Lattice Bingo: Asynchrony and One-Shot Adaptivity in Verifiable Secret Sharing via Erasure Code Commitments

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Asynchronous verifiable secret sharing (AVSS) allows a dealer to distribute a secret among parties while preserving privacy and consistent reconstruction, despite Byzantine faults and arbitrary message delays. It is a fundamental building block for Byzantine agreement, distributed key generation, and secure multiparty computation. Packed AVSS protocols share many secrets together to reduce communication per secret. The best known AVSS protocols achieve quadratic communication while sharing linea