The attacker tends to forge the signature share [s.sub.i] of the message m produced by the participant [U.sub.i] according to the threshold signature scheme, then use 2t + 1 signature shares to forge the threshold signature s of the message m according to the interpolation formula
MASJED-JAMEI, On constructing new interpolation formulas
using linear operators and an operator type of quadrature rules, J.
The distinctive features of our framework consist in (i) using the boundary element method with real values; (ii) applying the successive approximation method for solving the integral equation of the velocity potential; and (iii) using the Lagrange interpolation formula
through five points for calculating the derivatives of the velocity potential.
With frequency distributions, we use interpolation formulas
for the first and third quartiles quite similar to that for the median, as in equations 2.11 and 2.12.
Lagrange's interpolation formula
is also known as Lagrange's interpolating polynomial.
The main goal of this example is to emphasize the exceptional numerical stability of the Hermite interpolation formulas
of Section 3.
With the knowledge of any t or more than t verification shares, the participants can recover verification polynomial [F.sub.w](x) = [[summation].sup.k.sub.[alpha]=1] [w.sub.[alpha]] [f.sub.[alpha]](x) with the help of the property of additive homomorphism and applying Lagrange interpolation formula
on the verification shares.
Actually, the conditions [C.sub.2], [C.sub.3], [C.sub.4] are sufficient to write the Lagrange interpolation formula
for the "ghost sequence" u 
And, finally, the quadratic interpolation formula
was applied to calculate the definite integral as
In the next section we will give an interpolation formula
for a class of nonstationary random fields using an approach proposed by Piranashvili .
We have recently proved that the Lebesgue constant of these points grows like [log.sup.2] of the degree (as with the best known points for the square), and we have implemented an accurate version of their Lagrange interpolation formula
at linear cost.
"Appendix A: Interpolation Formulas
for the Adjustment of Index Numbers.