[messaging] Encrypted Pulic Contact Discovery

[Trevor Perrin]

On Wed, Aug 19, 2015 at 6:17 PM, Daniel Reichert <daniel1555 at gmail.com> wrote:
> Private Set Intersection has come a long ways since 2009.  Just this year a
> paper[1] was published where private contact discovery is a primary use
> case.  Detailed benchmarks for varying sizes of the client and server set
> sizes are included.  Sadly it's still not practical since the only way to
> prevent a brute force search requires making the protocol O(n1*n2) where n1
> is the client set size and n2 is the server set size.

It's nice to see people looking at this, but I agree with Moxie (and I
think you) that a scaleable solution based on PIR or PSI doesn't seem
to exist.  From the paper you cite:

http://eprint.iacr.org/2015/634.pdf
"""
Private contact discovery
[...]
In these cases each user has a small number of records n2, e.g., n2 =
256, whereas the service has millions of registered users (in our
experiments we use n1 = 2^24). It therefore holds that n2 << n1. In
our best PSI protocol, the client needs only O(n2 * log n1) memory,
O(n2) symmetric cryptographic operations and O(n1) cheap hash table
lookups, and the communication is O(n1 *
log n1).
"""

In other words, the communication overhead is worse than the trivial
PIR of sending a compressed list of users to the client = O(n1).  For
n2=256, n1=2^24, their example protocols send hundreds of MB.


Trevor