5
votes
1answer
110 views

How come Shamir Secret Sharing uses Lagrange interpolation?

I've read that Newton polynomials have better computational complexity, but Shamir's uses Lagrange polynomials instead. Does anyone know if there are particular reason why Newton polynomials aren't ...
4
votes
1answer
94 views

Back up an information as $n$ pieces and require exactly $n-1$ to recover it

Let $X\in \Bbb F_2^p$ be some information. How do I create $Y_1,\dots,Y_n \in \Bbb F_2^q$ so that having less than $n-1$ of the $Y_i$s gives you no information on $X$ but having $n-1$ of them allows ...
1
vote
2answers
213 views

Shamir's Simple Sharing Scheme - preventing partial recovery of data

In SSSS, if you recreate the original secret with one of the decoder inputs being slightly damaged (e.g. one or two chars incorrect), you receive a slightly damaged version of the original secret. So ...
4
votes
3answers
300 views

Is there a way to use Shamir Secret Sharing with updatable data?

I want to divide a system that maintains these properties, based on Shamir's Secret Sharing: A secret key is split up to N pieces, where T of them are enough to reconstruct the key. The original key ...