Suppose there are $n$ players. Each player has a $k$-length bit vector. Is there an efficient way of encoding the $k$ length bit vectors, such that after receiving the $n$ encoded outputs, one can only infer the counts of $1$'s at each of the $k$ positions but not the $n$ original bits. That is after receiving the $n$ encoded vectors, one can infer how many players had $1$s in the $i$th bit $\forall i$.
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You might as well let $k=1$ and encode the separate bits in each vector in parallel. In that case each party has a bit and you wish to hide each party's bit but reveal the sum. You can do that using a standard multi-party computation algorithm on an arithmetic circuit consisting of just addition gates like BGW.
answered Feb 3, 2015 at 22:04
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$\begingroup$ Thanks for the answer. It is taking me a little time to parse it, as I am not familiar with a lot of cryptography. I will get back to you, if I have any more questions after reading the relevant literature. $\endgroup$ Feb 4, 2015 at 17:06
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$\begingroup$ @rajatsen91 Okay. Please let me know if I should expand it. $\endgroup$ Feb 4, 2015 at 17:11
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$\begingroup$ Hi, I think I have it figured out. Thanks. $\endgroup$ Feb 4, 2015 at 19:45