---
OA_place: publisher
OA_type: gold
_id: '20587'
abstract:
- lang: eng
  text: "The blocks in the Bitcoin blockchain \"record\" the amount of work W that
    went into creating them through proofs of work. When honest parties control a
    majority of the work, consensus is achieved by picking the chain with the highest
    recorded weight. Resources other than work have been considered to secure such
    longest-chain blockchains. In Chia, blocks record the amount of disk-space S (via
    a proof of space) and sequential computational steps V (through a VDF).\r\nIn
    this paper, we ask what weight functions Γ(S,V,W) (that assign a weight to a block
    as a function of the recorded space, speed, and work) are secure in the sense
    that whenever the weight of the resources controlled by honest parties is larger
    than the weight of adversarial parties, the blockchain is secure against private
    double-spending attacks.\r\nWe completely classify such functions in an idealized
    \"continuous\" model: Γ(S,V,W) is secure against private double-spending attacks
    if and only if it is homogeneous of degree one in the \"timed\" resources V and
    W, i.e., αΓ(S,V,W) = Γ(S,α V, α W). This includes the Bitcoin rule Γ(S,V,W) =
    W and the Chia rule Γ(S,V,W) = S ⋅ V. In a more realistic model where blocks are
    created at discrete time-points, one additionally needs some mild assumptions
    on the dependency on S (basically, the weight should not grow too much if S is
    slightly increased, say linear as in Chia).\r\nOur classification is more general
    and allows various instantiations of the same resource. It provides a powerful
    tool for designing new longest-chain blockchains. E.g., consider combining different
    PoWs to counter centralization, say the Bitcoin PoW W₁ and a memory-hard PoW W₂.
    Previous work suggested to use W₁+W₂ as weight. Our results show that using e.g.,
    √{W₁}⋅ √{W₂} or min{W₁,W₂} are also secure, and we argue that in practice these
    are much better choices."
acknowledgement: "This research was funded in whole or in part by the Austrian Science
  Fund (FWF)\r\n10.55776/F85. For open access purposes, the author has applied a CC
  BY public copyright license\r\nto any author-accepted manuscript version arising
  from this submission."
alternative_title:
- LIPIcs
article_number: '16'
article_processing_charge: Yes
arxiv: 1
author:
- first_name: Mirza Ahad
  full_name: Baig, Mirza Ahad
  id: 3EDE6DE4-AA5A-11E9-986D-341CE6697425
  last_name: Baig
- first_name: Christoph Ullrich
  full_name: Günther, Christoph Ullrich
  id: ec98511c-eb8e-11eb-b029-edd25d7271a1
  last_name: Günther
- first_name: Krzysztof Z
  full_name: Pietrzak, Krzysztof Z
  id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
  last_name: Pietrzak
  orcid: 0000-0002-9139-1654
citation:
  ama: 'Baig MA, Günther CU, Pietrzak KZ. Nakamoto consensus from multiple resources.
    In: <i>7th Conference on Advances in Financial Technologies</i>. Vol 354. Schloss
    Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href="https://doi.org/10.4230/LIPIcs.AFT.2025.16">10.4230/LIPIcs.AFT.2025.16</a>'
  apa: 'Baig, M. A., Günther, C. U., &#38; Pietrzak, K. Z. (2025). Nakamoto consensus
    from multiple resources. In <i>7th Conference on Advances in Financial Technologies</i>
    (Vol. 354). Pittsburgh, PA, United States: Schloss Dagstuhl - Leibniz-Zentrum
    für Informatik. <a href="https://doi.org/10.4230/LIPIcs.AFT.2025.16">https://doi.org/10.4230/LIPIcs.AFT.2025.16</a>'
  chicago: Baig, Mirza Ahad, Christoph Ullrich Günther, and Krzysztof Z Pietrzak.
    “Nakamoto Consensus from Multiple Resources.” In <i>7th Conference on Advances
    in Financial Technologies</i>, Vol. 354. Schloss Dagstuhl - Leibniz-Zentrum für
    Informatik, 2025. <a href="https://doi.org/10.4230/LIPIcs.AFT.2025.16">https://doi.org/10.4230/LIPIcs.AFT.2025.16</a>.
  ieee: M. A. Baig, C. U. Günther, and K. Z. Pietrzak, “Nakamoto consensus from multiple
    resources,” in <i>7th Conference on Advances in Financial Technologies</i>, Pittsburgh,
    PA, United States, 2025, vol. 354.
  ista: 'Baig MA, Günther CU, Pietrzak KZ. 2025. Nakamoto consensus from multiple
    resources. 7th Conference on Advances in Financial Technologies. AFT: Conference
    on Advances in Financial Technologies, LIPIcs, vol. 354, 16.'
  mla: Baig, Mirza Ahad, et al. “Nakamoto Consensus from Multiple Resources.” <i>7th
    Conference on Advances in Financial Technologies</i>, vol. 354, 16, Schloss Dagstuhl
    - Leibniz-Zentrum für Informatik, 2025, doi:<a href="https://doi.org/10.4230/LIPIcs.AFT.2025.16">10.4230/LIPIcs.AFT.2025.16</a>.
  short: M.A. Baig, C.U. Günther, K.Z. Pietrzak, in:, 7th Conference on Advances in
    Financial Technologies, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025.
conference:
  end_date: 2025-10-10
  location: Pittsburgh, PA, United States
  name: 'AFT: Conference on Advances in Financial Technologies'
  start_date: 2025-10-08
corr_author: '1'
date_created: 2025-11-02T23:01:34Z
date_published: 2025-10-06T00:00:00Z
date_updated: 2026-04-15T08:45:18Z
day: '06'
ddc:
- '000'
department:
- _id: KrPi
doi: 10.4230/LIPIcs.AFT.2025.16
external_id:
  arxiv:
  - '2508.01448'
file:
- access_level: open_access
  checksum: b638adcd4fbffa77116c35393e165eb7
  content_type: application/pdf
  creator: dernst
  date_created: 2025-11-04T08:19:02Z
  date_updated: 2025-11-04T08:19:02Z
  file_id: '20598'
  file_name: 2025_LIPIcsAFT_Baig.pdf
  file_size: 1061847
  relation: main_file
  success: 1
file_date_updated: 2025-11-04T08:19:02Z
has_accepted_license: '1'
intvolume: '       354'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://eprint.iacr.org/2025/1410
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 34a4ce89-11ca-11ed-8bc3-8cc37fb6e11f
  grant_number: F8512
  name: Security and Privacy by Design for Complex Systems
- _id: 34a34d57-11ca-11ed-8bc3-a2688a8724e1
  grant_number: F8509
  name: Security and Privacy by Design for Complex Systems
publication: 7th Conference on Advances in Financial Technologies
publication_identifier:
  isbn:
  - '9783959774000'
  issn:
  - 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
related_material:
  record:
  - id: '21651'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Nakamoto consensus from multiple resources
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 354
year: '2025'
...