Welcome to the resource topic for 2025/1953
Title:
Adaptively Secure Partially Non-Interactive Threshold Schnorr Signatures in the AGM
Authors: Renas Bacho, Yanbo Chen, Julian Loss, Stefano Tessaro, Chenzhi Zhu
Abstract:Very recently, Crites et al. (CRYPTO 2025) gave a proof for the full adaptive security of FROST (Komlo and Goldberg, SAC 2020), the state-of-the-art two-round threshold Schnorr signature scheme, which is currently used in real-world applications and is covered by an RFC standard. Their security proof, however, relies on the computational hardness of a new search problem they call “low-dimensional vector representation” (LDVR). In fact, the authors show that hardness of LDVR is necessary for adaptive security of a large class of threshold Schnorr signatures to hold, including FROST and its two-round variants. Given that LDVR is a new assumption and its hardness has not been seriously scrutinized, it remains an open problem whether a two-round threshold Schnorr signature with full adaptive security can be constructed based on more well-established assumptions.
In this paper, we resolve this open problem by presenting ms-FROST. Our scheme is partially non-interactive and supports any t - 1 < n adaptive corruptions, where n is the number of signers and t is the signing threshold. Its security relies on the algebraic one-more discrete logarithm (AOMDL) assumption, the algebraic group model (AGM), and the random oracle model (ROM). Further, it achieves the strongest security notion (TS-UF-4) in the security hierarchy of Bellare et al. (CRYPTO 2022). To justify our use of the algebraic group model, we show an impossibility result: We rule out any black-box algebraic security reduction in the ROM from AOMDL to the adaptive TS-UF-0 security of ms-FROST.
ePrint: https://eprint.iacr.org/2025/1953
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