{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,9]],"date-time":"2025-07-09T22:55:20Z","timestamp":1752101720291},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T00:00:00Z","timestamp":1710460800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T00:00:00Z","timestamp":1710460800000},"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":["Cluster Comput"],"published-print":{"date-parts":[[2024,8]]},"DOI":"10.1007\/s10586-024-04329-2","type":"journal-article","created":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T12:01:54Z","timestamp":1710504114000},"page":"7007-7022","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["EPVM: efficient and publicly verifiable computation for matrix multiplication with privacy preservation"],"prefix":"10.1007","volume":"27","author":[{"given":"Chang","family":"Xu","sequence":"first","affiliation":[]},{"given":"Hongzhou","family":"Rao","sequence":"additional","affiliation":[]},{"given":"Liehuang","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"Chuan","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Kashif","family":"Sharif","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,3,15]]},"reference":[{"key":"4329_CR1","doi-asserted-by":"crossref","unstructured":"Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: Outsourcing computation to untrusted workers. In: Annual Cryptology Conference, pages 465\u2013482. Springer, (2010)","DOI":"10.1007\/978-3-642-14623-7_25"},{"key":"4329_CR2","doi-asserted-by":"publisher","unstructured":"Zhang, C., Zhu, L., Xu, C., Liu, X., Sharif, K.: Reliable and privacy-preserving truth discovery for mobile crowdsensing systems. IEEE Trans. Dep. Secur. Comput. https:\/\/doi.org\/10.1109\/TDSC.2019.2919517","DOI":"10.1109\/TDSC.2019.2919517"},{"key":"4329_CR3","doi-asserted-by":"crossref","unstructured":"Golub, G., Van\u00a0Loan, C.: Matrix computations, 4th edn. johns hopkins, (2013)","DOI":"10.56021\/9781421407944"},{"key":"4329_CR4","doi-asserted-by":"crossref","unstructured":"Fahim, M., Jeong, H., Haddadpour, F., Dutta, S., Cadambe, V., Grover, P.: On the optimal recovery threshold of coded matrix multiplication. In: 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 1264\u20131270. IEEE, (2017)","DOI":"10.1109\/ALLERTON.2017.8262882"},{"key":"4329_CR5","doi-asserted-by":"crossref","unstructured":"Zhang, X., Jiang, T., Li, K.C., Castiglione, A., Chen, X.: New publicly verifiable computation for batch matrix multiplication. Information Ences, page S0020025517311246, (2017)","DOI":"10.1007\/978-3-319-57186-7_5"},{"key":"4329_CR6","doi-asserted-by":"publisher","first-page":"2835","DOI":"10.1007\/s10586-020-03049-7","volume":"23","author":"F Erfan","year":"2020","unstructured":"Erfan, F., Mala, H.: Secure and efficient publicly verifiable outsourcing of matrix multiplication in online mode. Cluster Comput. 23, 2835\u20132845 (2020)","journal-title":"Cluster Comput."},{"key":"4329_CR7","doi-asserted-by":"crossref","unstructured":"Zhang, S., Li, H., Jia, K., Dai, Y-S., Zhao, L.: Efficient secure outsourcing computation of matrix multiplication in cloud computing. In: 2016 IEEE Global Communications Conference, GLOBECOM 2016, Washington, DC, USA, December 4-8, 2016, pages 1\u20136, (2016)","DOI":"10.1109\/GLOCOM.2016.7841783"},{"issue":"6","key":"4329_CR8","doi-asserted-by":"publisher","first-page":"5076","DOI":"10.1109\/JIOT.2018.2867113","volume":"5","author":"S Zhang","year":"2018","unstructured":"Zhang, S., Li, H., Dai, Y., Li, J., He, M., Rongxing, L.: Verifiable outsourcing computation for matrix multiplication with improved efficiency and applicability. IEEE Internet Things J. 5(6), 5076\u20135088 (2018)","journal-title":"IEEE Internet Things J."},{"key":"4329_CR9","doi-asserted-by":"crossref","unstructured":"Parno, B., Raykova, M., Vaikuntanathan, V.: How to delegate and verify in public: Verifiable computation from attribute-based encryption. In: International Conference on Theory of Cryptography, (2011)","DOI":"10.1007\/978-3-642-28914-9_24"},{"issue":"6","key":"4329_CR10","first-page":"1","volume":"14","author":"J Liu","year":"2020","unstructured":"Liu, J., Bi, J., Li, M.: Secure outsourcing of large matrix determinant computation. Front. Comput. ence 14(6), 1\u201312 (2020)","journal-title":"Front. Comput. ence"},{"key":"4329_CR11","doi-asserted-by":"crossref","unstructured":"Zhang, J., Yang, Y., Wang, Z.: Outsourcing large-scale systems of linear matrix equations in cloud computing. In: IEEE International Conference on Parallel & Distributed