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Twinkle: Threshold Signatures from DDH with Full Adaptive Security.

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posted on 2024-02-19, 09:34 authored by Renas BachoRenas Bacho, Julian LossJulian Loss, Stefano Tessaro, Benedikt WagnerBenedikt Wagner, Chenzhi Zhu
Sparkle is the first threshold signature scheme in the pairing-free discrete logarithm setting (Crites, Komlo, Maller, Crypto 2023) to be proven secure under adaptive corruptions. However, without using the algebraic group model, Sparkle's proof imposes an undesirable restriction on the adversary. Namely, for a signing threshold , the adversary is restricted to corrupt at most parties. In addition, Sparkle's proof relies on a strong one-more assumption. In this work, we propose Twinkle, a new threshold signature scheme in the pairing-free setting which overcomes these limitations. Twinkle is the first pairing-free scheme to have a security proof under up to adaptive corruptions without relying on the algebraic group model. It is also the first such scheme with a security proof under adaptive corruptions from a well-studied non-interactive assumption, namely, the Decisional Diffie-Hellman (DDH) assumption. We achieve our result in two steps. First, we design a generic scheme based on a linear function that satisfies several abstract properties and prove its adaptive security under a suitable one-more assumption related to this function. In the context of this proof, we also identify a gap in the security proof of Sparkle and develop new techniques to overcome this issue. Second, we give a suitable instantiation of the function for which the corresponding one-more assumption follows from DDH.

History

Primary Research Area

  • Algorithmic Foundations and Cryptography

Journal

Cryptology ePrint Archive

Volume

2023

Page Range

1482-1482

Sub Type

  • Article

BibTeX

@article{Bacho:Loss:Tessaro:Wagner:Zhu:2023, title = "Twinkle: Threshold Signatures from DDH with Full Adaptive Security.", author = "Bacho, Renas" AND "Loss, Julian" AND "Tessaro, Stefano" AND "Wagner, Benedikt" AND "Zhu, Chenzhi", year = 2023, month = 10, journal = "Cryptology ePrint Archive", pages = "1482--1482" }

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