[{"arxiv":1,"abstract":[{"lang":"eng","text":"It is impossible to deterministically solve wait-free consensus in an asynchronous system. The classic proof uses a valency argument, which constructs an infinite execution by repeatedly extending a finite execution. We introduce extension-based proofs, a class of impossibility proofs that are modelled as an interaction between a prover and a protocol and that include valency arguments.\r\n\r\nUsing proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve k-set agreement among n > k ≥ 2 processes in a wait-free manner. However, it was unknown whether proofs based on simpler techniques were possible. We show that this impossibility result cannot be obtained by an extension-based proof and, hence, extension-based proofs are limited in power."}],"publisher":"ACM Press","publication":"Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing","title":"Why extension-based proofs fail","department":[{"_id":"DaAl"}],"date_created":"2019-07-24T09:13:05Z","oa_version":"Preprint","external_id":{"arxiv":["1811.01421"],"isi":["000523199100089"]},"oa":1,"status":"public","publication_identifier":{"isbn":["9781450367059"]},"citation":{"apa":"Alistarh, D.-A., Aspnes, J., Ellen, F., Gelashvili, R., &#38; Zhu, L. (2019). Why extension-based proofs fail. In <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing</i> (pp. 986–996). Phoenix, AZ, United States: ACM Press. <a href=\"https://doi.org/10.1145/3313276.3316407\">https://doi.org/10.1145/3313276.3316407</a>","chicago":"Alistarh, Dan-Adrian, James Aspnes, Faith Ellen, Rati Gelashvili, and Leqi Zhu. “Why Extension-Based Proofs Fail.” In <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing</i>, 986–96. ACM Press, 2019. <a href=\"https://doi.org/10.1145/3313276.3316407\">https://doi.org/10.1145/3313276.3316407</a>.","ieee":"D.-A. Alistarh, J. Aspnes, F. Ellen, R. Gelashvili, and L. Zhu, “Why extension-based proofs fail,” in <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing</i>, Phoenix, AZ, United States, 2019, pp. 986–996.","short":"D.-A. Alistarh, J. Aspnes, F. Ellen, R. Gelashvili, L. Zhu, in:, Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, ACM Press, 2019, pp. 986–996.","ista":"Alistarh D-A, Aspnes J, Ellen F, Gelashvili R, Zhu L. 2019. Why extension-based proofs fail. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. STOC: Symposium on Theory of Computing, 986–996.","mla":"Alistarh, Dan-Adrian, et al. “Why Extension-Based Proofs Fail.” <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing</i>, ACM Press, 2019, pp. 986–96, doi:<a href=\"https://doi.org/10.1145/3313276.3316407\">10.1145/3313276.3316407</a>.","ama":"Alistarh D-A, Aspnes J, Ellen F, Gelashvili R, Zhu L. Why extension-based proofs fail. In: <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing</i>. ACM Press; 2019:986-996. doi:<a href=\"https://doi.org/10.1145/3313276.3316407\">10.1145/3313276.3316407</a>"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","type":"conference","page":"986-996","year":"2019","_id":"6676","article_processing_charge":"No","doi":"10.1145/3313276.3316407","related_material":{"record":[{"id":"14364","status":"public","relation":"later_version"}]},"date_updated":"2023-12-13T12:28:28Z","date_published":"2019-06-01T00:00:00Z","author":[{"full_name":"Alistarh, Dan-Adrian","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87","first_name":"Dan-Adrian","last_name":"Alistarh","orcid":"0000-0003-3650-940X"},{"full_name":"Aspnes, James","last_name":"Aspnes","first_name":"James"},{"first_name":"Faith","last_name":"Ellen","full_name":"Ellen, Faith"},{"full_name":"Gelashvili, Rati","first_name":"Rati","last_name":"Gelashvili"},{"full_name":"Zhu, Leqi","last_name":"Zhu","first_name":"Leqi"}],"quality_controlled":"1","scopus_import":"1","conference":{"location":"Phoenix, AZ, United States","start_date":"2019-06-23","name":"STOC: Symposium on Theory of Computing","end_date":"2019-06-26"},"day":"01","month":"06","isi":1,"language":[{"iso":"eng"}],"publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1811.01421","open_access":"1"}]},{"day":"01","isi":1,"month":"06","language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"258AA5B2-B435-11E9-9278-68D0E5697425","name":"Teaching Old Crypto New Tricks","grant_number":"682815"}],"main_file_link":[{"url":"https://eprint.iacr.org/2019/549","open_access":"1"}],"publication_status":"published","date_published":"2019-06-01T00:00:00Z","author":[{"full_name":"Choudhuri, Arka Rai","first_name":"Arka Rai","last_name":"Choudhuri"},{"full_name":"Hubáček, Pavel","first_name":"Pavel","last_name":"Hubáček"},{"first_name":"Chethan","last_name":"Kamath Hosdurg","full_name":"Kamath Hosdurg, Chethan","id":"4BD3F30E-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pietrzak","orcid":"0000-0002-9139-1654","first_name":"Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","full_name":"Pietrzak, Krzysztof Z"},{"last_name":"Rosen","first_name":"Alon","full_name":"Rosen, Alon"},{"last_name":"Rothblum","first_name":"Guy N.","full_name":"Rothblum, Guy N."