[Cryptography] Advances in homomorphic encryption

[Christian Huitema]

> Of course there are other possibilities like discrete integral fields 
> for year, month, day, hour, minute, that could be checked quickly 
> in succession -- first by stepping through years looking for equality,
> then months, then days, then hours, then minutes.  You could figure
> out whether a particular transaction is within a given date range by 
> making a relatively quick and simple series of equality checks. 

I don't think you can do that if the encryption provides true semantic security. In van Dijk and Gentry's proposal, encryption of is achieved by mixing the original number with a random number r, so that the encryption depends on r but the decryption does not. This ensures that the same number can be encrypted in multiple different ways. It also precludes any simple comparisons, pretty much by design.

-- Christian Huitema