{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T04:28:27Z","timestamp":1741667307797,"version":"3.38.0"},"reference-count":45,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T00:00:00Z","timestamp":1524614400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computer Security"],"published-print":{"date-parts":[[2018,7,10]]},"abstract":"<jats:p> We present a privacy-assured multiplication protocol using which an arbitrary arithmetic formula with inputs from two parties over a finite field can be jointly computed on encrypted data using an additively homomorphic encryption scheme. Our protocol is secure against malicious adversaries. To motivate and illustrate applications of this technique, we demonstrate an attack on a class of known protocols showing how to compromise location privacy of honest users by manipulating messages in protocols with additively homomorphic encryption. We demonstrate how to apply the technique in order to solve different problems in geometric applications. We evaluate our approach using a prototypical implementation. The results show that the added overhead of our approach is small compared to insecure outsourced multiplication. <\/jats:p>","DOI":"10.3233\/jcs-171085","type":"journal-article","created":{"date-parts":[[2018,4,29]],"date-time":"2018-04-29T15:38:41Z","timestamp":1525016321000},"page":"557-587","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Assuring BetterTimes"],"prefix":"10.1177","volume":"26","author":[{"given":"Per","family":"Hallgren","sequence":"first","affiliation":[{"name":"Chalmers University of Technology, Gothenburg, Sweden"}]},{"given":"Ravi","family":"Kishore","sequence":"additional","affiliation":[{"name":"International Institute of Information Technology, Hyderabad, India"}]},{"given":"Mart\u00edn","family":"Ochoa","sequence":"additional","affiliation":[{"name":"Singapore University of Technology and Design, Singapore"},{"name":"Department of Applied Mathematics and Computer Science, Universidad del Rosario, Bogot\u00e1, Colombia"}]},{"given":"Andrei","family":"Sabelfeld","sequence":"additional","affiliation":[{"name":"Chalmers University of Technology, Gothenburg, Sweden"}]}],"member":"179","published-online":{"date-parts":[[2018,4,25]]},"reference":[{"key":"ref001","doi-asserted-by":"crossref","unstructured":"G.\u00a0Barthe, B.\u00a0Gr\u00e9goire and S.Z.\u00a0B\u00e9guelin, Formal certification of code-based cryptographic proofs, in: Proceedings of the 36th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 2009), Savannah, GA, USA, January 21\u201323, 2009, Z.\u00a0Shao and B.C.\u00a0Pierce, eds, ACM, New York, 2009, pp.\u00a090\u2013101.","DOI":"10.1145\/1480881.1480894"},{"key":"ref002","doi-asserted-by":"crossref","unstructured":"M.\u00a0Bellare, A.\u00a0Boldyreva and S.\u00a0Micali, Public-key encryption in a multi-user setting: Security proofs and improvements, in: Proceedings of International Conference on the Theory and Application of Cryptographic Techniques Advances in Cryptology (EUROCRYPT 2000), Bruges, Belgium, May 14\u201318, 2000, B.\u00a0Preneel, ed. Lecture Notes in Computer Science, Vol.\u00a01807, Springer, Berlin, 2000, pp.\u00a0259\u2013274.","DOI":"10.1007\/3-540-45539-6_18"},{"key":"ref003","doi-asserted-by":"crossref","unstructured":"D.\u00a0Bogdanov, S.