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Documents authored by Villacis, Juan

Document
DOI: 10.4230/LIPIcs.AFT.2026.5
The Consensus Number of Untraceable Cryptocurrencies

Authors: Christian Cachin, David Lehnherr, Juan Villacis, and François-Xavier Wicht

Published in: LIPIcs, Volume 395, 8th Conference on Advances in Financial Technologies (AFT 2026)

Abstract
Privacy-preserving cryptocurrencies hide which account funds a transfer among a set of candidate accounts, called its masking set. To prevent the hidden account from being spent twice, classical schemes retain the candidates and append a nullifier that marks the spent account without revealing it. Their ledgers therefore grow with every transfer. Constant-state schemes instead consume and replace the entire masking set. Here, we study the synchronization cost of this second design. We introduce the constant untraceable asset transfer (CUAT) object. A CUAT transfer atomically replaces every account in its masking set; hence two transfers with intersecting sets cannot both succeed. We capture this contention by a conflict graph on transfer invocations, whose edges join invocations with intersecting masking sets. In one-round protocols, the relevant sets form a clique at a critical configuration. In general protocols, only sets from opposite valency classes must intersect. Under weak untraceability, which considers one transaction in isolation, CUAT has unbounded consensus number even for one-round protocols. Under strong untraceability, which considers the complete history, accounts in a common masking set must have equal incidence. This condition makes both the one-round consensus power and CUAT’s consensus number grow quadratically with the masking-set size. Cyclic and projective-plane constructions establish the corresponding one-round lower bounds, while a recursive grid construction shows that CUAT’s consensus number is exactly the square of the masking-set size. CUAT is also not starvation-free. The full version studies the complementary linear untraceable asset transfer (LUAT) object, which retains its masking set and records a nullifier. Its state grows, but its consensus number is two for every masking-set size and under either untraceability notion, and it is starvation-free. Thus LUAT pays for untraceability in storage, whereas CUAT pays in synchronization and fairness.
Cite as

Christian Cachin, David Lehnherr, Juan Villacis, and François-Xavier Wicht. The Consensus Number of Untraceable Cryptocurrencies. In 8th Conference on Advances in Financial Technologies (AFT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 395, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cachin_et_al:LIPIcs.AFT.2026.5,
  author =	{Cachin, Christian and Lehnherr, David and Villacis, Juan and Wicht, Fran\c{c}ois-Xavier},
  title =	{{The Consensus Number of Untraceable Cryptocurrencies}},
  booktitle =	{8th Conference on Advances in Financial Technologies (AFT 2026)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-451-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{395},
  editor =	{Kiayias, Aggelos and Kyropoulou, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2026.5},
  URN =		{urn:nbn:de:0030-drops-278593},
  doi =		{10.4230/LIPIcs.AFT.2026.5},
  annote =	{Keywords: Consensus number, untraceability, privacy-preserving cryptocurrencies, wait-freedom, masking sets, concurrent objects}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.8
Weaker Assumptions for Asymmetric Trust

Authors: Ignacio Amores-Sesar, Christian Cachin, Simon Holmgaard Kamp, and Juan Villacis

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
In distributed systems with asymmetric trust, each participant is free to make its own trust assumptions about others, captured by an asymmetric quorum system. This contrasts with ordinary, symmetric quorum systems and threshold models, where trust assumptions are uniformly shared among participants. Fundamental problems like reliable broadcast and consensus are unsolvable in the asymmetric model if quorum systems satisfy only the classical properties of consistency and availability. Existing approaches overcome this by introducing stronger assumptions. We show that some of these assumptions are overly restrictive, so much so that they effectively eliminate the benefits of asymmetric trust. To address this, we propose a new approach to characterize asymmetric problems and, building upon it, present algorithms for reliable broadcast and consensus that require weaker assumptions than previous solutions. Our methods are general and can be extended to other core problems in systems with asymmetric trust.
Cite as

Ignacio Amores-Sesar, Christian Cachin, Simon Holmgaard Kamp, and Juan Villacis. Weaker Assumptions for Asymmetric Trust. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{amoressesar_et_al:LIPIcs.OPODIS.2025.8,
  author =	{Amores-Sesar, Ignacio and Cachin, Christian and Kamp, Simon Holmgaard and Villacis, Juan},
  title =	{{Weaker Assumptions for Asymmetric Trust}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.8},
  URN =		{urn:nbn:de:0030-drops-251812},
  doi =		{10.4230/LIPIcs.OPODIS.2025.8},
  annote =	{Keywords: Asymmetric Trust, Quorum Systems, Reliable Broadcast, Consensus}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.50
Brief Announcement: Weaker Assumptions for Asymmetric Trust

Authors: Christian Cachin and Juan Villacis

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
In protocols with asymmetric trust, each participant is free to make its own trust assumptions about others, captured by an asymmetric quorum system. This contrasts with ordinary, symmetric quorum systems and threshold models, where trust assumptions are uniformly shared among participants. Fundamental problems like reliable broadcast and consensus are unsolvable in the asymmetric model if quorum systems satisfy only the classical properties of consistency and availability. As a result, existing solutions introduce stronger assumptions to circumvent this limitation. We show that some requirements used by state-of-the-art approaches are overly restrictive, so much so that they effectively eliminate the benefits of asymmetric trust. To address this, we propose a new approach to characterize asymmetric problems and, building upon it, present an asymmetric asynchronous unauthenticated reliable broadcast algorithm that significantly weakens the assumptions needed to solve the problem. Our techniques are general and can be readily adapted to other core problems in the asymmetric trust setting.
Cite as

Christian Cachin and Juan Villacis. Brief Announcement: Weaker Assumptions for Asymmetric Trust. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 50:1-50:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cachin_et_al:LIPIcs.DISC.2025.50,
  author =	{Cachin, Christian and Villacis, Juan},
  title =	{{Brief Announcement: Weaker Assumptions for Asymmetric Trust}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{50:1--50:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.50},
  URN =		{urn:nbn:de:0030-drops-248667},
  doi =		{10.4230/LIPIcs.DISC.2025.50},
  annote =	{Keywords: Asymmetric Trust, Quorum Systems, Reliable Broadcast}
}

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