# Question about publication “Efficient (k,n) Threshold Secret Sharing Schemes Secure Against Cheating from n − 1 Cheaters”

In the paper on section "4 Proposed Scheme", I suppose that the scheme does not protect if an adversary has access to the $$k - 1$$ original shares, am I correct?

If the adversary has $$k - 1$$ of both polynomials then it can obtain the difference: $$\sum^{k-1}_{j=1} (g_{j} \cdot l^{'}_{j} - f_{j} \cdot l^{''}_{j}) = (f_{n} \cdot l^{''}_{n} - g_{n} \cdot l^{'}_{n}) = d$$ and perform an attack by selecting polynomials and values such that $$\sum^{k-1}_{j=1} (g_{j} \cdot l^{'}_{j} - f_{j} \cdot l^{''}_{j})^{'} = d$$ to get the forged values for $$v_{n}$$. Would this be feasible?

I don't see this as part of their threat model, but in practice it is a reasonable assumption.