> Unfortunately, for a reasonably large user base, this strategy doesn’t work because the bloom filters themselves are too large to transmit to mobile clients. For 10 million TextSecure users, a bloom filter like this would be ~40MB, requested from the server 116 times a second if every client refreshes it once a day.
They decided to run computations inside a 'secure' hardware environment instead (SGX specifically) so that they can't get access to the computation themselves but it also doesn't need to be run client side. I assume you meant the former thing, but the approach they actually use is fundamentally different from homomorphic encryption / PIR.