{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T14:05:12Z","timestamp":1777039512879,"version":"3.51.4"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,11,10]],"date-time":"2020-11-10T00:00:00Z","timestamp":1604966400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,11,10]],"date-time":"2020-11-10T00:00:00Z","timestamp":1604966400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61672239"],"award-info":[{"award-number":["61672239"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61632012"],"award-info":[{"award-number":["61632012"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2021,2]]},"DOI":"10.1007\/s10623-020-00816-w","type":"journal-article","created":{"date-parts":[[2020,11,10]],"date-time":"2020-11-10T07:02:51Z","timestamp":1604991771000},"page":"241-253","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Extended Galbraith\u2019s test on the anonymity of IBE schemes from higher residuosity"],"prefix":"10.1007","volume":"89","author":[{"given":"Xiaopeng","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5250-5030","authenticated-orcid":false,"given":"Zhenfu","family":"Cao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolei","family":"Dong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Shao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,11,10]]},"reference":[{"issue":"3","key":"816_CR1","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1007\/s00145-007-9006-6","volume":"21","author":"M Abdalla","year":"2008","unstructured":"Abdalla M., Bellare M., Catalano D., Kiltz E., Kohno T., Lange T., Malone-Lee J., Neven G., Paillier P., Shi H.: Searchable encryption revisited: consistency properties, relation to anonymous IBE, and extensions. J. Cryptol. 21(3), 350\u2013391 (2008). https:\/\/doi.org\/10.1007\/s00145-007-9006-6.","journal-title":"J. Cryptol."},{"key":"816_CR2","doi-asserted-by":"publisher","unstructured":"Ateniese G., Gasti P.: Universally anonymous IBE based on the quadratic residuosity assumption. In: Fischlin M. (ed.) Topics in Cryptology\u2014CT-RSA 2009. LNCS, vol.\u00a05473, pp. 32\u201347. Springer, Berlin (2009). https:\/\/doi.org\/10.1007\/978-3-642-00862-7_3.","DOI":"10.1007\/978-3-642-00862-7_3."},{"key":"816_CR3","unstructured":"Bellare M., Boldyreva A., Desai A., Pointcheval D.: Key-privacy in public-key encryption. In: International Conference on the Theory and Application of Cryptology and Information Security, pp. 566\u2013582. Springer, Berlin (2001)."},{"key":"816_CR4","doi-asserted-by":"publisher","unstructured":"Boneh D., Crescenzo G.D., Ostrovsky R., Persiano G.: Public key encryption with keyword search. In: Cachin C., Camenisch J. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 506\u2013522. Springer, Berlin (2004). https:\/\/doi.org\/10.1007\/978-3-540-24676-3_30.","DOI":"10.1007\/978-3-540-24676-3_30"},{"key":"816_CR5","doi-asserted-by":"publisher","unstructured":"Boneh D., Franklin M.K.: Identity-based encryption from the weil pairing. In: Kilian J. (ed.) CRYPTO 2001. LNCS, vol.\u00a02139, pp. 213\u2013229. Springer, Berlin (2001). https:\/\/doi.org\/10.1007\/3-540-44647-8_13.","DOI":"10.1007\/3-540-44647-8_13"},{"key":"816_CR6","doi-asserted-by":"crossref","unstructured":"Boneh D., Gentry C., Hamburg M.: Space-efficient identity based encryption without pairings. In: 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS\u201907), pp. 647\u2013657. IEEE (2007).","DOI":"10.1109\/FOCS.2007.4389533"},{"key":"816_CR7","unstructured":"Boneh D., LaVigne R., Sabin M.: Identity-based encryption with $$e^{th}$$ residuosity and its incompressibility. In: Autumn 2013 TRUST Conference. Washington DC (Oct 9-10, 2013), poster presentation (2013)."},{"issue":"1","key":"816_CR8","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1515\/jmc-2019-0035","volume":"14","author":"E Brier","year":"2020","unstructured":"Brier E., Ferradi H., Joye M., Naccache D.: New number-theoretic cryptographic primitives. J. Math. Cryptol. 