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I don't think the approach you sketched helps very much. If the server is compromised, the attacker can pretty easily modify the server-side software to log and record all the cryptographic keys, and then you haven't gained anything. Therefore, I don't think the approach you sketch is likely to be a great way to spend your limited software development ...

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The best answer is to use verifiable secret sharing (VSS), as I describe here: http://crypto.stackexchange.com/a/6618/351 VSS gives the best parameters and best solution to this problem. If you have a $k$-out-of-$n$ secret sharing scheme, VSS can detect any cheater and enable you to reconstruct the secret as long as you have at least $k$ good shares (even ...

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Suppose $s_0, s_1, s_2, \ldots, s_{k-1}$ are elements from the finite field you are working in, where $s_0$ is the secret to be shared, and the $s_i, i > 0$ are randomly chosen nonzero elements of the field. Then, the polynomial used to construct the shares is $$S(x) = s_0 + s_1x + s_2x^2+ \cdots + s_{k-1}x^{k-1}$$ and the shares themselves are $y_i = ... 1 The easy way to reconstruct the secret is using Neville's algorithm. Basically, let the array y contain n shares (assumed to be represented as the type gf_t here), let the array x contain the points at which the polynomial was evaluated to generate those shares, and let sub(), mul() and inv() be functions/macros that perform the appropriate finite field ... 2 The formula you are looking for is Lagrange Basis Polynomials. Essentially, each share consists of two values, an x coordinate and an y coordinate. The x coordinate might, depending on your specific needs, be implicitly determined by context, such as a preexisting identifier for the entity holding the share. The only requirement is that it is non-zero and ... 0 Have you considered using Shamir's Secret Sharing algorithm? First, Bob encrypts the message with a symmetric algorithm. Then, he divides the secret key into four parts using SSA such that it requires three parts to decrypt (a$(3,4)\$ threshold). Bob then distributes one part each to Alice and Mark, and two parts to Jim. When Alice wants to decrypt, ...

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