Manifesting Unobtainable Secrets: Threshold Elliptic Curve Key Generation using Nested Shamir Secret Sharing

Abstract: 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 specificationThreshold modes in elliptic curves'' published in 2020 and updated in 2022.