Re: Someone had wikipedia open when they wrote that
"Shamir Secret Sharing". First time I read about it was in Donald Knuth's "Art of Computer Programming", printed some time in the 1980's. Of course you might tell Adi Shamir to not write his own crypto, but he'd probably just say "and who are you?"
And it works perfectly fine for k out of m people. Just a polynomial of degree k-1, evaluated at m points, so k results reconstruct the polynomial, an doing everything over some finite field makes sure there is ZERO information out from k-1 results.