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<p>Starting from links between Coding Theory and Secret Sharing Schemes, we develop an extensible and decentralized version of Shamir Secret Sharing, that allows the addition of new users after the initial share distribution. On top of it we design a totally decentralized (<i>t</i>,&#xa0;<i>n</i>)-threshold Schnorr signature scheme that needs only <i>t</i> 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 strengthened 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.</p>

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Extensible decentralized secret sharing and application to Schnorr signatures

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年12月14日

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  • Michele Battagliola,
  • Riccardo Longo,
  • Alessio Meneghetti

摘要

Starting from links between Coding Theory and Secret Sharing Schemes, we develop an extensible and decentralized version of Shamir Secret Sharing, that allows the addition of new users after the initial share distribution. On top of it we design a totally decentralized (t, n)-threshold 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 strengthened 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.