{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T05:47:40Z","timestamp":1782712060154,"version":"3.54.5"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100031839","name":"Korea Research Institute for Defense Technology Planning and Advancement","doi-asserted-by":"publisher","award":["KRIT-CT-24-001"],"award-info":[{"award-number":["KRIT-CT-24-001"]}],"id":[{"id":"10.13039\/100031839","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002642","name":"Korea University","doi-asserted-by":"crossref","award":["K2511691 and K2511701"],"award-info":[{"award-number":["K2511691 and K2511701"]}],"id":[{"id":"10.13039\/501100002642","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s10623-026-01862-6","type":"journal-article","created":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T08:43:15Z","timestamp":1780476195000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the $$\\gamma $$-spreadness of average-case to worst-case transformations"],"prefix":"10.1007","volume":"94","author":[{"given":"Hyun Ji","family":"Kwag","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonghyun","family":"Kim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changmin","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jong Hwan","family":"Park","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,3]]},"reference":[{"key":"1862_CR1","unstructured":"Dent, A.W.: A designer\u2019s guide to KEMs. Cryptology ePrint Archive, Paper 2002\/174 (2002) https:\/\/eprint.iacr.org\/2002\/174."},{"key":"1862_CR2","doi-asserted-by":"crossref","unstructured":"Hofheinz, D., H\u00f6velmanns, K., Kiltz, E.: A modular analysis of the Fujisaki-Okamoto transformation. In: Theory of Cryptography Conference, pp. 341\u2013371. Springer (2017).","DOI":"10.1007\/978-3-319-70500-2_12"},{"key":"1862_CR3","doi-asserted-by":"crossref","unstructured":"Fujisaki, E., Okamoto, T.: How to enhance the security of public-key encryption at minimum cost. In: International Workshop on Public Key Cryptography, pp. 53\u201368. Springer (1999).","DOI":"10.1007\/3-540-49162-7_5"},{"key":"1862_CR4","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1007\/s00145-011-9114-1","volume":"26","author":"E Fujisaki","year":"2013","unstructured":"Fujisaki E., Okamoto T.: Secure integration of asymmetric and symmetric encryption schemes. J. Cryptol. 26, 80\u2013101 (2013).","journal-title":"J. Cryptol."},{"key":"1862_CR5","doi-asserted-by":"crossref","unstructured":"Bindel, N., Hamburg, M., H\u00f6velmanns, K., H\u00fclsing, A., Persichetti, E.: Tighter proofs of CCA security in the quantum random oracle model. In: Theory of Cryptography Conference, pp. 61\u201390. Springer (2019).","DOI":"10.1007\/978-3-030-36033-7_3"},{"key":"1862_CR6","doi-asserted-by":"crossref","unstructured":"Kuchta V., Sakzad A., Stehl\u00e9 D., Steinfeld R., Sun S.-F.: Measure-rewind-measure: Tighter quantum random oracle model proofs for one-way to hiding and cca security. In: Canteaut A., Ishai Y. (eds.) Advances in Cryptology - EUROCRYPT 2020, pp. 703\u2013728. Springer, Cham (2020).","DOI":"10.1007\/978-3-030-45727-3_24"},{"key":"1862_CR7","first-page":"677","volume-title":"Annual International Conference on the Theory and Applications of Cryptographic Techniques","author":"J Don","year":"2022","unstructured":"Don J., Fehr S., Majenz C., Schaffner C.: Online-extractability in the quantum random-oracle model. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 677\u2013706. Springer, New York (2022)."},{"key":"1862_CR8","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1007\/978-3-031-22972-5_15","volume-title":"Failing gracefully: decryption failures and the Fujisaki-Okamoto transform","author":"K H\u00f6velmanns","year":"2023","unstructured":"H\u00f6velmanns K., H\u00fclsing A., Majenz C.: Failing gracefully: decryption failures and the Fujisaki-Okamoto transform, pp. 414\u2013443. Springer, Berlin, Heidelberg (2023) https:\/\/doi.org\/10.1007\/978-3-031-22972-5_15."},{"key":"1862_CR9","doi-asserted-by":"crossref","unstructured":"Ge, J., Shan, T., Xue, R.: Tighter QCCA-secure key encapsulation mechanism with explicit rejection in the quantum random oracle model. Cryptology ePrint Archive, Paper 2023\/862 (2023) https:\/\/eprint.iacr.org\/2023\/862.","DOI":"10.1007\/978-3-031-38554-4_10"},{"key":"1862_CR10","unstructured":"H\u00f6velmanns, K., Majenz, C.: A note on failing gracefully: completing the picture for explicitly rejecting Fujisaki-Okamoto transforms using worst-case correctness. Cryptology ePrint Archive, Paper 2023\/1811 (2023) https:\/\/eprint.iacr.org\/2023\/1811."},{"key":"1862_CR11","unstructured":"Ge, J., Yang, K., Yu, Y., Yu, Y.: Fujisaki-Okamoto Transformation under average-case decryption error: tighter and more general proofs with applications to PQC. Cryptology ePrint Archive, Paper 2025\/1641 (2025) https:\/\/eprint.iacr.org\/2025\/1641."},{"key":"1862_CR12","doi-asserted-by":"crossref","unstructured":"Duman, J., H\u00f6velmanns, K., Kiltz, E., Lyubashevsky, V., Seiler, G., Unruh, D.: A thorough treatment of highly-efficient ntru instantiations. In: IACR International Conference on Public-Key Cryptography, pp. 65\u201394. Springer (2023).","DOI":"10.1007\/978-3-031-31368-4_3"},{"key":"1862_CR13","doi-asserted-by":"crossref","unstructured":"Kim, J., Park, J.H.: Ntru+: Compact construction of NTRU using simple encoding method. IEEE Transactions on Information Forensics and Security (2023).","DOI":"10.1109\/TIFS.2023.3299172"},{"key":"1862_CR14","unstructured":"Bernstein, D.J., Persichetti, E.: Towards KEM unification. Cryptology ePrint Archive (2018)."},{"key":"1862_CR15","unstructured":"Raimondo, G.M., Locascio, L.E.: Fips 203 federal information processing standards publication module-lattice-based key-encapsulation mechanism standard. Nist Natl. Inst. Stand. Technol 47 (2024)."},{"key":"1862_CR16","doi-asserted-by":"crossref","unstructured":"H\u00f6velmanns, K., Kudinov, M.: Treating dishonest ciphertexts in post-quantum KEMs\u2013explicit vs. implicit rejection in the FO transform. Cryptology ePrint Archive (2025).","DOI":"10.1007\/978-3-031-86602-9_12"},{"key":"1862_CR17","unstructured":"Kim, J., Park, J.H.: NTRU+ PKE: efficient public-key encryption schemes from the NTRU problem. Cryptology ePrint Archive (2024)."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-026-01862-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-026-01862-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-026-01862-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T05:38:27Z","timestamp":1782711507000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-026-01862-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":17,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["1862"],"URL":"https:\/\/doi.org\/10.1007\/s10623-026-01862-6","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"3 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"129"}}