For Shamir's secret key sharing algorithm, we develop the procedure for detection of faulty shares. This procedure consists of the error locator polynomial construction for the data set {(x(j), y(j))}(j=1)(N) with y values generated from x ones by a polynomial interpolant of a degree n <N 1 with possible occurrence of some errors. The error locator polynomial is sought out in the form of an appropriate Hankel polynomial

H-L(x;{tau}) := vertical bar tau(0) tau(1) tau(2) ... tau(L) tau(1) tau(2) tau(3) ... tau(L+1)

... ... ... ...

tau(L-1) tau(L) tau(L+1) ... tau(L-1)

1 x x(2) ... x(L)

where T-l := Sigma(j=1)y(j) x(j)/W'(x(j)); W(x) := Pi(j=1)(x - x(j)).