\u00a0Laur and J.\u00a0Willemson, Sharemind: A framework for fast privacy-preserving computations, in: Proceedings of 13th European Symposium on Research in Computer Security Computer Security (ESORICS 2008), M\u00e1laga, Spain, October 6\u20138, 2008, S.\u00a0Jajodia and J.\u00a0L\u00f3pez, eds, Lecture Notes in Computer Science, Vol.\u00a05283, Springer, Berlin, 2008, pp.\u00a0192\u2013206. doi:10.1007\/978-3-540-88313-5_13.","DOI":"10.1007\/978-3-540-88313-5_13"},{"key":"ref004","doi-asserted-by":"crossref","unstructured":"P.\u00a0Bogetoft, D.L.\u00a0Christensen, I.\u00a0Damg\u00e5rd, M.\u00a0Geisler, T.P.\u00a0Jakobsen, M.\u00a0Kr\u00f8igaard, J.D.\u00a0Nielsen, J.B.\u00a0Nielsen, K.\u00a0Nielsen, J.\u00a0Pagter, M.I.\u00a0Schwartzbach and T.\u00a0Toft, Secure multiparty computation goes live, in: Revised Selected Papers of 13th International Conference on Financial Cryptography and Data Security (FC 2009), Accra Beach, Barbados, February 23\u201326, 2009, R.\u00a0Dingledine and P.\u00a0Golle, eds, Lecture Notes in Computer Science, Vol.\u00a05628, Springer, Berlin, 2009, pp.\u00a0325\u2013343. doi:10.1007\/978-3-642-03549-4_20.","DOI":"10.1007\/978-3-642-03549-4_20"},{"key":"ref005","unstructured":"Z.\u00a0Brakerski, C.\u00a0Gentry and V.\u00a0Vaikuntanathan, Fully homomorphic encryption without bootstrapping, Electronic Colloquium on Computational Complexity (ECCC) 18 (2011), 111."},{"key":"ref006","doi-asserted-by":"crossref","unstructured":"D.\u00a0Catalano and D.\u00a0Fiore, Using linearly-homomorphic encryption to evaluate degree-2 functions on encrypted data, in: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, Denver, CO, USA, October 12\u201316, 2015, I.\u00a0Ray, N.\u00a0Li and C.\u00a0Kruegel, eds, ACM, New York, 2015, pp.\u00a01518\u20131529.","DOI":"10.1145\/2810103.2813624"},{"key":"ref007","doi-asserted-by":"crossref","unstructured":"D.\u00a0Chaum and T.P.\u00a0Pedersen, Wallet databases with observers, in: 12th Annual International Cryptology Conference on Advances in Cryptology (CRYPTO\u201992), Santa Barbara, California, USA, August 16\u201320, 1992, E.F.\u00a0Brickell, ed. Lecture Notes in Computer Science, Vol.\u00a0740, Springer, 1992, pp.\u00a089\u2013105. doi:10.1007\/3-540-48071-4_7.","DOI":"10.1007\/3-540-48071-4_7"},{"key":"ref008","unstructured":"D.\u00a0Coldewey, \u201cGirls Around Me\u201d Creeper App Just Might Get People To Pay Attention To Privacy Settings, http:\/\/techcrunch.com\/2012\/03\/30\/girls-around-me-creeper-app-just-might-get-people-to-pay-attention-to-privacy-settings\/, Mar. 2012."},{"key":"ref009","doi-asserted-by":"crossref","unstructured":"R.\u00a0Cramer, I.\u00a0Damg\u00e5rd and J.B.\u00a0Nielsen, Multiparty computation from threshold homomorphic encryption, in: Proceedings of International Conference on the Theory and Application of Cryptographic Techniques Advances in Cryptology (EUROCRYPT 2001), Innsbruck, Austria, May 6\u201310, 2001, B.\u00a0Pfitzmann, ed. Lecture Notes in Computer Science, Vol.\u00a02045, Springer, Berlin, 2001, pp.\u00a0280\u2013299. doi:10.1007\/3-540-44987-6_18.","DOI":"10.1007\/3-540-44987-6_18"},{"key":"ref010","unstructured":"I.\u00a0Damg\u00e5rd, M.\u00a0Geisler and M.