Once this subset of valid tokens is determined, Lagrange
interpolation formula is executed to test each remaining token one at a time to identify whether it is an invalid token or not.
When the number of the signature shares got by any one participant or signature receiver reaches 2t + 1, he can compute the signature s according to the
interpolation formula. Thus the signature (r, s) of the message m is got.
In [21, Section 1.5], Phillips has studied two new
interpolation formulas on q-integers.
3 Secret Reconstruction Algorithm: In the secret reconstruction algorithm, any authorized subset of n participants with order has 4, S can be obtained using Lagrange's
interpolation formula as in equations (2, 3) to reconstruct the polynomial f (x), and then find f (16) = S.
Using the Lagrange
interpolation formula through five points, [V.sup.I.sub.[tau]i] and [V.sup.I.sub.ni] are calculated.
These formulas are independent of the true value of the spectrum, and then the
interpolation formulas are obtained by Fourier series developments.
Computational procedures for the two types of data are generally different because
interpolation formulas are often necessary when dealing with frequency distributions.
Yet another method for completing step 4 is to use Lagrange's
interpolation formula.
As an application of the previous results, in Section 3, we obtain Hermite
interpolation formulas for nodal systems on [-1,1].
Meanwhile, with the knowledge of any t master shares with respect to the threshold structure, matrix S* can be recovered by Lagrange
interpolation formula (denoted by [F.sub.X](x)).
Stirling's
interpolation formula is based on a finite number of evaluations of the function and does not require derivatives, with the first-order approximation yielding
When the conditions [C.sub.1], [C.sub.2], [C.sub.3], [C.sub.4] are verified, the following
interpolation formula is true: