{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T07:08:00Z","timestamp":1772867280876,"version":"3.50.1"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T00:00:00Z","timestamp":1718323200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T00:00:00Z","timestamp":1718323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["U23B2002"],"award-info":[{"award-number":["U23B2002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62072207"],"award-info":[{"award-number":["62072207"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-024-04424-8","type":"journal-article","created":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T06:02:20Z","timestamp":1718344940000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Breaking permutation-based pseudorandom cryptographic schemes using distributed exact quantum algorithms"],"prefix":"10.1007","volume":"23","author":[{"given":"Ping","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Yiyuan","family":"Luo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,14]]},"reference":[{"issue":"5","key":"4424_CR1","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1137\/S0097539795293172","volume":"26","author":"PW Shor","year":"1997","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484\u20131509 (1997). https:\/\/doi.org\/10.1137\/S0097539795293172","journal-title":"SIAM J. Comput."},{"issue":"3","key":"4424_CR2","doi-asserted-by":"publisher","first-page":"1633","DOI":"10.1103\/PhysRevA.58.R1633","volume":"58","author":"D Collins","year":"1998","unstructured":"Collins, D., Kim, K., Holton, W.: Deutsch\u2013Jozsa algorithm as a test of quantum computation. Phys. Rev. A 58(3), 1633 (1998). https:\/\/doi.org\/10.1103\/PhysRevA.58.R1633","journal-title":"Phys. Rev. A"},{"issue":"5","key":"4424_CR3","doi-asserted-by":"publisher","first-page":"1161","DOI":"10.1007\/s10623-018-0510-5","volume":"87","author":"H Xie","year":"2019","unstructured":"Xie, H., Yang, L.: Using Bernstein\u2013Vazirani algorithm to attack block ciphers. Des. Codes Cryptogr. 87(5), 1161\u20131182 (2019). https:\/\/doi.org\/10.1007\/s10623-018-0510-5","journal-title":"Des. Codes Cryptogr."},{"key":"4424_CR4","doi-asserted-by":"publisher","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Miller, G.L. (ed.) Proceedings of the Twenty-Eighth Annual ACM symposium on the theory of computing, Philadelphia, Pennsylvania, USA, May 22-24, 1996, pp. 212\u2013219. ACM, New York (1996). https:\/\/doi.org\/10.1145\/237814.237866","DOI":"10.1145\/237814.237866"},{"issue":"5","key":"4424_CR5","doi-asserted-by":"publisher","first-page":"1474","DOI":"10.1137\/S0097539796298637","volume":"26","author":"DR Simon","year":"1997","unstructured":"Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474\u20131483 (1997). https:\/\/doi.org\/10.1137\/S0097539796298637","journal-title":"SIAM J. Comput."},{"issue":"15","key":"4424_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.103.150502","volume":"103","author":"AW Harrow","year":"2009","unstructured":"Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103(15), 150502 (2009). https:\/\/doi.org\/10.1103\/PhysRevLett.103.150502","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"4424_CR7","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1137\/S0097539703436345","volume":"35","author":"G Kuperberg","year":"2005","unstructured":"Kuperberg, G.: A subexponential-time quantum algorithm for the dihedral hidden subgroup problem. SIAM J. Comput. 35(1), 170\u2013188 (2005). https:\/\/doi.org\/10.1137\/S0097539703436345","journal-title":"SIAM J. Comput."},{"issue":"2","key":"4424_CR8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.97.022304","volume":"97","author":"Z Wang","year":"2018","unstructured":"Wang, Z., Hadfield, S., Jiang, Z., Rieffel, E.G.: Quantum approximate optimization algorithm for maxcut: a fermionic view. Phys. Rev. A 97(2), 022304 (2018). https:\/\/doi.org\/10.1103\/PhysRevA.97.022304","journal-title":"Phys. Rev. A"},{"issue":"9","key":"4424_CR9","doi-asserted-by":"publisher","first-page":"1889","DOI":"10.1103\/PhysRevLett.86.1889","volume":"86","author":"YS Weinstein","year":"2001","unstructured":"Weinstein, Y.S., Pravia, M., Fortunato, E., Lloyd, S., Cory, D.G.: Implementation of the quantum Fourier transform. Phys. Rev. Lett. 86(9), 1889 (2001). https:\/\/doi.org\/10.1103\/PhysRevLett.86.1889","journal-title":"Phys. Rev. Lett."},{"key":"4424_CR10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cosrev.2021.100419","volume":"41","author":"K Kadian","year":"2021","unstructured":"Kadian, K., Garhwal, S., Kumar, A.: Quantum walk and its application domains: a systematic review. Comput. Sci. Rev. 41, 100419 (2021). https:\/\/doi.org\/10.1016\/j.cosrev.2021.100419","journal-title":"Comput. Sci. Rev."},{"key":"4424_CR11","doi-asserted-by":"publisher","unstructured":"Leander, G., May, A.: Grover meets simon - quantumly attacking the fx-construction. In: Takagi, T., Peyrin, T. (eds.) Advances in vryptology\u2014ASIACRYPT 2017\u201423rd international conference on the theory and applications of cryptology and information security, Hong Kong, China, December 3\u20137, 2017, proceedings, Part II. Lecture notes in computer science, vol. 10625, pp. 161\u2013178. Springer, Heidelberg (2017). https:\/\/doi.org\/10.1007\/978-3-319-70697-9_6","DOI":"10.1007\/978-3-319-70697-9_6"},{"issue":"10","key":"4424_CR12","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1007\/s11128-021-03256-0","volume":"20","author":"B Zhou","year":"2021","unstructured":"Zhou, B., Yuan, Z.: Quantum key-recovery attack on Feistel constructions: Bernstein\u2013Vazirani meet grover algorithm. Quantum Inf. Process. 20(10), 330 (2021). https:\/\/doi.org\/10.1007\/s11128-021-03256-0","journal-title":"Quantum Inf. Process."},{"key":"4424_CR13","unstructured":"Li, H., Qiu, D., Luo, L.: Distributed Deutsch\u2013Jozsa algorithm. Available at SSRN 4698889"},{"key":"4424_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2024.114461","author":"D Qiu","year":"2024","unstructured":"Qiu, D., Luo, L., Xiao, L.: Distributed Grover\u2019s algorithm. Theoret. Comput. Sci. (2024). https:\/\/doi.org\/10.1016\/j.tcs.2024.114461","journal-title":"Theoret. Comput. Sci."},{"issue":"3","key":"4424_CR15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.106.032417","volume":"106","author":"J Tan","year":"2022","unstructured":"Tan, J., Xiao, L., Qiu, D., Luo, L., Mateus, P.: Distributed quantum algorithm for Simon\u2019s problem. Phys. Rev. A 106(3), 032417 (2022). https:\/\/doi.org\/10.1103\/PhysRevA.106.032417","journal-title":"Phys. Rev. A"},{"key":"4424_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2023.129209","volume":"629","author":"X Zhou","year":"2023","unstructured":"Zhou, X., Qiu, D., Luo, L.: Distributed Bernstein\u2013Vazirani algorithm. Physica A 629, 129209 (2023). https:\/\/doi.org\/10.1016\/j.physa.2023.129209","journal-title":"Physica A"},{"issue":"5","key":"4424_CR17","doi-asserted-by":"publisher","first-page":"51305","DOI":"10.1007\/s11467-023-1327-x","volume":"18","author":"X Zhou","year":"2023","unstructured":"Zhou, X., Qiu, D., Luo, L.: Distributed exact grover\u2019s algorithm. Front. Phys. 18(5), 51305 (2023). https:\/\/doi.org\/10.1007\/s11467-023-1327-x","journal-title":"Front. Phys."},{"key":"4424_CR18","doi-asserted-by":"publisher","unstructured":"Li, H., Qiu, D., Luo, L.: Distributed exact quantum algorithms for deutsch-jozsa problem. arXiv:2303.10663 (2023). https:\/\/doi.org\/10.48550\/arXiv.2303.10663","DOI":"10.48550\/arXiv.2303.10663"},{"key":"4424_CR19","doi-asserted-by":"publisher","unstructured":"Li, H., Qiu, D., Luo, L., Paulo, M.: Exact distributed quantum algorithm for generalized simon\u2019s problem. arXiv:2307.14315 (2023). https:\/\/doi.org\/10.48550\/arXiv.2307.14315","DOI":"10.48550\/arXiv.2307.14315"},{"issue":"2","key":"4424_CR20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.64.022307","volume":"64","author":"G-L Long","year":"2001","unstructured":"Long, G.