy, not replacements.
[1]: https://en.wikipedia.org/wiki/Local_differential_privacy