Welcome to the resource topic for 2022/1551
Extensible Decentralized Secret Sharing and Application to Schnorr Signatures
Authors: Michele Battagliola, Riccardo Longo, Alessio MeneghettiAbstract:
Starting from links between coding theory and secret sharing we develop an extensible and decentralized version of Shamir Secret Sharing, that allows the addition of new users after the initial shares distribution.
On top of it we design a totally decentralized (t,n)-threshld Schnorr signature scheme that needs only t users online during the key generation phase, while the others join later.
Under standard assumptions we prove our scheme secure against adaptive malicious adversaries.
Furthermore, we show how our security notion can be strengthen when considering a rushing adversary.
Using a classical game-based argument, we prove that if there is an adversary capable of forging the scheme with non-negligible probability, then we can build a forger for the centralized Schnorr scheme with non-negligible probability.
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