In this paper we present a series of applications steming from a formal treatment of linear secret-sharing isomorphisms, which are linear transformations between different secret-sharing schemes defined over vector spaces over a field 픽 and allow for efficient multiparty conversion from one secret-sharing scheme to the other. This concept generalizes the folklore idea that moving from a secret-sharing scheme over 픽_p to a secret sharing “in the exponent” can be done non-interactively by multiplying the share unto a generator of e.g., an elliptic curve group. We generalize this idea and show that it can also be used to compute arbitrary bilinear maps and in particular pairings over elliptic curves.