\u00a0Kr\u00f8igaard, Efficient and secure comparison for on-line auctions, in: Proceedings of 12th Australasian Conference Information Security and Privacy (ACISP 2007), Townsville, Australia, July 2\u20134, 2007, J.\u00a0Pieprzyk, H.\u00a0Ghodosi and E.\u00a0Dawson, eds, Lecture Notes in Computer Science, Vol.\u00a04586, Springer, Berlin, 2007, pp.\u00a0416\u2013430."},{"key":"ref011","doi-asserted-by":"crossref","unstructured":"I.\u00a0Damg\u00e5rd and M.\u00a0Jurik, A generalisation, a simplification and some applications of paillier\u2019s probabilistic public-key system, in: Proceedings of 4th International Workshop on Practice and Theory in Public Key Cryptography (PKC 2001), Cheju Island, Korea, February 13\u201315, 2001, K.\u00a0Kim, ed. Lecture Notes in Computer Science, Vol.\u00a01992, Springer, Berlin, 2001, pp.\u00a0119\u2013136.","DOI":"10.1007\/3-540-44586-2_9"},{"key":"ref012","doi-asserted-by":"crossref","unstructured":"R.\u00a0Dingledine, N.\u00a0Mathewson and P.F.\u00a0Syverson, Tor: The second-generation onion router, in: Proceedings of the 13th USENIX Security Symposium, San Diego, CA, USA, August 9\u201313, 2004, M.\u00a0Blaze, ed. USENIX, 2004, pp.\u00a0303\u2013320.","DOI":"10.21236\/ADA465464"},{"key":"ref013","doi-asserted-by":"crossref","unstructured":"Z.\u00a0Erkin, M.\u00a0Franz, J.\u00a0Guajardo, S.\u00a0Katzenbeisser, I.\u00a0Lagendijk and T.\u00a0Toft, Privacy-preserving face recognition, in: Proceedings of 9th International Symposium on Privacy Enhancing Technologies (PETS 2009), Seattle, WA, USA, August 5\u20137, 2009, I.\u00a0Goldberg and M.J.\u00a0Atallah, eds, Lecture Notes in Computer Science, Vol.\u00a05672, Springer, Berlin, 2009, pp.\u00a0235\u2013253.","DOI":"10.1007\/978-3-642-03168-7_14"},{"key":"ref014","unstructured":"Free Software Foundation, The GNU multiple precision arithmetic library, http:\/\/gmplib.org\/, 1991\u20132013."},{"key":"ref015","doi-asserted-by":"crossref","unstructured":"C.\u00a0Gentry, Fully homomorphic encryption using ideal lattices, in: Proceedings of the 41st Annual ACM Symposium on Theory of Computing (STOC 2009), Bethesda, MD, USA, May 31\u2013June 2, 2009, M.\u00a0Mitzenmacher, ed. ACM, New York, 2009, pp.\u00a0169\u2013178. doi:10.1145\/1536414.1536440.","DOI":"10.1145\/1536414.1536440"},{"key":"ref016","doi-asserted-by":"crossref","unstructured":"C.\u00a0Gentry, A.\u00a0Sahai and B.\u00a0Waters, Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based, in: Proceedings of 33rd Annual Cryptology Conference on Advances in Cryptology (CRYPTO 2013), Part I, Santa Barbara, CA, USA, August 18\u201322, 2013, R.\u00a0Canetti and J.A.\u00a0Garay, eds, Lecture Notes in Computer Science, Vol.\u00a08042, Springer, Berlin, 2013, pp.\u00a075\u201392.","DOI":"10.1007\/978-3-642-40041-4_5"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1999.1689"},{"key":"ref018","unstructured":"O.\u00a0Goldreich, The Foundations of Cryptography \u2013 Volume 2, Basic Applications, Cambridge University Press, Cambridge, 2004."},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1145\/116825.116852"},{"key":"ref020","unstructured":"P.\u00a0Hallgren, Bettertimes, 2017, https:\/\/bitbucket.org\/hallgrep\/bettertimes."},{"key":"ref021","unstructured":"P.A.\u00a0Hallgren, M.\u00a0Ochoa and A.\u00a0Sabelfeld, Bettertimes \u2013 privacy-assured outsourced multiplications for additively homomorphic encryption on finite fields, in: 9th International Conference Provable Security (ProvSec 2015), Kanazawa, Japan, November 24\u201326, 2015, M.H.\u00a0Au and A.\u00a0Miyaji, eds, Lecture Notes in Computer Science, Vol.\u00a09451, Springer, Berlin, 2015, pp.\u00a0291\u2013309."},{"key":"ref022","doi-asserted-by":"crossref","unstructured":"P.A.\u00a0Hallgren, M.\u00a0Ochoa and A.\u00a0Sabelfeld, Innercircle: A parallelizable decentralized privacy-preserving location proximity protocol, in: 13th Annual Conference on Privacy, Security and Trust (PST 2015), Izmir, Turkey, July 21\u201323, 2015, A.A.\u00a0Ghorbani, V.\u00a0Torra, H.\u00a0Hisil, A.\u00a0Miri, A.\u00a0Koltuksuz, J.\u00a0Zhang, M.\u00a0Sensoy, J.\u00a0Garc\u00eda-Alfaro and I.\u00a0Zincir, eds, IEEE Computer Society, 2015, pp.\u00a01\u20136.","DOI":"10.1109\/PST.2015.7232947"},{"key":"ref023","doi-asserted-by":"crossref","unstructured":"P.A.\u00a0Hallgren, M.\u00a0Ochoa and A.\u00a0Sabelfeld, Maxpace: Speed-constrained location queries, in: 2016 IEEE Conference on Communications and Network Security (CNS 2016), Philadelphia, PA, USA, October 17\u201319, IEEE, 2016, pp.\u00a0136\u2013144. doi:10.1109\/CNS.2016.7860479.","DOI":"10.1109\/CNS.2016.7860479"},{"key":"ref024","doi-asserted-by":"crossref","unstructured":"W.\u00a0Henecka, A.R.\u00a0Sadeghi, T.\u00a0Schneider, I.\u00a0Wehrenberg et al., Tasty: Tool for automating secure two-party computations, in: Proceedings of the 17th ACM Conference on Computer and Communications Security, ACM, New York, 2010, pp.\u00a0451\u2013462.","DOI":"10.1145\/1866307.1866358"},{"key":"ref025","unstructured":"Y.\u00a0Huang, D.\u00a0Evans, J.\u00a0Katz and L.\u00a0Malka, Faster secure two-party computation using garbled circuits, in: Proceedings of 20th USENIX Security Symposium, San Francisco, CA, USA, August 8\u201312, 2011, USENIX Association, 2011."},{"key":"ref026","doi-asserted-by":"crossref","unstructured":"Y.\u00a0Huang, J.\u00a0Katz and D.\u00a0Evans, Quid-pro-quo-tocols: Strengthening semi-honest protocols with dual execution, in: IEEE Symposium on Security and Privacy (SP 2012), San Francisco, California, USA, 21\u201323 May, 2012, IEEE Computer Society, Los Alamitos, 2012, pp.\u00a0272\u2013284. doi:10.1109\/SP.2012.43.","DOI":"10.1109\/SP.2012.43"},{"key":"ref027","unstructured":"V.\u00a0Kolesnikov, A.\u00a0Sadeghi and T.\u00a0Schneider, From dust to dawn: Practically efficient two-party secure function evaluation protocols and their modular design, IACR Cryptology ePrint Archive 2010 (2010), 79."},{"key":"ref028","doi-asserted-by":"publisher","DOI":"10.3233\/JCS-130464"},{"key":"ref029","unstructured":"V.\u00a0Kolesnikov and T.\u00a0Schneider, Improved garbled circuit: Free XOR gates and applications, in: 35th International Colloquium on Automata, Languages and Programming (ICALP 2008), Proceedings, Part II \u2013 Track B: Logic, Semantics, and Theory of Programming & Track C: Security and Cryptography Foundations, Reykjavik, Iceland, July 7\u201311, 2008, L.\u00a0Aceto, I.\u00a0Damg\u00e5rd, L.A.\u00a0Goldberg, M.M.\u00a0Halld\u00f3rsson, A.\u00a0Ing\u00f3lfsd\u00f3ttir and I.\u00a0Walukiewicz, eds, Lecture Notes in Computer Science, Vol.\u00a05126, Springer, Berlin, 2008, pp.\u00a0486\u2013498."},{"key":"ref030","unstructured":"B.\u00a0Kreuter, A.\u00a0Shelat and C.