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1

Reform the problem. Instead of each participant picking their givee (which they give to), have them select a giver (which they receive from). Each participant randomly generates a number (appropriately large) and anonymously submits it (e.g., via the tor network) to the site. This number represents them as giver. After all participants have entered, the ...

3

To answer your question, the cryptographic complexity will reduce by $2^{k-n}$ where $k$ is the key length and $n$ is the number of bits known. A slightly better scheme that doesn't use a cryptographic key sharing scheme can be as follows: Generate three random numbers $B_1$, $B_2$, $B_3$ with bit length equal to the size of your key $K_p$. Generate each ...

3

Just use Shamir's Secret sharing: wiki link It's designed by Adi Shamir, who is the "S" in RSA. It's fairly simple to use and there are no known weaknesses in it. While it doesn't split the data, splitting the key may work just as well (unless you absolutely must split the data.)

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