{"status":"public","publisher":"ACM Press","ec_funded":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","language":[{"iso":"eng"}],"date_published":"2019-06-01T00:00:00Z","related_material":{"record":[{"relation":"dissertation_contains","id":"7896","status":"public"}]},"publication_identifier":{"isbn":["9781450367059"]},"author":[{"last_name":"Choudhuri","first_name":"Arka Rai","full_name":"Choudhuri, Arka Rai"},{"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","first_name":"Krzysztof Z","full_name":"Pietrzak, Krzysztof Z","id":"3E04A7AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9139-1654"},{"first_name":"Alon","last_name":"Rosen","full_name":"Rosen, Alon"},{"full_name":"Rothblum, Guy N.","first_name":"Guy N.","last_name":"Rothblum"}],"date_created":"2019-07-24T09:20:53Z","oa":1,"_id":"6677","title":"Finding a Nash equilibrium is no easier than breaking Fiat-Shamir","abstract":[{"lang":"eng","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)."}],"publication":"Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing  - STOC 2019","quality_controlled":"1","day":"01","scopus_import":"1","year":"2019","doi":"10.1145/3313276.3316400","isi":1,"conference":{"location":"Phoenix, AZ, United States","name":"STOC: Symposium on Theory of Computing","start_date":"2019-06-23","end_date":"2019-06-26"},"month":"06","type":"conference","citation":{"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>.","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.","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>","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>."},"department":[{"_id":"KrPi"}],"publication_status":"published","page":"1103-1114","project":[{"name":"Teaching Old Crypto New Tricks","grant_number":"682815","call_identifier":"H2020","_id":"258AA5B2-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","main_file_link":[{"url":"https://eprint.iacr.org/2019/549","open_access":"1"}],"date_updated":"2023-09-07T13:15:55Z","external_id":{"isi":["000523199100100"]}}