\u00a0Shen, Billion-gate secure computation with malicious adversaries, in: Proceedings of the 21th USENIX Security Symposium, Bellevue, WA, USA, August 8\u201310, 2012, T.\u00a0Kohno, ed. USENIX Association, 2012, pp.\u00a0285\u2013300."},{"key":"ref031","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2012.2219653"},{"key":"ref032","doi-asserted-by":"crossref","unstructured":"M.\u00a0Li, H.\u00a0Zhu, Z.\u00a0Gao, S.\u00a0Chen, L.\u00a0Yu, S.\u00a0Hu and K.\u00a0Ren, All your location are belong to us: Breaking mobile social networks for automated user location tracking, in: The Fifteenth ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc\u201914), Philadelphia, PA, USA, August 11\u201314, 2014, J.\u00a0Wu, X.\u00a0Cheng, X.\u00a0Li and S.\u00a0Sarkar, eds, ACM, New York, 2014, pp.\u00a043\u201352.","DOI":"10.1145\/2632951.2632953"},{"key":"ref033","doi-asserted-by":"crossref","unstructured":"Y.\u00a0Lindell and B.\u00a0Pinkas, Secure multiparty computation for privacy-preserving data mining, IACR Cryptology ePrint Archive 2008 (2008), 197.","DOI":"10.29012\/jpc.v1i1.566"},{"key":"ref034","doi-asserted-by":"crossref","unstructured":"C.\u00a0Liu, X.S.\u00a0Wang, K.\u00a0Nayak, Y.\u00a0Huang and E.\u00a0Shi, Oblivm: A programming framework for secure computation, in: 2015 IEEE Symposium on Security and Privacy (SP 2015), San Jose, CA, USA, May 17\u201321, 2015, IEEE Computer Society, Los Alamitos, 2015, pp.\u00a0359\u2013376. doi:10.1109\/SP.2015.29.","DOI":"10.1109\/SP.2015.29"},{"key":"ref035","unstructured":"A.\u00a0Narayanan, N.\u00a0Thiagarajan, M.\u00a0Lakhani, M.\u00a0Hamburg and D.\u00a0Boneh, Location privacy via private proximity testing, in: Proceedings of the Network and Distributed System Security Symposium (NDSS 2011), San Diego, California, USA, 6th February\u20139th February 2011, The Internet Society, 2011."},{"key":"ref036","doi-asserted-by":"crossref","unstructured":"P.\u00a0Paillier, Public-key cryptosystems based on composite degree residuosity classes, in: Proceedings of International Conference on the Theory and Application of Cryptographic Techniques Advances in Cryptology (EUROCRYPT 1999), Prague, Czech Republic, May 2\u20136, 1999, J.\u00a0Stern, ed. Lecture Notes in Computer Science, Vol.\u00a01592, Springer, Berlin, 1999, pp.\u00a0223\u2013238.","DOI":"10.1007\/3-540-48910-X_16"},{"key":"ref037","doi-asserted-by":"crossref","unstructured":"I.\u00a0Polakis, G.\u00a0Argyros, T.\u00a0Petsios, S.\u00a0Sivakorn and A.D.\u00a0Keromytis, Where\u2019s wally? Precise user discovery attacks in location proximity services, in: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, Denver, CO, USA, October 12\u201316, 2015, I.\u00a0Ray, N.\u00a0Li and C.\u00a0Kruegel, eds, ACM, New York, 2015, pp.\u00a0817\u2013828.","DOI":"10.1145\/2810103.2813605"},{"key":"ref038","unstructured":"I.\u00a0Ray, N.\u00a0Li and C.\u00a0Kruegel (eds), Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, Denver, CO, USA, October 12\u201316, 2015, ACM, New York, 2015."},{"key":"ref039","doi-asserted-by":"crossref","unstructured":"A.\u00a0Sadeghi, T.\u00a0Schneider and I.\u00a0Wehrenberg, Efficient privacy-preserving face recognition, in: Revised Selected Papers of 12th International Conference on Information, Security and Cryptology (ICISC 2009), Seoul, Korea, December 2\u20134, 2009, D.H.