Extensible Decentralized Secret Sharing and Application to Schnorr Signatures

Michele Battagliola; Riccardo Longo; Alessio Meneghetti

Paper 2022/1551

Extensible Decentralized Secret Sharing and Application to Schnorr Signatures

Michele Battagliola

, University of Trento

Riccardo Longo

, University of Trento

Alessio Meneghetti

, University of Trento

Abstract

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 share distribution. On top of it we design a totally decentralized -threshold Schnorr signature scheme that needs only 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.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Secret Sharing VSS Schnorr Signature Threshold Signature
Contact author(s): michele battagliola @ unitn it
riccardolongomath @ gmail com
alessio meneghetti @ unitn it
History: 2023-04-06: revised; 2022-11-08: received; See all versions
Short URL: https://ia.cr/2022/1551
License: CC BY-SA

BibTeX

@misc{cryptoeprint:2022/1551,
      author = {Michele Battagliola and Riccardo Longo and Alessio Meneghetti},
      title = {Extensible Decentralized Secret Sharing and Application to Schnorr Signatures},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/1551},
      year = {2022},
      url = {https://eprint.iacr.org/2022/1551}
}