I started some work here as prop280, and gotten some feedback. Carolin Zöbelein has also written some outlines for a Shamir-based protocol. I've taken a shot at a variation of a Shamir-based protocol at https://github.com/nmathewson/privcount_shamir , where it appears as a python prototype.
Current open question: does Shamir-style secret sharing actually do anything to help with the case where some Data Collectors are misbehaving? So far as I can tell, it only really helps us handle malfunctioning Tally Reporters.
Trac: Owner: N/Ato nickm Status: new to accepted Keywords: N/Adeleted, prop280 added Cc: N/Ato teor, robgjansen, amj703
An answer to Nick's question: secret sharing only helps deal with failures of Tally Reporters. Handling failures (i.e. crashes/dropouts) of DCs can be done simply by having the TRs agree on all the DCs they have data from before adding their individual shares from those DCs. Handling malicious inputs can be mitigated somewhat by choosing multiple different DC subsets, aggregating each one, and taking the median of the resulting values.
Also, I would be interested to hear cypherpunks' concerns in more detail.