Threshold cryptosystem with a required share I am trying to find an implementation or variant of a (k, n) threshold cryptosystem (as described here Shamir's Secret Sharing) where we can fix at least one of the k key parts, i.e., instead of ANY k key parts able to decrypt the ciphertext I want at least one of the k key parts to be a certain/fixed key part. So sort of a joint account cheque where k out of n signatures are required but the signature of the accountant should always be there. Any ideas?
Here's an easy way to do it:


Take your secret $S$, and select a random value $R$ of the same size, and compute $T = S \oplus R$
Give the accountant the value $R$
Use a $(k-1, n-1)$ secret sharing method to share $T$ to the other parties.


The accountant plus any set of $k-1$ other parties can reconstruct the secret.  And, any smaller subset cannot get any information on the secret $S$.