{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:05:06Z","timestamp":1760148306355,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T00:00:00Z","timestamp":1681689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ADAPT","award":["13\/RC\/2106_P2","13\/RC\/2077_P2"],"award-info":[{"award-number":["13\/RC\/2106_P2","13\/RC\/2077_P2"]}]},{"DOI":"10.13039\/501100001602","name":"CONNECT","doi-asserted-by":"publisher","award":["13\/RC\/2106_P2","13\/RC\/2077_P2"],"award-info":[{"award-number":["13\/RC\/2106_P2","13\/RC\/2077_P2"]}],"id":[{"id":"10.13039\/501100001602","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>All anonymous identity-based encryption (IBE) schemes that are group homomorphic (to the best of our knowledge) require knowledge of the identity to compute the homomorphic operation. This paper is motivated by this open problem, namely to construct an anonymous group-homomorphic IBE scheme that does not sacrifice anonymity to perform homomorphic operations. Note that even when strong assumptions, such as indistinguishability obfuscation (iO), are permitted, no schemes are known. We succeed in solving this open problem by assuming iO and the hardness of the DBDH problem over rings (specifically, ZN2 for RSA modulus N). We then use the existence of such a scheme to construct an IBE scheme with re-randomizable anonymous encryption keys, which we prove to be IND-ID-RCCA secure. Finally, we use our results to construct identity-based anonymous aggregation protocols.<\/jats:p>","DOI":"10.3390\/cryptography7020022","type":"journal-article","created":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T04:45:32Z","timestamp":1681706732000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Anonymous Homomorphic IBE with Application to Anonymous Aggregation"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5529-2280","authenticated-orcid":false,"given":"Michael","family":"Clear","sequence":"first","affiliation":[{"name":"School of Computer Science and Statistics, Trinity College Dublin, D02 PN40 Dublin, Ireland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1738-527X","authenticated-orcid":false,"given":"Hitesh","family":"Tewari","sequence":"additional","affiliation":[{"name":"School of Computer Science and Statistics, Trinity College Dublin, D02 PN40 Dublin, Ireland"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,17]]},"reference":[{"key":"ref_1","first-page":"61","article-title":"Homomorphic Encryption with Access Policies: Characterization and New Constructions","volume":"Volume 7918","author":"Youssef","year":"2013","journal-title":"Proceedings of the AFRICACRYPT 13"},{"key":"ref_2","first-page":"496","article-title":"Additively Homomorphic IBE from Higher Residuosity","volume":"Volume 11442","author":"Lin","year":"2019","journal-title":"Proceedings of the Public Key Cryptography (1)"},{"key":"ref_3","first-page":"225","article-title":"Identity-Based Cryptosystems and Quadratic Residuosity","volume":"Volume 9614","author":"Cheng","year":"2016","journal-title":"Proceedings of the Public Key Cryptography (1)"},{"key":"ref_4","first-page":"573","article-title":"Trapdooring Discrete Logarithms on Elliptic Curves over Rings","volume":"Volume 1976","author":"Okamoto","year":"2000","journal-title":"Proceedings of the ASIACRYPT"},{"key":"ref_5","first-page":"242","article-title":"Additively Homomorphic Encryption with a Double Decryption Mechanism, Revisited","volume":"Volume 7483","author":"Gollmann","year":"2012","journal-title":"Proceedings of the ISC"},{"key":"ref_6","first-page":"1","article-title":"Bootstrappable Identity-Based Fully Homomorphic Encryption","volume":"Volume 8813","author":"Gritzalis","year":"2014","journal-title":"Proceedings of the CANS"},{"key":"ref_7","first-page":"10","article-title":"A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms","volume":"Volume 196","author":"Blakley","year":"1984","journal-title":"Proceedings of the CRYPTO\u201984"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s10623-011-9601-2","article-title":"Group homomorphic encryption: Characterizations, impossibility results, and applications","volume":"67","author":"Armknecht","year":"2012","journal-title":"Des. Codes Cryptogr."},{"key":"ref_9","first-page":"104","article-title":"Symmetric Subgroup Membership Problems","volume":"Volume 3386","author":"Vaudenay","year":"2005","journal-title":"Proceedings of the PKC 2005"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1007\/3-540-45325-3_32","article-title":"An Identity Based Encryption Scheme Based on Quadratic Residues","volume":"Volume 2260","author":"Honary","year":"2001","journal-title":"Proceedings of the Cryptography and Coding, 8th IMA International Conference"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.ipl.2008.05.017","article-title":"On the security of public key cryptosystems with a double decryption mechanism","volume":"108","author":"Galindo","year":"2008","journal-title":"Inf. Process. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., and Waters, B. (2013, January 26\u201329). Candidate Indistinguishability Obfuscation and Functional Encryption for all Circuits. Proceedings of the 54th FOCS, Berkeley, CA, USA.","DOI":"10.1109\/FOCS.2013.13"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s00145-001-0015-6","article-title":"Elliptic Curve Paillier Schemes","volume":"15","author":"Galbraith","year":"2002","journal-title":"J. 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