  We present a mechanism to manifest unobtainable secrets using a nested Shamir
secret sharing scheme to create public/private key pairs for elliptic curves. A
threshold secret sharing scheme can be used as a decentralised trust mechanism
with applications in identity validation, message decryption, and agreement
empowerment. Decentralising trust means that there is no single point
vulnerability which could enable compromise of a system. Our primary interest
is in twisted Edwards curves as used in EdDSA, and the related Diffie-Hellman
key-exchange algorithms. The key generation is also decentralised, so can be
used as a decentralised secret RNG suitable for use in other algorithms. The
algorithms presented could be used to fill a ``[TBS]'' in the draft IETF
specification ``Threshold modes in elliptic curves'' published in 2020 and
updated in 2022.
