# how to use the secret perfect shamir in Sage?

Good Morning. I need to resorve this problem. I have three fragments that I make with shamir's secret perfect and now I need to find the polinomy, but I don`t know if there is a method which I can to solve the polinomy and have the secret with Sage.

For exemple I have this polinomy 56 + 10*x + 5*x^2 mod 101. I know that the secret is 56 and three fragments [25, 98], [47, 57], [19, 31], (56 +10*25+5*25^2)mod 101 = 98

How I can to find the polinomy with these fragments? I can't use Lagrange because it is arithmetic modular.

Thank you.

This sounds like homework. Can you give us a reference to "shamir's secret perfect"? It sounds like a key-sharing or encryption scheme, perhaps one not implemented in Sage. Certainly we should have the infrastructure to deal with any polynomial stuff over Z_n, though.