[geal]

Homomorphic encryption is interesting from a business standpoint (think: manipulating credit card numbers without being able to read them).

For anonymization systems, care must be taken: being able to manipulate encrypted data could very well create information leaks.

There have been some interesting theoretical uses of the Pallier cryptosystem in private information retrieval systems, though.

[swordswinger12]

What kind of arithmetic operations would you ever need to do on a credit card number? Other than maybe verifying the checksum digit.