alt Hacker NewsI think the opening example involving Google is misleading. When I hear "Google" I think "search the web".
The articles is about getting an input encrypted with key k, processing it without decrypting it, and sending back an output that is encrypted with key k, too. Now it looks to me that the whole input must be encrypted with key k. But in the search example, the inputs include a query (which could be encrypted with key k) and a multi-terabyte database of pre-digested information that's Google's whole selling point, and there's no way this database could be encrypted with key k.
In other words this technique can be used when you have the complete control of all the inputs, and are renting the compute power from a remote host.
Not saying it's not interesting, but the reference to Google can be misunderstood.
Replies
Homomorphically encrypted services don't need a priori knowledge of the encryption key. That's literally the whole point.
Consider the following (very weak) encryption scheme:
m, k ∈ Z[p], E(m) = m * k mod p, D(c) = c * k⁻¹ mod p
With this, I can implement a service that receives two cyphertexts and computes their encrypted sum, without knowledge of the key k:
E(x) + E(y) = x * k + y * k mod p = (x + y) * k mod p = E(x + y)
Of course, such a service is not too interesting, but if you could devise an algebraic structure that supported sufficiently complex operations on cyphertexts (and with a stronger encryption), then by composing these operations one could implement arbitrarily complex computations.
I don't know, when I hear Google I hear Gmail, Google docs, and every other service they have to know about people. My mom would probably think mostly about search, but then she would not read an article about HME
> Now it looks to me that the whole input must be encrypted with key k. But in the search example, the inputs include a query […] and a multi-terabyte database […]
That’s not the understanding I got from Apple’s CallerID example[0][1]. They don’t seem to be making an encrypted copy of their entire database for each user.
[0]: https://machinelearning.apple.com/research/homomorphic-encry...
[1]: https://machinelearning.apple.com/research/wally-search