Systems, (2017)","DOI":"10.1109\/ICPADS.2016.0066"},{"key":"4329_CR12","doi-asserted-by":"publisher","first-page":"53823","DOI":"10.1109\/ACCESS.2019.2913591","volume":"7","author":"S Zhang","year":"2019","unstructured":"Zhang, S., Tian, C., Zhang, H., Jia, Y., Li, F..: Practical and secure outsourcing algorithms of matrix operations based on a novel matrix encryption method. IEEE Access 7, 53823\u201353838 (2019)","journal-title":"IEEE Access"},{"key":"4329_CR13","doi-asserted-by":"crossref","unstructured":"Yamane, M., Iwamura, K.: Secure and efficient outsourcing of matrix multiplication based on secret sharing scheme using only one server. In: IEEE 17th Annual Consumer Communications & Networking Conference, CCNC 2020, Las Vegas, NV, USA, January 10-13, 2020, pages 1\u20136, (2020)","DOI":"10.1109\/CCNC46108.2020.9045277"},{"key":"4329_CR14","doi-asserted-by":"crossref","unstructured":"Fu, S., Yu, Y., Xu, M.: A secure algorithm for outsourcing matrix multiplication computation in the cloud. In: \"Proceedings of the Fifth ACM International Workshop on Security in Cloud Computing, SCC@AsiaCCS 2017, Abu Dhabi, United Arab Emirates, April 2, 2017\", pages 27\u201333, (2017)","DOI":"10.1145\/3055259.3055263"},{"key":"4329_CR15","first-page":"372","volume":"479","author":"Y Xixun","year":"2018","unstructured":"Xixun, Y., Yan, Z., Zhang, R.: Verifiable outsourced computation over encrypted data. Inf. Sci. 479, 372\u2013385 (2018)","journal-title":"Inf. Sci."},{"key":"4329_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cose.2019.101712","volume":"90","author":"RM Dorsala","year":"2020","unstructured":"Dorsala, R.M., Sastry, V.N., Chapram, S.: Fair payments for verifiable cloud services using smart contracts. Comput. Secur. 90, 101712 (2020)","journal-title":"Comput. Secur."},{"key":"4329_CR17","doi-asserted-by":"crossref","unstructured":"Avizheh, S., Nabi, M., Safavi-Naini, R., Venkateswarlu\u00a0K.M.: Verifiable computation using smart contracts. In Proceedings of the 2019 ACM SIGSAC Conference on Cloud Computing Security Workshop, CCSW\u201919, page 17-28, New York, NY, USA, (2019). Association for Computing Machinery","DOI":"10.1145\/3338466.3358925"},{"key":"4329_CR18","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1016\/j.ins.2018.06.018","volume":"462","author":"Y Zhang","year":"2018","unstructured":"Zhang, Y., Deng, R.H., Liu, X., Zheng, D.: Blockchain based efficient and robust fair payment for outsourcing services in cloud computing. Inf. Sci. 462, 262\u2013277 (2018)","journal-title":"Inf. Sci."},{"key":"4329_CR19","doi-asserted-by":"crossref","unstructured":"Dong, C., Wang, Y., Aldweesh, A., Mccorry, P., Van\u00a0Moorsel, A.: Betrayal, distrust, and rationality: Smart counter-collusion contracts for verifiable cloud computing. MISSING INFORMATION, (2017)","DOI":"10.1145\/3133956.3134032"},{"key":"4329_CR20","doi-asserted-by":"publisher","DOI":"10.1109\/TSC.2019.2961992","author":"C Zhang","year":"2019","unstructured":"Zhang, C., Zhu, L., Xu, C., Kashif, S., Kai, D., Liu, X., Du, X., Guizani, M.: Tppr: a trust-based and privacy-preserving platoon recommendation scheme in vanet. IEEE Trans. Serv. Comput. (2019). https:\/\/doi.org\/10.1109\/TSC.2019.2961992","journal-title":"IEEE Trans. Serv. Comput."},{"issue":"4","key":"4329_CR21","doi-asserted-by":"publisher","first-page":"14","DOI":"10.4018\/IJDCF.2019100102","volume":"11","author":"D Xie","year":"2019","unstructured":"Xie, D., Yang, H., Qin, J., Ma, J.: Privacy-preserving and publicly verifiable protocol for outsourcing polynomials evaluation to a malicious cloud. Int. J. Digit. Crime Forensics 11(4), 14\u201327 (2019)","journal-title":"Int. J. Digit. Crime Forensics"},{"key":"4329_CR22","doi-asserted-by":"publisher","first-page":"2334","DOI":"10.1109\/TIFS.2017.2705628","volume":"12","author":"W Song","year":"2017","unstructured":"Song, W., Wang, B., Wang, Q., Shi, C., Lou, W., Peng, Z.: Publicly verifiable computation of polynomials over outsourced data with multiple sources. IEEE Trans. Inf. Forensics Secur. 12, 2334\u20132347 (2017)","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"4329_CR23","doi-asserted-by":"crossref","unstructured":"Salinas, S., Luo, C., Chen, X., Pan, L.: Efficient secure outsourcing of large-scale linear systems of equations. In: 2015 IEEE Conference on Computer Communications (INFOCOM), (2015)","DOI":"10.1109\/INFOCOM.2015.7218476"},{"issue":"5","key":"4329_CR24","doi-asserted-by":"publisher","first-page":"6445","DOI":"10.3233\/JIFS-179725","volume":"38","author":"M Kumar","year":"2020","unstructured":"Kumar, M., Mishra, V., Shukla, A., Singh, M., Vardhan, M.: A novel publicly delegable secure outsourcing algorithm for large-scale matrix multiplication. J. Intell. Fuzzy Syst. 38(5), 6445\u20136455 (2020)","journal-title":"J. Intell. Fuzzy Syst."