{"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959774000"]},"file_date_updated":"2025-11-04T08:19:02Z","arxiv":1,"project":[{"_id":"34a4ce89-11ca-11ed-8bc3-8cc37fb6e11f","grant_number":"F8512","name":"Security and Privacy by Design for Complex Systems"},{"name":"Security and Privacy by Design for Complex Systems","grant_number":"F8509","_id":"34a34d57-11ca-11ed-8bc3-a2688a8724e1"}],"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":354,"conference":{"start_date":"2025-10-08","name":"AFT: Conference on Advances in Financial Technologies","location":"Pittsburgh, PA, United States","end_date":"2025-10-10"},"intvolume":"       354","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","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.","day":"06","date_published":"2025-10-06T00:00:00Z","date_created":"2025-11-02T23:01:34Z","type":"conference","external_id":{"arxiv":["2508.01448"]},"_id":"20587","article_processing_charge":"Yes","OA_place":"publisher","doi":"10.4230/LIPIcs.AFT.2025.16","corr_author":"1","date_updated":"2025-11-04T08:20:29Z","title":"Nakamoto consensus from multiple resources","abstract":[{"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.","lang":"eng"}],"author":[{"full_name":"Baig, Mirza Ahad","last_name":"Baig","id":"3EDE6DE4-AA5A-11E9-986D-341CE6697425","first_name":"Mirza Ahad"},{"last_name":"Günther","id":"ec98511c-eb8e-11eb-b029-edd25d7271a1","full_name":"Günther, Christoph Ullrich","first_name":"Christoph Ullrich"},{"first_name":"Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","last_name":"Pietrzak","orcid":"0000-0002-9139-1654","full_name":"Pietrzak, Krzysztof Z"}],"quality_controlled":"1","alternative_title":["LIPIcs"],"oa_version":"Published Version","oa":1,"scopus_import":"1","status":"public","language":[{"iso":"eng"}],"ddc":["000"],"citation":{"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>.","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.","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.","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>","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."},"year":"2025","OA_type":"gold","has_accepted_license":"1","main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2025/1410"}],"department":[{"_id":"KrPi"}],"month":"10","publication":"7th Conference on Advances in Financial Technologies","article_number":"16","file":[{"date_updated":"2025-11-04T08:19:02Z","file_size":1061847,"relation":"main_file","date_created":"2025-11-04T08:19:02Z","file_name":"2025_LIPIcsAFT_Baig.pdf","content_type":"application/pdf","creator":"dernst","access_level":"open_access","success":1,"file_id":"20598","checksum":"b638adcd4fbffa77116c35393e165eb7"}]}