One time Pads are Key Safegaurding Schemes, not Cryptosystems. Fast Key Safeguarding Schemes (Threshold Schemes) Exist.

Common sense, David Kahn [KA67] and Gilles Brassard [BR79] all argue that there are no unbreakable cryptosystems. What, then, is to be made of the -- provably [D179a, pp. 399-400] unbreakable -- Vernam one-time pad? The somewhat surprising answer is that it is not a cryptosystem at all, but rather a key safeguarding scheme [BL79] used, as all such schemes can be, in the courier mode. This suggests that proofs of invulnerability of key safeguarding schemes, what A. Shamir [SH79] calls threshold schemes, are as natural as proofs of difficulty of breaking cryptosystems are un-natural (perhaps impossible). Indeed, such an approach sets the Vernam one-time pad securely into context. Both the projective geometric threshold scheme [BL79] and the Lagrange interpolation threshold scheme [SH79] profit from being generalized from the field of integers modulo some prime p to arbitrary Galois fields. In particular, their computer implementations are particularly felicitous in some fields with 2n elements.