\u00a0Lee and S.\u00a0Hong, eds, Lecture Notes in Computer Science, Vol.\u00a05984, Springer, Berlin, 2009, pp.\u00a0229\u2013244. doi:10.1007\/978-3-642-14423-3_16.","DOI":"10.1007\/978-3-642-14423-3_16"},{"key":"ref040","doi-asserted-by":"crossref","unstructured":"J.\u00a0Sedenka and P.\u00a0Gasti, Privacy-preserving distance computation and proximity testing on Earth, done right, in: 9th ACM Symposium on Information, Computer and Communications Security (ASIA CCS\u201914), Kyoto, Japan, June 03\u201306, 2014, S.\u00a0Moriai, T.\u00a0Jaeger and K.\u00a0Sakurai, eds, ACM, New York, 2014, pp.\u00a099\u2013110.","DOI":"10.1145\/2590296.2590307"},{"key":"ref041","doi-asserted-by":"publisher","DOI":"10.1561\/0400000039"},{"key":"ref042","unstructured":"M.\u00a0Veytsman, How I was able to track the location of any Tinder user, http:\/\/blog.includesecurity.com\/2014\/02\/how-i-was-able-to-track-location-of-any.html, Feb. 2014."},{"key":"ref043","doi-asserted-by":"crossref","unstructured":"M.\u00a0Wachs, M.\u00a0Schanzenbach and C.\u00a0Grothoff, On the feasibility of a censorship resistant decentralized name system, in: Revised Selected Papers of the 6th International Symposium on Foundations and Practice of Security (FPS 2013), La Rochelle, France, October 21\u201322, 2013, J.L.\u00a0Danger, M.\u00a0Debbabi, J.\u00a0Marion, J.\u00a0Garc\u00eda-Alfaro and A.N.\u00a0Zincir-Heywood, eds, Lecture Notes in Computer Science, Vol.\u00a08352, Springer, New York, 2013, pp.\u00a019\u201330. doi:10.1007\/978-3-319-05302-8_2.","DOI":"10.1007\/978-3-319-05302-8_2"},{"key":"ref044","doi-asserted-by":"crossref","unstructured":"A.C.\u00a0Yao, Protocols for secure computations (extended abstract), in: 23rd Annual Symposium on Foundations of Computer Science, Chicago, Illinois, USA, 3\u20135 November, 1982, IEEE Computer Society, Los Alamitos 1982, pp.\u00a0160\u2013164.","DOI":"10.1109\/SFCS.1982.38"},{"key":"ref045","doi-asserted-by":"crossref","unstructured":"G.\u00a0Zhong, I.\u00a0Goldberg and U.\u00a0Hengartner, Louis, Lester and Pierre: Three protocols for location privacy, in: Revised Selected Papers of 7th International Symposium on Privacy Enhancing Technologies (PET 2007), Ottawa, Canada, June 20\u201322, 2007, N.\u00a0Borisov and P.\u00a0Golle, eds, Lecture Notes in Computer Science, Vol.\u00a04776, Springer, Berlin, 2007, pp.\u00a062\u201376. doi:10.1007\/978-3-540-75551-7_5.","DOI":"10.1007\/978-3-540-75551-7_5"}],"container-title":["Journal of Computer Security"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JCS-171085","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JCS-171085","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JCS-171085","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T18:19:32Z","timestamp":1741630772000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JCS-171085"}},"subtitle":["Private arithmetic formulas"],"short-title":[],"issued":{"date-parts":[[2018,4,25]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,7,10]]}},"alternative-id":["10.3233\/JCS-171085"],"URL":"https:\/\/doi.org\/10.3233\/jcs-171085","relation":{},"ISSN":["0926-227X","1875-8924"],"issn-type":[{"type":"print","value":"0926-227X"},{"type":"electronic","value":"1875-8924"}],"subject":[],"published":{"date-parts":[[2018,4,25]]}}}