},{"key":"4329_CR25","doi-asserted-by":"publisher","first-page":"227556","DOI":"10.1109\/ACCESS.2020.3045999","volume":"8","author":"W Yu","year":"2020","unstructured":"Yu, W., Liao, Y., Liang, Y., Liu, Y.: Secure and efficient protocol for outsourcing large-scale matrix multiplication to the cloud. IEEE Access 8, 227556\u2013227565 (2020)","journal-title":"IEEE Access"},{"key":"4329_CR26","unstructured":"Liu, C., Hu, X., Chen, X., Wei, J., Liu, W.: An efficient matrix multiplication with enhanced privacy protection in cloud computing and its applications. CoRR, abs\/2105.05525, (2021)"},{"issue":"1","key":"4329_CR27","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1186\/s40537-020-00362-1","volume":"7","author":"R Bagheri","year":"2020","unstructured":"Bagheri, R., Amini, M., Somayeh Dolatnezhad, S.: Efficient verification of parallel matrix multiplication in public cloud: the mapreduce case. J. Big Data 7(1), 86 (2020)","journal-title":"J. Big Data"},{"key":"4329_CR28","doi-asserted-by":"crossref","unstructured":"Hu, C., Alhothaily, A., Alrawais, A., Cheng, X., Sturtivant, C., Liu, H.: A secure and verifiable outsourcing scheme for matrix inverse computation. In 2017 IEEE Conference on Computer Communications, INFOCOM 2017, Atlanta, GA, USA, May 1-4, 2017, pages 1\u20139. IEEE, (2017)","DOI":"10.1109\/INFOCOM.2017.8057199"},{"issue":"2","key":"4329_CR29","first-page":"283","volume":"18","author":"J Ye","year":"2016","unstructured":"Ye, J., Zhang, H., Changyou, F.: Verifiable delegation of polynomials. Int. J. Netw. Secur. 18(2), 283\u2013290 (2016)","journal-title":"Int. J. Netw. Secur."},{"key":"4329_CR30","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.jnca.2018.06.003","volume":"118","author":"F Anmin","year":"2018","unstructured":"Anmin, F., Li, S., Shui, Y., Zhang, Y., Sun, Y.: Privacy-preserving composite modular exponentiation outsourcing with optimal checkability in single untrusted cloud server. J. Netw. Comput. Appl. 118, 102\u2013112 (2018)","journal-title":"J. Netw. Comput. Appl."},{"key":"4329_CR31","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/6128437","author":"K Zhang","year":"2017","unstructured":"Zhang, K., Wei, L., Li, X., Qian, H.: Scalable and soundness verifiable outsourcing computation in marine mobile computing. Wirel. Commun. Mob. Comput. (2017). https:\/\/doi.org\/10.1155\/2017\/6128437","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"4329_CR32","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1109\/TSC.2019.2937486","volume":"15","author":"C Tian","year":"2019","unstructured":"Tian, C., Yu, J., Zhang, H., Xue, H., Wang, C., Ren, K.: Novel secure outsourcing of modular inversion for arbitrary and variable modulus. IEEE Trans. Serv. Comput. 15, 241\u2013253 (2019)","journal-title":"IEEE Trans. Serv. Comput."},{"issue":"4","key":"4329_CR33","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1007\/s10623-019-00704-y","volume":"88","author":"LF Zhang","year":"2020","unstructured":"Zhang, L.F., Safavi-Naini, R.: Protecting data privacy in publicly verifiable delegation of matrix and polynomial functions. Des. Codes Cryptogr. 88(4), 677\u2013709 (2020)","journal-title":"Des. Codes Cryptogr."}],"container-title":["Cluster Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10586-024-04329-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10586-024-04329-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10586-024-04329-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,12]],"date-time":"2024-08-12T14:05:34Z","timestamp":1723471534000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10586-024-04329-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,15]]},"references-count":33,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["4329"],"URL":"https:\/\/doi.org\/10.1007\/s10586-024-04329-2","relation":{},"ISSN":["1386-7857","1573-7543"],"issn-type":[{"type":"print","value":"1386-7857"},{"type":"electronic","value":"1573-7543"}],"subject":[],"published":{"date-parts":[[2024,3,15]]},"assertion":[{"value":"1 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 April 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 March 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Authors do not have any conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}