I think there is a big difference between private contact discovery and contact discovery that isn't brute forceable like we are seeing with SnapChat and others. One change that could be made for these very small pre image corpuses would be to ask the target user if they should be exposed to the searcher. 1) I upload the hashes of my contacts which enqueues a request to those that match the hashes 2) The target of th…
RTFA. He addresses that in the first few paragraphs. Because there are 10^10 possible phone numbers (approximately), it is very easy to build a rainbow table of all hashed phone numbers and back-track a hash to it's phone number.
Case in point: I work with a guy who used to work at his dads office. He and his dad both have the same name, and they both had the same office number. This algorithm would incorrectly identify both people as being the same person when in fact they are not.