}],"article_processing_charge":"No","date_updated":"2023-09-07T13:15:55Z","doi":"10.1145/3313276.3316400","related_material":{"record":[{"id":"7896","status":"public","relation":"dissertation_contains"}]},"scopus_import":"1","quality_controlled":"1","conference":{"location":"Phoenix, AZ, United States","start_date":"2019-06-23","name":"STOC: Symposium on Theory of Computing","end_date":"2019-06-26"},"oa":1,"status":"public","external_id":{"isi":["000523199100100"]},"citation":{"ama":"Choudhuri AR, Hubáček P, Kamath Hosdurg C, Pietrzak KZ, Rosen A, Rothblum GN. Finding a Nash equilibrium is no easier than breaking Fiat-Shamir. In: <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019</i>. ACM Press; 2019:1103-1114. doi:<a href=\"https://doi.org/10.1145/3313276.3316400\">10.1145/3313276.3316400</a>","short":"A.R. Choudhuri, P. Hubáček, C. Kamath Hosdurg, K.Z. Pietrzak, A. Rosen, G.N. Rothblum, in:, Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019, ACM Press, 2019, pp. 1103–1114.","mla":"Choudhuri, Arka Rai, et al. “Finding a Nash Equilibrium Is No Easier than Breaking Fiat-Shamir.” <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019</i>, ACM Press, 2019, pp. 1103–14, doi:<a href=\"https://doi.org/10.1145/3313276.3316400\">10.1145/3313276.3316400</a>.","ista":"Choudhuri AR, Hubáček P, Kamath Hosdurg C, Pietrzak KZ, Rosen A, Rothblum GN. 2019. Finding a Nash equilibrium is no easier than breaking Fiat-Shamir. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019. STOC: Symposium on Theory of Computing, 1103–1114.","ieee":"A. R. Choudhuri, P. Hubáček, C. Kamath Hosdurg, K. Z. Pietrzak, A. Rosen, and G. N. Rothblum, “Finding a Nash equilibrium is no easier than breaking Fiat-Shamir,” in <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019</i>, Phoenix, AZ, United States, 2019, pp. 1103–1114.","chicago":"Choudhuri, Arka Rai, Pavel Hubáček, Chethan Kamath Hosdurg, Krzysztof Z Pietrzak, Alon Rosen, and Guy N. Rothblum. “Finding a Nash Equilibrium Is No Easier than Breaking Fiat-Shamir.” In <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019</i>, 1103–14. ACM Press, 2019. <a href=\"https://doi.org/10.1145/3313276.3316400\">https://doi.org/10.1145/3313276.3316400</a>.","apa":"Choudhuri, A. R., Hubáček, P., Kamath Hosdurg, C., Pietrzak, K. Z., Rosen, A., &#38; Rothblum, G. N. (2019). Finding a Nash equilibrium is no easier than breaking Fiat-Shamir. In <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019</i> (pp. 1103–1114). Phoenix, AZ, United States: ACM Press. <a href=\"https://doi.org/10.1145/3313276.3316400\">https://doi.org/10.1145/3313276.3316400</a>"},"publication_identifier":{"isbn":["9781450367059"]},"page":"1103-1114","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","type":"conference","_id":"6677","year":"2019","abstract":[{"text":"The Fiat-Shamir heuristic transforms a public-coin interactive proof into a non-interactive argument, by replacing the verifier with a cryptographic hash function that is applied to the protocol’s transcript. Constructing hash functions for which this transformation is sound is a central and long-standing open question in cryptography.\r\n\r\nWe show that solving the END−OF−METERED−LINE problem is no easier than breaking the soundness of the Fiat-Shamir transformation when applied to the sumcheck protocol. In particular, if the transformed protocol is sound, then any hard problem in #P gives rise to a hard distribution in the class CLS, which is contained in PPAD. Our result opens up the possibility of sampling moderately-sized games for which it is hard to find a Nash equilibrium, by reducing the inversion of appropriately chosen one-way functions to #SAT.\r\n\r\nOur main technical contribution is a stateful incrementally verifiable procedure that, given a SAT instance over n variables, counts the number of satisfying assignments. This is accomplished via an exponential sequence of small steps, each computable in time poly(n). Incremental verifiability means that each intermediate state includes a sumcheck-based proof of its correctness, and the proof can be updated and verified in time poly(n).","lang":"eng"}],"publication":"Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019","title":"Finding a Nash equilibrium is no easier than breaking Fiat-Shamir","department":[{"_id":"KrPi"}],"publisher":"ACM Press","date_created":"2019-07-24T09:20:53Z","ec_funded":1,"oa_version":"Preprint"}]