Suppose we have a (5, 8) Shamir secret sharing scheme. Everything is mod the prime . Five of the shares are
Find the secret.
SOLUTION
The function interppoly(x,f,m) calculates the interpolating polynomial that passes through the points . The arithmetic is done mod .
In order to use this function, we need to make a vector that contains the values, and another vector that contains the share values. This can be done using the following two commands:
>> x=[9853 4421 6543 93293 12398];
>> s=[853 4387 1234 78428 7563];
Now we calculate the coefficients for the interpolating polynomial.
>> y=interppoly(x,s,987541)
y =
678987 14728 1651 574413 456741
The first value corresponds to the constant term in the interpolating polynomial and is the secret value. Therefore, 678987 is the secret.