{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T23:08:31Z","timestamp":1743116911162,"version":"3.40.3"},"publisher-location":"Cham","reference-count":33,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031529467"},{"type":"electronic","value":"9783031529474"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-52947-4_12","type":"book-chapter","created":{"date-parts":[[2024,1,20]],"date-time":"2024-01-20T09:02:17Z","timestamp":1705741337000},"page":"157-177","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Efficient Small Modulus Test and\u00a0Its Applications to\u00a0Delegated Computation Without Preprocessing"],"prefix":"10.1007","author":[{"given":"Matluba","family":"Khodjaeva","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5138-1144","authenticated-orcid":false,"given":"Giovanni","family":"di Crescenzo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,21]]},"reference":[{"issue":"1","key":"12_CR1","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/0022-0000(89)90018-4","volume":"39","author":"M Abadi","year":"1989","unstructured":"Abadi, M., Feigenbaum, J., Kilian, J.: On hiding information from an oracle. J. Comput. Syst. Sci. 39(1), 21\u201350 (1989)","journal-title":"J. Comput. Syst. Sci."},{"key":"12_CR2","doi-asserted-by":"crossref","unstructured":"Ahmad, H., et al.: Primitives towards verifiable computation: a survey. Front. Comput. Sci. 12(3), 451\u2013478 (2018)","DOI":"10.1007\/s11704-016-6148-4"},{"key":"12_CR3","doi-asserted-by":"publisher","unstructured":"Bellare, M., Garay, J.A., Rabin, T.: Fast batch verification for modular exponentiation and digital signatures. In: Nyberg, K. (eds.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 236\u2013250. Springer, Heidelberg (1998). https:\/\/doi.org\/10.1007\/BFb0054130","DOI":"10.1007\/BFb0054130"},{"issue":"9","key":"12_CR4","doi-asserted-by":"publisher","first-page":"2299","DOI":"10.1093\/comjnl\/bxab066","volume":"65","author":"C Bouillaguet","year":"2022","unstructured":"Bouillaguet, C., Martinez, F., Vergnaud, D.: Cryptanalysis of modular exponentiation outsourcing protocols. Comput. J. 65(9), 2299\u20132314 (2022)","journal-title":"Comput. J."},{"key":"12_CR5","doi-asserted-by":"publisher","unstructured":"Cavallo, B., Di Crescenzo, G., Kahrobaei, D., Shpilrain, V.: Efficient and secure delegation of group exponentiation to a single server. In: Mangard, S., Schaumont, P. (eds.) Radio Frequency Identification. Security and Privacy Issues, pp. 156\u2013173. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-24837-0_10","DOI":"10.1007\/978-3-319-24837-0_10"},{"key":"12_CR6","doi-asserted-by":"publisher","unstructured":"Crandall, R., Pomerance, C.: Prime Numbers: A Computational Perspective, 2nd edn. Springer, New York (2005). https:\/\/doi.org\/10.1007\/0-387-28979-8","DOI":"10.1007\/0-387-28979-8"},{"key":"12_CR7","doi-asserted-by":"crossref","unstructured":"Di Crescenzo, G., Khodjaeva, M., Shpilrain, V., Kahrobaei, D., Krishnan, R.: Single-server delegation of ring multiplications from quasilinear-time clients. In: Proceedings of SINCONF 2021, pp. 1\u20138 (2021)","DOI":"10.1109\/SIN54109.2021.9699330"},{"key":"12_CR8","doi-asserted-by":"publisher","unstructured":"Di Crescenzo, G., et al.: On single-server delegation of RSA. In: Bella, G., Doinea, M., Janicke, H. (eds.) SecITC 2022. LNCS, vol. 13809, pp. 81\u2013101. