New answers tagged secret-sharing
2
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 ...
1
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 ...
2
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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