Expand a tiny shared seed into a huge supply of matching random data for secure computation.
The idea: Secure computation burns through huge amounts of matching random material, such as pairs of values with a fixed relationship between the two parties' halves. Sending all of it would be slow. A PCG gives each party a short seed, and each expands its seed locally into a long string. The expansion uses LPN, a noisy linear map, and because it's linear, seeds that are related the right way produce long outputs related the same way. Millions of correlations, with almost nothing sent.
Why it matters: Makes computing on private data much cheaper.
On the map: cheap correlated randomness for MPC
Pseudorandom correlation generators let two parties expand short seeds into huge amounts of correlated randomness, for example millions of random oblivious transfers, while exchanging very little data[1] ("silent" OT).
They rest on LPN-style assumptions and make the preprocessing for MPC dramatically cheaper. They still need a few base OTs, so public-key assumptions, to get started.
If any of these breaks, this breaks too.
If this breaks, these break with it.
Nothing on the map depends on it: it is an end point, something people use directly.