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-32636-3_5","DOI":"10.1007\/978-3-031-32636-3_5"},{"key":"12_CR9","doi-asserted-by":"crossref","unstructured":"Di Crescenzo, G., Khodjaeva, M., Kahrobaei, D., Shpilrain, V.: Computing multiple exponentiations in discrete log and RSA groups: from batch verification to batch delegation. In: Proceedings of CNS 2017, pp. 531\u2013539 (2017)","DOI":"10.1109\/CNS.2017.8228702"},{"key":"12_CR10","doi-asserted-by":"crossref","unstructured":"Di Crescenzo, G., Khodjaeva, M., Morales Caro, D.: Single-server batch delegation of variable-input pairings with unbounded client lifetime. In: Proceedings of ADIoT 2023, ESORICS 2023 Workshops, LNCS. Springer, to appear (2023)","DOI":"10.1007\/978-3-031-54129-2_14"},{"key":"12_CR11","doi-asserted-by":"publisher","unstructured":"Feigenbaum, J.: Encrypting problem instances. In: Williams, H.C. (eds.) CRYPTO 1985. LNCS, vol. 218, pp. 477\u2013488. Springer, Heidelberg (1986). https:\/\/doi.org\/10.1007\/3-540-39799-X_38","DOI":"10.1007\/3-540-39799-X_38"},{"key":"12_CR12","doi-asserted-by":"publisher","unstructured":"Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: outsourcing computation to untrusted workers. In: Rabin, T. (eds.). CRYPTO 2010. LNCS, vol. 6223, pp. 465\u2013488. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-14623-7_25","DOI":"10.1007\/978-3-642-14623-7_25"},{"key":"12_CR13","doi-asserted-by":"publisher","unstructured":"Girault, M., Lefranc, D.: Server-aided verification: theory and practice. In: Roy, B. (eds.). ASIACRYPT 2005. LNCS, vol. 3788, pp. 605\u2013623. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11593447_33","DOI":"10.1007\/11593447_33"},{"key":"12_CR14","doi-asserted-by":"publisher","unstructured":"Hohenberger, S., Lysyanskaya, A.: How to securely outsource cryptographic computations. In: Kilian, J. (eds.). TCC 2005. LNCS, vol. 3378, pp. 264\u2013282. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/978-3-540-30576-7_15","DOI":"10.1007\/978-3-540-30576-7_15"},{"key":"12_CR15","doi-asserted-by":"crossref","unstructured":"Kaminski, M.: A note on probabilistically verifying integer and polynomial products. J. ACM 36(1), 142\u2013149 (1989)","DOI":"10.1145\/58562.214082"},{"key":"12_CR16","unstructured":"Karatsuba, A., Ofman, Y.: Multiplication of many-digital numbers by automatic computers. Proc. USSR Acad. Sci. 145, 293\u2013294 (1963). Translation in Physics-Doklady 7, 595\u2013596 (1963)"},{"key":"12_CR17","unstructured":"Karatsuba, A.A.: The complexity of computations. Proc. Steklov Inst. Math. 211, 169\u2013183 (1995). Translation from Trudy Mat. Inst. Steklova 211, 186\u2013202 (1995)"},{"key":"12_CR18","unstructured":"Karp, R.M., Rabin, M.O.: Efficient randomized pattern-matching algorithms. In: Rep. TR-31-81. Harvard Univ. Center for Research in Computing Technology, Cambridge (1981)"},{"key":"12_CR19","doi-asserted-by":"crossref","unstructured":"Khodjaeva, M., Di Crescenzo, G.: On single-server delegation without precomputation. In: Proceedings of 20th International Conference on Security and Cryptography, SECRYPT 2023, ScitePress, pp. 540\u2013547 (2023)","DOI":"10.5220\/0012140100003555"},{"key":"12_CR20","doi-asserted-by":"crossref","unstructured":"Kalkar, O., Sertkaya, I., Tutdere, S.: On the batch outsourcing of pairing computations. Comput. J. 66(10), 2437\u20132446 (2022)","DOI":"10.1093\/comjnl\/bxac095"},{"key":"12_CR21","doi-asserted-by":"crossref","unstructured":"Liu, J.K., Au, M.H., Susilo, W.: Self-generated-certificate public-key cryptography and certificateless signature\/encryption scheme in the standard model. In: Proceedings of the ACM Symposium on Information, Computer and Communications Security. ACM Press (2007)","DOI":"10.1145\/1229285.1266994"},{"key":"12_CR22","doi-asserted-by":"publisher","unstructured":"Matsumoto, T., Kato, K., Imai, H.: Speeding up secret computations with insecure auxiliary devices. In: Goldwasser, S. (eds.). CRYPTO 1988. LNCS, vol. 403, pp. 497\u2013506. Springer, New York (1990). https:\/\/doi.org\/10.1007\/0-387-34799-2_35","DOI":"10.1007\/0-387-34799-2_35"},{"key":"12_CR23","unstructured":"Mefenza, T., Vergnaud, D.: Verifiable outsourcing of pairing computations. Technical report (2018)"},{"key":"12_CR24","doi-asserted-by":"publisher","unstructured":"Rangasamy, J., Kuppusamy, L.: Revisiting single-server algorithms for outsourcing modular exponentiation. In: Chakraborty, D., Iwata, T. (eds.). INDOCRYPT 2018. LNCS, vol. 11356, pp. 3\u201320. