Blind signatures from Zero knowledge in the Kummer variety

  • Paulo L. Barreto University of Washington
  • Devin D. Reich University of Washington
  • Marcos A. Simplicio Jr. USP
  • Gustavo H. M. Zanon USP


We show how to apply the BZ methodology (Blind signatures from Zero knowledge) to obtain blind signatures in the Kummer varieties defined by Montgomery curves. We also describe specially-tailored arithmetic algorithms to facilitate its efficient implementation. The result can be proved secure under appropriate assumptions, appears to resist even the ROS attack (to which most elliptic-curve blind signature schemes succumb), and is arguably one of the most efficient among those proposals that offer similar security guarantees.
Palavras-chave: Blind signatures, Zero-knowledge arguments, Kummer variety


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BARRETO, Paulo L.; REICH, Devin D.; SIMPLICIO JR., Marcos A.; ZANON, Gustavo H. M.. Blind signatures from Zero knowledge in the Kummer variety. In: SIMPÓSIO BRASILEIRO DE SEGURANÇA DA INFORMAÇÃO E DE SISTEMAS COMPUTACIONAIS (SBSEG), 23. , 2023, Juiz de Fora/MG. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2023 . p. 139-152. DOI:

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