14(1), 224\u2013235 (2020). https:\/\/doi.org\/10.1515\/jmc-2019-0035.","journal-title":"J. Math. Cryptol."},{"key":"816_CR9","unstructured":"Brier E., Naccache D.: The thirteenth power residue symbol. IACR Cryptology ePrint Archive 2019, 1176 (2019). https:\/\/eprint.iacr.org\/2019\/1176."},{"issue":"08","key":"816_CR10","doi-asserted-by":"publisher","first-page":"1831","DOI":"10.1142\/S1793042110003770","volume":"6","author":"PC Caranay","year":"2010","unstructured":"Caranay P.C., Scheidler R.: An efficient seventh power residue symbol algorithm. Int. J. Number Theory 6(08), 1831\u20131853 (2010).","journal-title":"Int. J. Number Theory"},{"issue":"2","key":"816_CR11","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1215\/S0012-7094-35-00114-4","volume":"1","author":"L Carlitz","year":"1935","unstructured":"Carlitz L.: On certain functions connected with polynomials in a Galois field. Duke Math. J. 1(2), 137\u2013168 (1935).","journal-title":"Duke Math. J."},{"key":"816_CR12","doi-asserted-by":"publisher","unstructured":"Clear M., Hughes A., Tewari H.: Homomorphic encryption with access policies: characterization and new constructions. In: Youssef A.M., Nitaj A., Hassanien A.E. (eds.) AFRICACRYPT 2013. LNCS, vol.\u00a07918, pp. 61\u201387. Springer, Berlin (2013). https:\/\/doi.org\/10.1007\/978-3-642-38553-7_4.","DOI":"10.1007\/978-3-642-38553-7_4"},{"key":"816_CR13","doi-asserted-by":"publisher","unstructured":"Clear M., McGoldrick C.: Additively homomorphic IBE from higher residuosity. In: Lin D., Sako K. (eds.) PKC 2019. LNCS, vol. 11442, pp. 496\u2013515. Springer, Berlin (2019). https:\/\/doi.org\/10.1007\/978-3-030-17253-4_17.","DOI":"10.1007\/978-3-030-17253-4_17"},{"key":"816_CR14","doi-asserted-by":"publisher","unstructured":"Clear M., Tewari H., McGoldrick C.: Anonymous IBE from quadratic residuosity with improved performance. In: Pointcheval D., Vergnaud D. (eds.) AFRICACRYPT 2014. LNCS, vol.\u00a08469, pp. 377\u2013397. Springer, Berlin (2014). https:\/\/doi.org\/10.1007\/978-3-319-06734-6_23.","DOI":"10.1007\/978-3-319-06734-6_23"},{"key":"816_CR15","doi-asserted-by":"publisher","unstructured":"Cocks C.C.: An identity based encryption scheme based on quadratic residues. In: Honary B. (ed.) Cryptography and Coding, 8th IMA International Conference, 2001, Proceedings. LNCS, vol.\u00a02260, pp. 360\u2013363. Springer, Berlin (2001). https:\/\/doi.org\/10.1007\/3-540-45325-3_32.","DOI":"10.1007\/3-540-45325-3_32"},{"key":"816_CR16","doi-asserted-by":"publisher","unstructured":"Crescenzo G.D., Saraswat V.: Public key encryption with searchable keywords based on Jacobi symbols. In: Srinathan K., Rangan C.P., Yung M. (eds.) INDOCRYPT 2007. LNCS, vol.\u00a04859, pp. 282\u2013296. Springer, Berlin (2007). https:\/\/doi.org\/10.1007\/978-3-540-77026-8_21.","DOI":"10.1007\/978-3-540-77026-8_21"},{"key":"816_CR17","unstructured":"de\u00a0Boer K.: Computing the power residue symbol. Master\u2019s thesis. Nijmegen, Radboud University. www.koendeboer.com (2016)."},{"issue":"1","key":"816_CR18","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s00145-011-9112-3","volume":"26","author":"DM Freeman","year":"2013","unstructured":"Freeman D.M., Goldreich O., Kiltz E., Rosen A., Segev G.: More constructions of lossy and correlation-secure trapdoor functions. J. Cryptol. 26(1), 39\u201374 (2013).","journal-title":"J. Cryptol."},{"key":"816_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03545-0","volume-title":"The Theory of Algebraic Number Fields","author":"D Hilbert","year":"1998","unstructured":"Hilbert D.: The Theory of Algebraic Number Fields. Springer, Berlin (1998)."},{"key":"816_CR20","doi-asserted-by":"publisher","unstructured":"Joye M.: Identity-based cryptosystems and quadratic residuosity. In: Cheng C., Chung K., Persiano G., Yang B. (eds.) Public-Key Cryptography - PKC 2016. LNCS, vol.