-L.: Grover algorithm with zero theoretical failure rate. Phys. Rev. A 64(2), 022307 (2001). https:\/\/doi.org\/10.1103\/PhysRevA.64.022307","journal-title":"Phys. Rev. A"},{"key":"4424_CR21","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1090\/conm\/305\/05215","volume":"305","author":"G Brassard","year":"2002","unstructured":"Brassard, G., Hoyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. Contemp. Math. 305, 53\u201374 (2002)","journal-title":"Contemp. Math."},{"key":"4424_CR22","doi-asserted-by":"publisher","unstructured":"Guo, T., Wang, P., Hu, L., Ye, D.: Attacks on beyond-birthday-bound macs in the quantum setting. In: Cheon, J.H., Tillich, J. (eds.) Post-quantum cryptography\u201412th international workshop, PQCrypto 2021, Daejeon, South Korea, July 20-22, 2021, Proceedings. lecture notes in computer science, vol. 12841, pp. 421\u2013441. Springer, Heidelberg (2021). https:\/\/doi.org\/10.1007\/978-3-030-81293-5_22","DOI":"10.1007\/978-3-030-81293-5_22"},{"key":"4424_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.compeleceng.2022.108122","volume":"101","author":"AK Malviya","year":"2022","unstructured":"Malviya, A.K., Tiwari, N., Chawla, M.: Quantum cryptanalytic attacks of symmetric ciphers: a review. Comput. Electr. Eng. 101, 108122 (2022). https:\/\/doi.org\/10.1016\/j.compeleceng.2022.108122","journal-title":"Comput. Electr. Eng."},{"issue":"1","key":"4424_CR24","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1587\/transfun.E102.A.27","volume":"102","author":"A Hosoyamada","year":"2019","unstructured":"Hosoyamada, A., Aoki, K.: On quantum related-key attacks on iterated even-mansour ciphers. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 102(1), 27\u201334 (2019). https:\/\/doi.org\/10.1587\/transfun.E102.A.27","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"4424_CR25","doi-asserted-by":"publisher","unstructured":"Kaplan, M., Leurent, G., Leverrier, A., Naya-Plasencia, M.: Breaking symmetric cryptosystems using quantum period finding. In: Robshaw, M., Katz, J. (eds.) Advances in Cryptology\u2014CRYPTO 2016\u201436th annual international cryptology conference, Santa Barbara, CA, USA, August 14-18, 2016, proceedings, Part II. lecture notes in computer science, vol. 9815, pp. 207\u2013237. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53008-5_8","DOI":"10.1007\/978-3-662-53008-5_8"},{"issue":"3","key":"4424_CR26","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s001459900025","volume":"10","author":"S Even","year":"1997","unstructured":"Even, S., Mansour, Y.: A construction of a cipher from a single pseudorandom permutation. J. Cryptol. 10(3), 151\u2013162 (1997). https:\/\/doi.org\/10.1007\/s001459900025","journal-title":"J. Cryptol."},{"key":"4424_CR27","doi-asserted-by":"publisher","unstructured":"Cogliati, B., Lampe, R., Seurin, Y.: Tweaking even-mansour ciphers. In: Gennaro, R., Robshaw, M. (eds.) Advances in cryptology\u2014CRYPTO 2015\u201435th annual cryptology conference, Santa Barbara, CA, USA, August 16-20, 2015, proceedings, Part I. Lecture notes in computer science, vol. 9215, pp. 189\u2013208. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-47989-6_9","DOI":"10.1007\/978-3-662-47989-6_9"},{"issue":"12","key":"4424_CR28","doi-asserted-by":"publisher","first-page":"2703","DOI":"10.1007\/S10623-018-0470-9","volume":"86","author":"B Cogliati","year":"2018","unstructured":"Cogliati, B., Seurin, Y.: Analysis of the single-permutation encrypted Davies\u2013Meyer construction. Des. Codes Cryptogr. 86(12), 2703\u20132723 (2018). https:\/\/doi.org\/10.1007\/S10623-018-0470-9","journal-title":"Des. Codes Cryptogr."