{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T03:12:57Z","timestamp":1775272377631,"version":"3.50.1"},"reference-count":36,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,11,15]],"date-time":"2018-11-15T00:00:00Z","timestamp":1542240000000},"content-version":"vor","delay-in-days":318,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61701322"],"award-info":[{"award-number":["61701322"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Wireless Communications and Mobile Computing"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>With the rapid development of the 5G network and Internet of Things (IoT), lots of mobile and IoT devices generate massive amounts of multisource heterogeneous data. Effective processing of such data becomes an urgent problem. However, traditional centralised models of cloud computing are challenging to process multisource heterogeneous data effectively. Mobile edge computing (MEC) emerges as a new technology to optimise applications or cloud computing systems. However, the features of MEC such as content perception, real\u2010time computing, and parallel processing make the data security and privacy issues that exist in the cloud computing environment more prominent. Protecting sensitive data through traditional encryption is a very secure method, but this will make it impossible for the MEC to calculate the encrypted data. The fully homomorphic encryption (FHE) overcomes this limitation. FHE can be used to compute ciphertext directly. Therefore, we propose a ciphertext arithmetic operation that implements data with integer homomorphic encryption to ensure data privacy and computability. Our scheme refers to the integer operation rules of complement, addition, subtraction, multiplication, and division. First, we use Boolean polynomials (BP) of containing logical AND, XOR operations to represent the rulers. Second, we convert the BP into homomorphic polynomials (HP) to perform ciphertext operations. Then, we optimise our scheme. We divide the ciphertext vector of integer encryption into subvectors of length 2 and increase the length of private key of FHE to support the 3\u2010multiplication level additional. We test our optimised scheme in DGHV and CMNT. In the number of ciphertext refreshes, the optimised scheme is reduced by 2\/3 compared to the original scheme, and the time overhead of our scheme is reduced by 1\/3. We also examine our scheme in CNT of without bootstrapping. The time overhead of optimised scheme over DGHV and CMNT is close to the original scheme over CNT.<\/jats:p>","DOI":"10.1155\/2018\/8142102","type":"journal-article","created":{"date-parts":[[2018,11,15]],"date-time":"2018-11-15T19:05:55Z","timestamp":1542308755000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Homomorphic Evaluation of the Integer Arithmetic Operations for Mobile Edge Computing"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4831-6069","authenticated-orcid":false,"given":"Changqing","family":"Gong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2390-3600","authenticated-orcid":false,"given":"Mengfei","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5829-6850","authenticated-orcid":false,"given":"Liang","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenzhou","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6921-7369","authenticated-orcid":false,"given":"Guangjie","family":"Han","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,11,15]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/MWC.2018.1700315"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/MNET.2017.1600213NM"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/JIOT.2018.2802913"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/2831347.2831354"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/LWC.2014.2337295"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPDS.2014.2365190"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.compeleceng.2016.12.031"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/COMST.2016.2544751"},{"key":"e_1_2_10_9_2","article-title":"Vehicular Communications: Standardization and Open Issues","author":"Zhao L.","year":"2019","journal-title":"IEEE Communications Standards Magazine"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/MNET.2018.1700202"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/LWC.2017.2740927"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1145\/1536414.1536440"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-57048-8_5"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13190-5_2"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20465-4_9"},{"key":"e_1_2_10_16_2","first-page":"420","article-title":"Fully homomorphic encryption with relatively small key and ciphertext sizes","volume":"6056","author":"Smart N. P.","year":"2010","journal-title":"Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface"},{"key":"e_1_2_10_17_2","doi-asserted-by":"crossref","unstructured":"CoronJ.