\u00a09614, pp. 225\u2013254. Springer, Berlin (2016). https:\/\/doi.org\/10.1007\/978-3-662-49384-7_9.","DOI":"10.1007\/978-3-662-49384-7_9"},{"key":"816_CR21","unstructured":"Joye M.: Evaluating octic residue symbols. IACR Cryptology ePrint Archive 2019, 1196 (2019). https:\/\/eprint.iacr.org\/2019\/1196."},{"key":"816_CR22","unstructured":"Joye M., Lapiha O., Nguyen K., Naccache D.: The eleventh power residue symbol. IACR Cryptology ePrint Archive 2019, \u00a0870 (2019), https:\/\/eprint.iacr.org\/2019\/870."},{"issue":"2","key":"816_CR23","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1007\/BF01175029","volume":"56","author":"O Perron","year":"1952","unstructured":"Perron O.: Bemerkungen uber die verteilung der quadratischen reste. Mathematische Zeitschrift 56(2), 122\u2013130 (1952).","journal-title":"Mathematische Zeitschrift"},{"key":"816_CR24","volume-title":"Number Theory in Function Fields","author":"M Rosen","year":"2013","unstructured":"Rosen M.: Number Theory in Function Fields, vol. 210. Springer, Berlin (2013)."},{"issue":"2","key":"816_CR25","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/BF01398010","volume":"6","author":"R Scheidler","year":"1995","unstructured":"Scheidler R., Williams H.C.: A public-key cryptosystem utilizing cyclotomic fields. Des. Codes Cryptogr. 6(2), 117\u2013131 (1995). https:\/\/doi.org\/10.1007\/BF01398010.","journal-title":"Des. Codes Cryptogr."},{"key":"816_CR26","doi-asserted-by":"publisher","unstructured":"Shamir A.: Identity-based cryptosystems and signature schemes. In: Blakley G.R., Chaum D. (eds.) Advances in Cryptology, Proceedings of CRYPTO \u201984. LNCS, vol.\u00a0196, pp. 47\u201353. Springer, Berlin (1984). https:\/\/doi.org\/10.1007\/3-540-39568-7_5.","DOI":"10.1007\/3-540-39568-7_5"},{"key":"816_CR27","unstructured":"Squirrel D.: Computing reciprocity symbols in number fields. Undergraduate thesis, Reed College (1997)."},{"key":"816_CR28","doi-asserted-by":"publisher","first-page":"124993","DOI":"10.1016\/j.amc.2019.124993","volume":"372","author":"FL Tiplea","year":"2020","unstructured":"Tiplea F.L., Iftene S., Teseleanu G., Nica A.: On the distribution of quadratic residues and non-residues modulo composite integers and applications to cryptography. Appl. Math. Comput. 372, 124993 (2020). https:\/\/doi.org\/10.1016\/j.amc.2019.124993.","journal-title":"Appl. Math. Comput."},{"key":"816_CR29","doi-asserted-by":"publisher","unstructured":"Williams H.C.: An M$${^3}$$ public-key encryption scheme. In: Williams H.C. (ed.) CRYPTO. LNCS, vol.\u00a0218, pp. 358\u2013368. Springer, Berlin (1985). https:\/\/doi.org\/10.1007\/3-540-39799-X_26.","DOI":"10.1007\/3-540-39799-X_26"},{"key":"816_CR30","doi-asserted-by":"publisher","unstructured":"Zhao X., Cao Z., Dong X., Shao J., Wang L., Liu Z.: New assumptions and efficient cryptosystems from the $$e$$-th power residue symbol. In: Liu J.K., Cui H. (eds.) ACISP. LNCS, vol. 12248, pp. 408\u2013424. Springer, Berlin (2020). https:\/\/doi.org\/10.1007\/978-3-030-55304-3_21.","DOI":"10.1007\/978-3-030-55304-3_21"},{"key":"816_CR31","unstructured":"Zhao X., Cao Z., Dong X., Zheng J.: Anonymous IBE from quadratic residuosity with fast encryption. IACR Cryptology ePrint Archive 2020, 712 (2020). https:\/\/eprint.iacr.org\/2020\/712."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-020-00816-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-020-00816-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-020-00816-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T21:26:09Z","timestamp":1612905969000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-020-00816-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,10]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["816"],"URL":"https:\/\/doi.org\/10.1007\/s10623-020-00816-w","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,10]]},"assertion":[{"value":"19 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 August 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 November 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}