},{"key":"4424_CR29","doi-asserted-by":"publisher","unstructured":"Zou, J., Wei, Z., Sun, S., Liu, X., Wu, W.: Quantum circuit implementations of AES with fewer qubits. In: Moriai, S., Wang, H. (eds.) Advances in Cryptology\u2014ASIACRYPT 2020\u201426th international conference on the theory and application of cryptology and information security, Daejeon, South Korea, December 7-11, 2020, proceedings, Part II. Lecture notes in computer science, vol. 12492, pp. 697\u2013726. Springer, Heidelberg (2020). https:\/\/doi.org\/10.1007\/978-3-030-64834-3_24","DOI":"10.1007\/978-3-030-64834-3_24"},{"key":"4424_CR30","doi-asserted-by":"publisher","first-page":"1028014","DOI":"10.3389\/fphy.2022.1028014\/full","volume":"10","author":"B Cai","year":"2022","unstructured":"Cai, B., Gao, F., Leander, G.: Quantum attacks on two-round even-mansour. Front. Phys. 10, 1028014 (2022). https:\/\/doi.org\/10.3389\/fphy.2022.1028014\/full","journal-title":"Front. Phys."},{"key":"4424_CR31","doi-asserted-by":"publisher","first-page":"213244","DOI":"10.1109\/ACCESS.2020.3039167","volume":"8","author":"S Cho","year":"2020","unstructured":"Cho, S., Kim, A., Choi, D., Choi, B., Seo, S.: Quantum modular multiplication. IEEE Access 8, 213244\u2013213252 (2020). https:\/\/doi.org\/10.1109\/ACCESS.2020.3039167","journal-title":"IEEE Access"},{"key":"4424_CR32","doi-asserted-by":"publisher","unstructured":"Chen, Y.L., Lambooij, E., Mennink, B.: How to build pseudorandom functions from public random permutations. In: Boldyreva, A., Micciancio, D. (eds.) Advances in Cryptology\u2014CRYPTO 2019\u201439th annual international cryptology conference, Santa Barbara, CA, USA, August 18-22, 2019, Proceedings, Part I. Lecture Notes in Computer Science, vol. 11692, pp. 266\u2013293. Springer, Heidelberg (2019). https:\/\/doi.org\/10.1007\/978-3-030-26948-7_10","DOI":"10.1007\/978-3-030-26948-7_10"},{"issue":"4","key":"4424_CR33","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1007\/S00145-018-9295-Y","volume":"31","author":"S Chen","year":"2018","unstructured":"Chen, S., Lampe, R., Lee, J., Seurin, Y., Steinberger, J.P.: Minimizing the two-round even-mansour cipher. J. Cryptol. 31(4), 1064\u20131119 (2018). https:\/\/doi.org\/10.1007\/S00145-018-9295-Y","journal-title":"J. Cryptol."},{"issue":"2","key":"4424_CR34","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.ipl.2021.106172","volume":"2021","author":"A Dutta","year":"2021","unstructured":"Dutta, A., Nandi, M., Talnikar, S.: Permutation based EDM: an inverse free BBB secure PRF. IACR Trans. Symmetric Cryptol. 2021(2), 31\u201370 (2021). https:\/\/doi.org\/10.1016\/j.ipl.2021.106172","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"4424_CR35","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2021.106172","volume":"173","author":"K Shinagawa","year":"2022","unstructured":"Shinagawa, K., Iwata, T.: Quantum attacks on sum of even-mansour pseudorandom functions. Inf. Process. Lett. 173, 106172 (2022). https:\/\/doi.org\/10.1016\/j.ipl.2021.106172","journal-title":"Inf. Process. Lett."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04424-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-024-04424-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04424-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T11:30:30Z","timestamp":1720006230000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-024-04424-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,14]]},"references-count":35,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["4424"],"URL":"https:\/\/doi.org\/10.1007\/s11128-024-04424-8","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,14]]},"assertion":[{"value":"12 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no Conflict of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"239"}}