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May 28, 2012 at 15:52 answer added none timeline score: 0
May 28, 2012 at 13:14 vote accept Vincent Tjeng
May 28, 2012 at 0:25 answer added Aaron Meyerowitz timeline score: 0
May 27, 2012 at 14:50 comment added Vincent Tjeng Hi @Max, I read up on the secret sharing scheme, and, based on what I've understood, I think that problem and the one I've posed could be related but are not the same. In fact, I believe that secret sharing is only "interesting" when $k>1$. Substituting $k=1$ into most solutions for the secret-sharing schemes I've found do not address conditions 2 & 3 since they are not designed to.
May 27, 2012 at 14:20 comment added Vincent Tjeng @zeb That sounds like a pretty good solution! When you say that there is no guarantee that factoring is hard, do you mean that the system would be approximately as secure as encryption schemes like the RSA algorithm?
May 27, 2012 at 9:46 comment added Max Horn This sounds like a special case of a $(n,k)$-threshold scheme. Such a scheme can be used to share a secrete among $n$ individuals, such that any subset of at least $k$ of them can recover the secret. You are interested in the case $k=1$. There are tons of material on that in the literature; indeed, the Wikipedia page might be a good starting point: en.wikipedia.org/wiki/Secret_sharing
May 27, 2012 at 8:37 answer added Federico Poloni timeline score: 3
May 27, 2012 at 8:08 comment added zeb Here's a simple idea: Let $P$ be the product of $2k$ large primes, half of which are congruent to $1$ modulo $4$, and consider the properties of being a prime, being a divisor of $P$, and being congruent to $1$ modulo $4$. Unfortunately, there is no guarantee that factoring is hard...
May 27, 2012 at 6:18 history asked Vincent Tjeng CC BY-SA 3.0