And a similar technique:
Pick a random polynomial f of degree m. The key is the value f(0). Then, generate n partial keys Kx=f(x) with n>m and x random. Throw away the polynomial and the real key. To reconstruct the polynomial and solve for the key, only m+1 partial keys are needed, but you can generate as many as you want. If you’re slightly forgetful, you can set m=17 and n=20 for example. That gives yourself a bit of wiggle-room without compromising the security of the remaining partial keys. IIRC you want to do the whole thing in some alternate arithmetic, say Galois arithmetic, but the same principle applies.