An exploration of how to modify the FROST distributed key generation (DKG) protocol to support Bring-Your-Own-Key (BYOK), allowing some participants to contribute pre-existing keys to a new FROST signing group. The author walks through the standard FROST DKG (Pedersen DKG), explains how signing shares relate to Shamir Secret Sharing, then proposes a modified DKG using Lagrange Interpolation to fix certain polynomial evaluations to pre-existing public keys. Limitations are discussed (at most t-1 BYOKs where t is the threshold), along with security considerations and potential use cases like composing hierarchical FROST groups or nested Fedimint instances. The author explicitly flags this as unreviewed, hypothetical cryptography.
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