Author: Russell O'Connor 2020-08-03 22:49:10
Published on: 2020-08-03T22:49:10+00:00
Pieter has made some mathematical observations about Bech32 codewords and Shamir's secret sharing. Two interesting facts have been observed: firstly, affine combinations of two Bech32 codewords is again a valid Bech32 codeword, and secondly, Lagrange polynomials form a partition of unity. This means that if all shares in Shamir's secret sharing have valid Bech32 checksums, the resulting secret will also have a valid Bech32 checksum. Conversely, if both secret and random shares have valid Bech32 checksums, then all derived shares will also have valid Bech32 checksums. This can be used to create a simple secret sharing scheme for dividing up a BIP-32 master seed. An example scheme for k-of-n Shamir's secret sharing is illustrated, with the aim of creating a hand-computable version of the same idea. However, this may become obsolete with the implementation of a threshold musig signature scheme.
Updated on: 2023-06-14T03:12:04.910130+00:00