Third-party security issues with Shamir's secret sharing scheme In Shamir's secret sharing scheme, we are trusting a third party who generates the secret polynomial.  

How can we ensure security here when we are involving a third party?
We simply have to trust this party because this scheme requires a trusted dealer (a party that distributes the shares to the secret to the participants - this can be you or some other party - but if its you you should trust yourself).

We can use verifiable secret sharing, that allows the parties to check whether the shares they have obtained are consistent, i.e. to verify if the dealer behaves honest (but the dealer still knows the secret and thus this is only a partial reduction of trust). 

If we do not want to have a trusted dealer who sets up the shares at all, we have to switch to dealer-free secret sharing schemes. See for instance, here.