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Password-Protected Threshold Signatures

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Advances in Cryptology – ASIACRYPT 2024 (ASIACRYPT 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15486))

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Abstract

We witness an increase in applications like cryptocurrency wallets, which involve users issuing signatures using private keys. To protect these keys from loss or compromise, users commonly outsource them to a custodial server. This creates a new point of failure, because compromise of such a server leaks the user’s key, and if user authentication is implemented with a password then this password becomes open to an offline dictionary attack (ODA). A better solution is to secret-share the key among a set of servers, possibly including user’s own device(s), and implement password authentication and signature computation using threshold cryptography.

We propose a notion of augmented password-protected threshold signature (aptSIG) scheme which captures the best possible security level for this setting. Using standard threshold cryptography techniques, i.e. threshold password authentication and threshold signatures, one can guarantee that compromising up to t out of n servers reveals no information on either the key or the password. However, we extend this with a novel property, that compromising even all n servers also does not leak any information, except via an unavoidable ODA attack, which reveals the key only if the attacker guesses the password.

We define aptSIG in the Universally Composable (UC) framework and show that it can be constructed very efficiently, using a black-box composition of any UC threshold signature [13] and a UC augmented Password-Protected Secret Sharing (aPPSS), which we define as an extension of prior notion of PPSS [30]. As concrete instantiations we obtain secure aptSIG schemes for ECDSA (in the case of \(t=n-1\)) and BLS signatures with very small overhead over the respective threshold signature.

Finally, we note that both the notion and our generic solution for augmented password-protected threshold signatures can be generalized to password-protecting MPC for any keyed functions.

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Notes

  1. 1.

    Authenticated channels between user and servers are needed at initialization in order for the user to identify the servers it is communicating with, but such channels, or PKI, are not needed for later signature generation.

  2. 2.

    McQuoid et al. [36] made a related observation, that a (non-threshold) OPRF implements secure 2PC for evaluating (non-secret-shared) obfuscated point functions, and used it to costruct 2PC on obfuscated inputs for a larger class of functions.

  3. 3.

    \(\mathcal {F} _{\textrm{aptSIG}}\) lets \(\mathcal {A}^*\) set the user instance’s message \(\textsf{m}\) to arbitrary \(\textsf{m}^*\) in the finalization of the signing protocol, but only for adversarial user instances, i.e. we allow adversarial signing instances to “late-commit” to their messages.

  4. 4.

    Due to space constraints we defer to the full version of the paper, which captures the top-level view of these interactions in the real-world and ideal-world executions.

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Acknowledgments

Stefan Dziembowski, Pawel Kedzior, Chan Nam Ngo: This work is part of a project that received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grants PROCONTRA-885666). Stefan Dziembowski was also partly supported by the Polish NCN Grant 2019/35/B/ST6/04138 and the Nicolaus Copernicus Polish-German Research Award 2020 COP/01/2020. Stanislaw Jarecki: This work was supported by NSF SaTC TTP award 2030575. Hugo Krawczyk: This work was done while the author was at the Algorand Foundation. Chan Nam Ngo: The majority of this work was done while the author was with the University of Warsaw, Poland.

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Authors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski & Pawel Kedzior

  2. IDEAS NCBR, Warsaw, Poland

    Stefan Dziembowski

  3. University of California Irvine, Irvine, USA

    Stanislaw Jarecki

  4. Amazon Web Services, Seattle, USA

    Hugo Krawczyk

  5. Privacy + Scaling Explorations, Ho Chi Minh City, Vietnam

    Chan Nam Ngo

  6. Oregon State University, Corvallis, USA

    Jiayu Xu

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  1. Stefan Dziembowski
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Correspondence to Stefan Dziembowski .

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  1. Academia Sinica, Taipei, Taiwan

    Kai-Min Chung

  2. NTT Social Informatics Laboratories, Tokyo, Japan

    Yu Sasaki

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Dziembowski, S., Jarecki, S., Kedzior, P., Krawczyk, H., Ngo, C.N., Xu, J. (2025). Password-Protected Threshold Signatures. In: Chung, KM., Sasaki, Y. (eds) Advances in Cryptology – ASIACRYPT 2024. ASIACRYPT 2024. Lecture Notes in Computer Science, vol 15486. Springer, Singapore. https://doi.org/10.1007/978-981-96-0891-1_6

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