{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T21:06:05Z","timestamp":1757624765346,"version":"3.44.0"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783032018779"},{"type":"electronic","value":"9783032018786"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-032-01878-6_8","type":"book-chapter","created":{"date-parts":[[2025,8,16]],"date-time":"2025-08-16T18:08:50Z","timestamp":1755367730000},"page":"237-268","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["How to\u00a0Model Unitary Oracles"],"prefix":"10.1007","author":[{"given":"Mark","family":"Zhandry","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,17]]},"reference":[{"issue":"6","key":"8_CR1","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/JHEP06(2024)155","volume":"2024","author":"C Akers","year":"2024","unstructured":"Akers, C., Engelhardt, N., Harlow, D., Penington, G., Vardhan, S.: The black hole interior from non-isometric codes and complexity. J. High Energy Phys. 2024(6), 155 (2024)","journal-title":"J. High Energy Phys."},{"issue":"7","key":"8_CR2","doi-asserted-by":"publisher","first-page":"129","DOI":"10.4086\/toc.2007.v003a007","volume":"3","author":"S Aaronson","year":"2007","unstructured":"Aaronson, S., Kuperberg, G.: Quantum versus classical proofs and advice. Theory Comput. 3(7), 129\u2013157 (2007)","journal-title":"Theory Comput."},{"issue":"5","key":"8_CR3","doi-asserted-by":"publisher","first-page":"1510","DOI":"10.1137\/S0097539796300933","volume":"26","author":"CH Bennett","year":"1997","unstructured":"Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26(5), 1510\u20131523 (1997)","journal-title":"SIAM J. Comput."},{"key":"8_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/978-3-642-25385-0_3","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2011","author":"D Boneh","year":"2011","unstructured":"Boneh, D., Dagdelen, \u00d6., Fischlin, M., Lehmann, A., Schaffner, C., Zhandry, M.: Random oracles in a quantum world. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 41\u201369. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-25385-0_3"},{"key":"8_CR5","unstructured":"Bostanci, J., Efron, Y., Metger, T., Poremba, A., Qian, L., Yuen, H.: Unitary complexity and the uhlmann transformation problem (2023)"},{"key":"8_CR6","unstructured":"Bouland, A., Fefferman, B., Vazirani, U.V.: Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS\/CFT duality (abstract). In: Vidick, T. (ed.) ITCS 2020. LIPIcs, vol. 151, pp. 63:1\u201363:2 (2020)"},{"key":"8_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-44647-8_1","volume-title":"Advances in Cryptology \u2014 CRYPTO 2001","author":"B Barak","year":"2001","unstructured":"Barak, B., et al.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1\u201318. Springer, Heidelberg (2001). https:\/\/doi.org\/10.1007\/3-540-44647-8_1"},{"key":"8_CR8","unstructured":"Bouland, A., Giurgica-Tiron, T.: Efficient universal quantum compilation: an inverse-free Solovay-Kitaev algorithm (2021)"},{"key":"8_CR9","doi-asserted-by":"crossref","unstructured":"Brassard, G., H\u00f8yer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation (2002)","DOI":"10.1090\/conm\/305\/05215"},{"key":"8_CR10","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/978-3-031-78017-2_2","volume-title":"TCC 2024, Part II","author":"Z Brakerski","year":"2024","unstructured":"Brakerski, Z., Magrafta, N.: Real-valued somewhat-pseudorandom unitaries. In: Boyle, E., Mahmoody, M. (eds.) TCC 2024, Part II. LNCS, vol. 15365, pp. 36\u201359. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-78017-2_2"},{"key":"8_CR11","doi-asserted-by":"crossref","unstructured":"Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Denning, D.E., Pyle, R., Ganesan, R., Sandhu, R.S., Ashby, V. (eds.) ACM CCS 1993, pp. 62\u201373. ACM Press (1993)","DOI":"10.1145\/168588.168596"},{"key":"8_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/3-540-38424-3_37","volume-title":"Advances in Cryptology-CRYPT0\u2019 90","author":"R Cleve","year":"1991","unstructured":"Cleve, R.: Complexity theoretic issues concerning block ciphers related to D.E.S. In: Menezes, A.J., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 531\u2013544. Springer, Heidelberg (1991). https:\/\/doi.org\/10.1007\/3-540-38424-3_37"},{"key":"8_CR13","doi-asserted-by":"crossref","unstructured":"Chiesa, A., Ma, F., Spooner, N., Zhandry, M.: Post-quantum succinct arguments: Breaking the quantum rewinding barrier. In: 62nd FOCS, pp. 49\u201358. IEEE Computer Society Press (2022)","DOI":"10.1109\/FOCS52979.2021.00014"},{"key":"8_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-540-85174-5_1","volume-title":"Advances in Cryptology \u2013 CRYPTO 2008","author":"J-S Coron","year":"2008","unstructured":"Coron, J.-S., Patarin, J., Seurin, Y.: The random oracle model and the ideal cipher model are equivalent. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 1\u201320. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-85174-5_1"},{"key":"8_CR15","doi-asserted-by":"crossref","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th FOCS, pp. 40\u201349. IEEE Computer Society Press (2013)","DOI":"10.1109\/FOCS.2013.13"},{"key":"8_CR16","doi-asserted-by":"crossref","unstructured":"Holenstein, T., K\u00fcnzler, R., Tessaro, S.: The equivalence of the random oracle model and the ideal cipher model, revisited. In: Fortnow, L., Vadhan, S.P. (eds.) 43rd ACM STOC, pp. 89\u201398. ACM Press (2011)","DOI":"10.1145\/1993636.1993650"},{"issue":"2","key":"8_CR17","doi-asserted-by":"publisher","first-page":"762","DOI":"10.1137\/070704770","volume":"30","author":"ICF Ipsen","year":"2008","unstructured":"Ipsen, I.C.F., Rehman, R.: Perturbation bounds for determinants and characteristic polynomials. SIAM J. Matrix Anal. Appl. 30(2), 762\u2013776 (2008)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"8_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/978-3-319-96878-0_5","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"Z Ji","year":"2018","unstructured":"Ji, Z., Liu, Y.-K., Song, F.: Pseudorandom quantum states. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part III. LNCS, vol. 10993, pp. 126\u2013152. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_5"},{"issue":"6","key":"8_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/JHEP06(2020)031","volume":"2020","author":"I Kim","year":"2020","unstructured":"Kim, I., Tang, E., Preskill, J.: The ghost in the radiation: robust encodings of the black hole interior. J. High Energy Phys. 2020(6), 1\u201365 (2020). https:\/\/doi.org\/10.1007\/JHEP06(2020)031","journal-title":"J. High Energy Phys."},{"key":"8_CR20","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-031-78017-2_1","volume-title":"TCC 2024, Part II","author":"L Chuhan","year":"2024","unstructured":"Chuhan, L., Qin, M., Song, F., Yao, P., Zhao, M.: Quantum pseudorandom scramblers. In: Boyle, E., Mahmoody, M. (eds.) TCC 2024, Part II. LNCS, vol. 15365, pp. 3\u201335. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-78017-2_1"},{"key":"8_CR21","doi-asserted-by":"crossref","unstructured":"Meckes, E.S.: The Random Matrix Theory of the Classical Compact Groups. Cambridge Tracts in Mathematics. Cambridge University Press (2019)","DOI":"10.1017\/9781108303453"},{"key":"8_CR22","doi-asserted-by":"crossref","unstructured":"Ma, F., Huang, H.-Y.: How to construct random unitaries. In: STOC 2025 (2025)","DOI":"10.1145\/3717823.3718254"},{"key":"8_CR23","doi-asserted-by":"crossref","unstructured":"Metger, T., Poremba, A., Sinha, M., Yuen, H.: Simple constructions of linear-depth t-designs and pseudorandom unitaries. In: 65th FOCS, pp. 485\u2013492. IEEE Computer Society Press (2024)","DOI":"10.1109\/FOCS61266.2024.00038"},{"key":"8_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/978-3-540-24638-1_2","volume-title":"Theory of Cryptography","author":"U Maurer","year":"2004","unstructured":"Maurer, U., Renner, R., Holenstein, C.: Indifferentiability, impossibility results on reductions, and applications to the random oracle methodology. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 21\u201339. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-24638-1_2"},{"key":"8_CR25","doi-asserted-by":"crossref","unstructured":"Mosca, M., Zalka, C.: Exact quantum Fourier transforms and discrete logarithm algorithms (2003)","DOI":"10.1142\/S0219749904000109"},{"key":"8_CR26","unstructured":"Poremba, A., Ragavan, S., Vaikuntanathan, V.: Cloning games, black holes and cryptography. Cryptology ePrint Archive, Report 2024\/1826 (2024)"},{"key":"8_CR27","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1137\/0220053","volume":"20","author":"S Toda","year":"1991","unstructured":"Toda, S.: PP is as hard as the polynomial-time hierarchy. SIAM J. Comput. 20, 865\u2013877 (1991)","journal-title":"SIAM J. Comput."},{"key":"8_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/978-3-642-29011-4_10","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"D Unruh","year":"2012","unstructured":"Unruh, D.: Quantum proofs of knowledge. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 135\u2013152. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-29011-4_10"},{"key":"8_CR29","unstructured":"Yang, L., Engelhardt, N.: The complexity of learning (pseudo)random dynamics of black holes and other chaotic systems (2023)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2025"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-01878-6_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T15:10:55Z","timestamp":1757430655000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-01878-6_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783032018779","9783032018786"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-01878-6_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"17 August 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CRYPTO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Cryptology Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Santa Barbara, CA","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 August 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 August 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"45","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"crypto2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/crypto.iacr.org\/2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}