-S. MandalA. NaccacheD. andTibouchiM. Fully homomorphic encryption over the integers with shorter public keys 6841 Proceedings of the 31st Annual International Cryptology Conference (CRYPTO \u203211) Santa Barbara Calif USA Springer 487\u2013504 Lecture Notes in Computer Science https:\/\/doi.org\/10.1007\/978-3-642-22792-9_28 MR2874875.","DOI":"10.1007\/978-3-642-22792-9_28"},{"key":"e_1_2_10_18_2","doi-asserted-by":"crossref","unstructured":"BrakerskiZ.andVaikuntanathanV. Efficient fully homomorphic encryption from (standard) LWE Proceedings of the IEEE 52nd Annual Symposium on Foundations of Computer Science (FOCS \u203211) October 2011 Palm Springs Calif USA 97\u2013106 https:\/\/doi.org\/10.1109\/FOCS.2011.12 2-s2.0-80955132201.","DOI":"10.1109\/FOCS.2011.12"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-22792-9_29"},{"key":"e_1_2_10_20_2","doi-asserted-by":"crossref","unstructured":"BrakerskiZ. GentryC. andVaikuntanathanV. (Leveled) fully homomorphic encryption without bootstrapping Proceedings of the 3rd Innovations in Theoretical Computer Science Conference 2012 ACM 309\u2013325 MR3388398.","DOI":"10.1145\/2090236.2090262"},{"key":"e_1_2_10_21_2","doi-asserted-by":"crossref","unstructured":"L\u00f3pez-AltA. TromerE. andVaikuntanathanV. On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption Proceedings of the 44th Annual ACM Symposium on Theory of Computing (STOC \u203212) May 2012 ACM 1219\u20131234 https:\/\/doi.org\/10.1145\/2213977.2214086 2-s2.0-84862629748.","DOI":"10.1145\/2213977.2214086"},{"key":"e_1_2_10_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-45239-0_4"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40041-4_5"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-32009-5_49"},{"key":"e_1_2_10_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-29011-4_28"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10623-012-9720-4"},{"key":"e_1_2_10_27_2","doi-asserted-by":"crossref","unstructured":"ChenY.andGongG. Integer arithmetic over ciphertext and homomorphic data aggregation Proceedings of the 3rd IEEE International Conference on Communications and Network Security CNS 2015 September 2015 Italy 628\u2013632 2-s2.0-84966286589.","DOI":"10.1109\/CNS.2015.7346877"},{"key":"e_1_2_10_28_2","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2017.2780885"},{"key":"e_1_2_10_29_2","doi-asserted-by":"crossref","unstructured":"GaiK. QiuM. LiY. andLiuX.-Y. Advanced Fully Homomorphic Encryption Scheme over Real Numbers Proceedings of the 4th IEEE International Conference on Cyber Security and Cloud Computing CSCloud 2017 and 3rd IEEE International Conference of Scalable and Smart Cloud SSC 2017 June 2017 USA 64\u201369 2-s2.0-85028680484.","DOI":"10.1109\/CSCloud.2017.61"},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCC.2015.2511769"},{"key":"e_1_2_10_31_2","doi-asserted-by":"crossref","unstructured":"CoronJ.-S. NaccacheD. andTibouchiM. Public key compression and modulus switching for fully homomorphic encryption over the integers 7237 Proceedings of the Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2012) Springer 446\u2013464 Lecture Notes in Comput. Sci. https:\/\/doi.org\/10.1007\/978-3-642-29011-4_27 MR2972913.","DOI":"10.1007\/978-3-642-29011-4_27"},{"key":"e_1_2_10_32_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-38348-9_20"},{"key":"e_1_2_10_33_2","doi-asserted-by":"crossref","unstructured":"CoronJ.-S. LepointT. TibouchiM. CheonJ. H. andKimJ. Batch fully homomorphic encryption over the integers Proceedings of the Annual International Conference on the Theory and Applications of Cryptographic Techniques 2013 Berlin Germany Springer 315\u2013335 https:\/\/doi.org\/10.1007\/978-3-642-54631-0_18 MR3178644.","DOI":"10.1007\/978-3-642-54631-0_18"},{"key":"e_1_2_10_34_2","unstructured":"KimJ. LeeM. S. YunA.et al. CRT-based fully homomorphic encryption over the integers Cryptology ePrint Archive https:\/\/eprint.iacr.org\/\/057.pdf."},{"key":"e_1_2_10_35_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-44371-2_31"},{"key":"e_1_2_10_36_2","doi-asserted-by":"publisher","DOI":"10.1093\/qjmam\/4.2.236"}],"container-title":["Wireless Communications and Mobile Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/wcmc\/2018\/8142102.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/wcmc\/2018\/8142102.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2018\/8142102","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T02:34:21Z","timestamp":1775270061000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2018\/8142102"}},"subtitle":[],"editor":[{"given":"Mianxiong","family":"Dong","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":36,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1155\/2018\/8142102"],"URL":"https:\/\/doi.org\/10.1155\/2018\/8142102","archive":["Portico"],"relation":{},"ISSN":["1530-8669","1530-8677"],"issn-type":[{"value":"1530-8669","type":"print"},{"value":"1530-8677","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]},"assertion":[{"value":"2018-09-26","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-10-31","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-11-15","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"8142102"}}