### Threshold Ring Signatures: New Definitions and Post-Quantum Security

Abida Haque and Alessandra Scafuro

##### Abstract

A $t$-out-of-$N$ threshold ring signature allows $t$ parties to jointly and anonymously compute a signature on behalf on $N$ public keys, selected in an arbitrary manner among the set of all public keys registered in the system. Existing definitions for $t$-out-of-$N$ threshold ring signatures guarantee security only when the public keys are honestly generated, and many even restrict the ability of the adversary to actively participate in the computation of the signatures. Such definitions do not capture the open settings envisioned for threshold ring signatures, where parties can independently add themselves to the system, and join other parties for the computation of the signature. Furthermore, known constructions of threshold ring signatures are not provably secure in the post-quantum setting, either because they are based on non-post quantum secure problems (e.g. Discrete Log, RSA), or because they rely on transformations such as Fiat-Shamir, that are not always secure in the quantum random oracle model (QROM). In this paper, we provide the first definition of $t$-out-of-$N$ threshold ring signatures against {\em active} adversaries who can participate in the system and arbitrarily deviate from the prescribed procedures. Second, we present a post-quantum secure realization based on {\em any} (post-quantum secure) trapdoor commitment, which we prove secure in the QROM. Our construction is black-box and it can be instantiated with any trapdoor commitment, thus allowing the use of a variety of hardness assumptions.

Available format(s)
Category
Cryptographic protocols
Publication info
A major revision of an IACR publication in PKC 2020
Keywords
Threshold Ring SignaturesQROMpost-quantum cryptography
Contact author(s)
ahaque3 @ ncsu edu
ascafur @ ncsu edu
History
Short URL
https://ia.cr/2020/135

CC BY

BibTeX

@misc{cryptoeprint:2020/135,
author = {Abida Haque and Alessandra Scafuro},
title = {Threshold Ring Signatures: New Definitions and Post-Quantum Security},
howpublished = {Cryptology ePrint Archive, Paper 2020/135},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/135}},
url = {https://eprint.iacr.org/2020/135}
}

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