{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:39:00Z","timestamp":1760060340389,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T00:00:00Z","timestamp":1756252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Minister of Science and Technology, Taiwan","award":["MOST 114-2221-E-002-101-MY3"],"award-info":[{"award-number":["MOST 114-2221-E-002-101-MY3"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>This paper enhances the multikey scenario in the Gentry\u2013Sahai\u2013Waters (GSW) fully homomorphic encryption scheme to increase its real-world applicability. We integrate the advantages of two existing GSW multikey approaches: one enabling distributed decryption and the other reducing memory requirements. We also apply the CRT decomposition and ciphertext compression techniques to the multikey settings. While leveraging the effectiveness of decomposition, we adapt the compression technique for practical cryptographic applications, as demonstrated through simulations in federated learning and multiparty communication scenarios. Our work\u2019s potential impact on the cryptography field is significant, as it offers a more efficient and secure solution for distributed data processing in real-world scenarios, thereby advancing the state of the art in secure communication systems.<\/jats:p>","DOI":"10.3390\/cryptography9030055","type":"journal-article","created":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T09:31:12Z","timestamp":1756373472000},"page":"55","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Enhancing the Multikey GSW Scheme with CRT Decomposition and Ciphertext Compression for Efficient Distributed Decryption"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-1306-6079","authenticated-orcid":false,"given":"Kung-Wei","family":"Hu","sequence":"first","affiliation":[{"name":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei City 10617, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-3868-399X","authenticated-orcid":false,"given":"Wun-Ting","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei City 10617, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1293-1510","authenticated-orcid":false,"given":"Huan-Chih","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei City 10617, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3631-1551","authenticated-orcid":false,"given":"Ja-Ling","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei City 10617, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,27]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Gentry, C., Sahai, A., and Waters, B. (2013, January 18\u201322). Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. Proceedings of the Advances in Cryptology\u2013CRYPTO 2013: 33rd Annual Cryptology Conference, Santa Barbara, CA, USA. Proceedings, Part I.","key":"ref_1","DOI":"10.1007\/978-3-642-40041-4_5"},{"doi-asserted-by":"crossref","unstructured":"Mukherjee, P., and Wichs, D. (2016, January 8\u201312). Two round multiparty computation via multi-key FHE. Proceedings of the Advances in Cryptology\u2013EUROCRYPT 2016: 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Vienna, Austria. Proceedings, Part II 35.","key":"ref_2","DOI":"10.1007\/978-3-662-49896-5_26"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6619476","DOI":"10.1155\/2021\/6619476","article-title":"Compressible multikey and multi-identity fully homomorphic encryption","volume":"2021","author":"Shen","year":"2021","journal-title":"Secur. Commun. Netw."},{"doi-asserted-by":"crossref","unstructured":"Hu, K.W., Wang, H.C., Lin, W.T., and Wu, J.L. (2025). Optimizing Message Range and Ciphertext Storage in Gentry\u2013Sahai\u2013Waters Encryption Using Chinese Remainder Theorem and PVW-like Compression Scheme. Cryptography, 9.","key":"ref_4","DOI":"10.3390\/cryptography9010014"},{"doi-asserted-by":"crossref","unstructured":"Gentry, C., and Halevi, S. (2019). Compressible FHE with applications to PIR. Theory of Cryptography Conference, Springer.","key":"ref_5","DOI":"10.1007\/978-3-030-36033-7_17"},{"key":"ref_6","first-page":"169","article-title":"On data banks and privacy homomorphisms","volume":"4","author":"Rivest","year":"1978","journal-title":"Found. Secur. Comput."},{"unstructured":"Gentry, C. (2009). A Fully Homomorphic Encryption Scheme, Stanford University.","key":"ref_7"},{"doi-asserted-by":"crossref","unstructured":"Brakerski, Z., and Vaikuntanathan, V. (2011, January 23\u201325). 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