--- _id: '7407' abstract: - lang: eng text: 'Proofs of space (PoS) [Dziembowski et al., CRYPTO''15] are proof systems where a prover can convince a verifier that he "wastes" disk space. PoS were introduced as a more ecological and economical replacement for proofs of work which are currently used to secure blockchains like Bitcoin. In this work we investigate extensions of PoS which allow the prover to embed useful data into the dedicated space, which later can be recovered. Our first contribution is a security proof for the original PoS from CRYPTO''15 in the random oracle model (the original proof only applied to a restricted class of adversaries which can store a subset of the data an honest prover would store). When this PoS is instantiated with recent constructions of maximally depth robust graphs, our proof implies basically optimal security. As a second contribution we show three different extensions of this PoS where useful data can be embedded into the space required by the prover. Our security proof for the PoS extends (non-trivially) to these constructions. We discuss how some of these variants can be used as proofs of catalytic space (PoCS), a notion we put forward in this work, and which basically is a PoS where most of the space required by the prover can be used to backup useful data. Finally we discuss how one of the extensions is a candidate construction for a proof of replication (PoR), a proof system recently suggested in the Filecoin whitepaper. ' alternative_title: - LIPIcs article_processing_charge: No author: - 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: 'Pietrzak KZ. Proofs of catalytic space. In: 10th Innovations in Theoretical Computer Science  Conference (ITCS 2019). Vol 124. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2018:59:1-59:25. doi:10.4230/LIPICS.ITCS.2019.59' apa: 'Pietrzak, K. Z. (2018). Proofs of catalytic space. In 10th Innovations in Theoretical Computer Science  Conference (ITCS 2019) (Vol. 124, p. 59:1-59:25). San Diego, CA, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.ITCS.2019.59' chicago: Pietrzak, Krzysztof Z. “Proofs of Catalytic Space.” In 10th Innovations in Theoretical Computer Science  Conference (ITCS 2019), 124:59:1-59:25. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. https://doi.org/10.4230/LIPICS.ITCS.2019.59. ieee: K. Z. Pietrzak, “Proofs of catalytic space,” in 10th Innovations in Theoretical Computer Science  Conference (ITCS 2019), San Diego, CA, United States, 2018, vol. 124, p. 59:1-59:25. ista: 'Pietrzak KZ. 2018. Proofs of catalytic space. 10th Innovations in Theoretical Computer Science  Conference (ITCS 2019). ITCS: Innovations in theoretical Computer Science Conference, LIPIcs, vol. 124, 59:1-59:25.' mla: Pietrzak, Krzysztof Z. “Proofs of Catalytic Space.” 10th Innovations in Theoretical Computer Science  Conference (ITCS 2019), vol. 124, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 59:1-59:25, doi:10.4230/LIPICS.ITCS.2019.59. short: K.Z. Pietrzak, in:, 10th Innovations in Theoretical Computer Science  Conference (ITCS 2019), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018, p. 59:1-59:25. conference: end_date: 2019-01-12 location: San Diego, CA, United States name: 'ITCS: Innovations in theoretical Computer Science Conference' start_date: 2019-01-10 date_created: 2020-01-30T09:16:05Z date_published: 2018-12-31T00:00:00Z date_updated: 2021-01-12T08:13:26Z day: '31' ddc: - '000' department: - _id: KrPi doi: 10.4230/LIPICS.ITCS.2019.59 ec_funded: 1 file: - access_level: open_access checksum: 5cebb7f7849a3beda898f697d755dd96 content_type: application/pdf creator: dernst date_created: 2020-02-04T08:17:52Z date_updated: 2020-07-14T12:47:57Z file_id: '7443' file_name: 2018_LIPIcs_Pietrzak.pdf file_size: 822884 relation: main_file file_date_updated: 2020-07-14T12:47:57Z has_accepted_license: '1' intvolume: ' 124' language: - iso: eng main_file_link: - open_access: '1' url: https://eprint.iacr.org/2018/194 month: '12' oa: 1 oa_version: Published Version page: 59:1-59:25 project: - _id: 258AA5B2-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '682815' name: Teaching Old Crypto New Tricks publication: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019) publication_identifier: isbn: - 978-3-95977-095-8 issn: - 1868-8969 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Proofs of catalytic space 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: 124 year: '2018' ...