Hello, I'm implementing a Blackley secret sharing scheme. With the generation of a secret, and then a point for it, as well as separation, of course, there are no problems.
But with the restoration of the secret there is: for this you need to solve the SLAE (to find the intersection of the planes), but the whole problem is that there all the calculations are performed modulo (simple) and, if the SLAE is solved by standard methods (for example, Gauss), the answer is fractional solution (since the module is not taken into account), and therefore to get the initial secret in this way does not work out (initially only integer coordinates).
The only option that comes to mind is to go through all the options from the module field, and find the only integer answer we need, but the number of all correct solutions in this case will be P to the K-th degree (P-module, K-number of unknowns).
You could not tell how to implement this scheme correctly.

  • Do you solve the system in the field? There are inverse elements, and they are not fractional. - VladD
  • This is exactly the question that interests me: how to solve a SLAU in the field. At the preliminary stages, you can do without it - just a couple of times to calculate the module. But to solve the equations will require a different method than the standard. So I would like to know how to do it. - Vladimir
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    So what's the problem? Gauss method rolls. Just instead of dividing the real numbers, you need division in the field. - VladD
  • Thank you. Something I forgot about the division in the field) - Vladimir

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