On 29.03.2014, at 18:46, Gregory Maxwell <gmaxwell@gmail.com> wrote:
> In this case I don't see anything wrong with specifying secret
> sharing, but I think— if possible— it should be carefully constructed
> so that the same polynomials and interpolation code can be used for
> threshold signatures (when encoding compatible data).

The paper http://www.cs.princeton.edu/~stevenag/bitcoin_threshold_signatures.pdf
does not mention anything special about the polynomial to use other than:
 "random polynomial f of degree t - 1 such that d = f(0)"

Do you have reasons to assume that there is more to this? Since this is compatible
with Matt's proposal.