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-05378-9_1","DOI":"10.1007\/978-3-030-05378-9_1"},{"issue":"2","key":"12_CR25","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R Rivest","year":"1978","unstructured":"Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120\u2013126 (1978)","journal-title":"Commun. ACM"},{"key":"12_CR26","doi-asserted-by":"crossref","unstructured":"Rosser, J., Schoenfeldl, L.: Approximate formulas for some functions of prime numbers. Ill. J. Math. 6, 64\u201394 (1962)","DOI":"10.1215\/ijm\/1255631807"},{"key":"12_CR27","doi-asserted-by":"crossref","unstructured":"Shan, Z., Ren, K., Blanton, M., Wang, C.: Practical secure computation outsourcing: a survey. ACM Comput. Surv. 51(2), 31:1\u201331:40 (2018)","DOI":"10.1145\/3158363"},{"key":"12_CR28","doi-asserted-by":"crossref","unstructured":"Su, Q., Zhang, R., Xue, R.: Secure outsourcing algorithms for composite modular exponentiation based on single untrusted cloud. Comput. J. 63, 1271 (2020)","DOI":"10.1093\/comjnl\/bxz165"},{"key":"12_CR29","doi-asserted-by":"crossref","unstructured":"Tong, L., Yu, J., Zhang, H.: Secure outsourcing algorithm for bilinear pairings without pre-computation. In: Proceedings of IEEE DSC (2019)","DOI":"10.1109\/DSC47296.2019.8937567"},{"key":"12_CR30","doi-asserted-by":"publisher","unstructured":"Tsang, P.P., Chow, S.S.M., Smith, S.W.: Batch pairing delegation. In: Miyaji, A., Kikuchi, H., Rannenberg, K. (eds.) Advances in Information and Computer Security. LNCS, vol. 4752, pp. 74\u201390. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-75651-4_6","DOI":"10.1007\/978-3-540-75651-4_6"},{"key":"12_CR31","doi-asserted-by":"crossref","unstructured":"Wasserman, H., Blum, M.: Software reliability via run-time result-checking. J. ACM 44(6), 826\u2013849 (1997). Proc. IEEE FOCS 94","DOI":"10.1145\/268999.269003"},{"key":"12_CR32","unstructured":"Yao, A.: A lower bound to palindrome recognition by probabilistic turing machines. In: Tech. Rep. STAN-CS-77-647 (1977)"},{"key":"12_CR33","doi-asserted-by":"crossref","unstructured":"Zhou, K., Afifi, M., Ren, J.: ExpSOS: secure and verifiable outsourcing of exponentiation operations for mobile cloud computing. IEEE Trans. Inf. Forens. Secur. 12(11), 2518\u20132531 (2017)","DOI":"10.1109\/TIFS.2017.2710941"}],"container-title":["Lecture Notes in Computer Science","Innovative Security Solutions for Information Technology and Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-52947-4_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T17:48:50Z","timestamp":1731088130000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-52947-4_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031529467","9783031529474"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-52947-4_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"21 January 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SecITC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Information Technology and Communications Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Bucharest","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Romania","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23 November 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 November 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"itc2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/secitc.eu\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"57","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"14","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"25% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.21","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.57","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}