{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:15:49Z","timestamp":1760235349869,"version":"build-2065373602"},"reference-count":57,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,8,21]],"date-time":"2021-08-21T00:00:00Z","timestamp":1629504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Estonian Personal Research Grant","award":["920"],"award-info":[{"award-number":["920"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>This paper formalises the security of programmable secure computation focusing on simplifying security proofs of new algorithms for existing computation frameworks. Security of the frameworks is usually well established but the security proofs of the algorithms are often more intuitive than rigorous. This work specifies a transformation from the usual hybrid execution model to an abstract model that is closer to the intuition. We establish various preconditions that are satisfied by natural secure computation frameworks and protocols, thus showing that mostly the intuitive proofs suffice. More elaborate protocols might still need additional proof details.<\/jats:p>","DOI":"10.3390\/cryptography5030022","type":"journal-article","created":{"date-parts":[[2021,8,22]],"date-time":"2021-08-22T23:00:09Z","timestamp":1629673209000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Foundations of Programmable Secure Computation"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9891-3347","authenticated-orcid":false,"given":"Sven","family":"Laur","sequence":"first","affiliation":[{"name":"Institute of Computer Science, University of Tartu, Narva mnt 18, 51009 Tartu, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3255-7001","authenticated-orcid":false,"given":"Pille","family":"Pullonen-Raudvere","sequence":"additional","affiliation":[{"name":"Cybernetica AS, M\u00e4ealuse 2\/1, 12618 Tallinn, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,21]]},"reference":[{"key":"ref_1","first-page":"192","article-title":"Sharemind: A Framework for Fast Privacy-Preserving Computations","volume":"Volume 5283","author":"Jajodia","year":"2008","journal-title":"Lecture Notes in Computer Science, Proceedings of the Computer Security\u2014ESORICS 2008, 13th European Symposium on Research in Computer Security, M\u00e1laga, Spain, 6\u20138 October 2008"},{"key":"ref_2","first-page":"643","article-title":"Multiparty Computation from Somewhat Homomorphic Encryption","volume":"Volume 7417","author":"Canetti","year":"2012","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014CRYPTO 2012\u201432nd Annual Cryptology Conference, Santa Barbara, CA, USA, 19\u201323 August 2012"},{"key":"ref_3","unstructured":"Bogdanov, D. (2013). Sharemind: Programmable Secure Computations with Practical Applications. [Ph.D. Thesis, University of Tartu]."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Demmler, D., Schneider, T., and Zohner, M. (2015, January 8\u201311). ABY\u2014A Framework for Efficient Mixed-Protocol Secure Two-Party Computation. Proceedings of the 22nd Annual Network and Distributed System Security Symposium, NDSS 2015, San Diego, CA, USA.","DOI":"10.14722\/ndss.2015.23113"},{"key":"ref_5","unstructured":"Alexandra Institute (2021, August 20). FRESCO\u2014A Framework for Efficient Secure Computation. Available online: http:\/\/github.com\/aicis\/fresco."},{"key":"ref_6","unstructured":"KU Leuven (2021, August 20). SCALE-MAMBA Software. Available online: https:\/\/github.com\/KULeuven-COSIC\/SCALE-MAMBA."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Keller, M. (2020, January 9\u201313). MP-SPDZ: A Versatile Framework for Multi-Party Computation. Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security\u2014CCS\u201920, Virtual Event.","DOI":"10.1145\/3372297.3417872"},{"key":"ref_8","first-page":"325","article-title":"Secure Multiparty Computation Goes Live","volume":"Volume 5628","author":"Dingledine","year":"2009","journal-title":"Lecture Notes in Computer Science, Proceedings of the Financial Cryptography and Data Security, 13th International Conference, FC 2009, Accra Beach, Barbados, 23\u201326 February 2009"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Mohassel, P., and Zhang, Y. (2017, January 22\u201326). SecureML: A System for Scalable Privacy-Preserving Machine Learning. Proceedings of the 2017 IEEE Symposium on Security and Privacy, SP 2017, San Jose, CA, USA.","DOI":"10.1109\/SP.2017.12"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1515\/popets-2016-0019","article-title":"Students and Taxes: A Privacy-Preserving Study Using Secure Computation","volume":"2016","author":"Bogdanov","year":"2016","journal-title":"PoPETs"},{"key":"ref_11","first-page":"1749","article-title":"From Keys to Databases\u2014Real-World Applications of Secure Multi-Party Computation","volume":"61","author":"Archer","year":"2018","journal-title":"Comput. J."},{"key":"ref_12","unstructured":"Lie, D., Mannan, M., Backes, M., and Wang, X. (2018, January 15\u201319). ABY3: A Mixed Protocol Framework for Machine Learning. Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, CCS 2018, Toronto, ON, Canada."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1186\/s12920-018-0400-8","article-title":"Privacy-preserving record linkage in large databases using secure multiparty computation","volume":"11","author":"Laud","year":"2018","journal-title":"BMC Med. Genom."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Canetti, R. (2001, January 14\u201317). Universally Composable Security: A New Paradigm for Cryptographic Protocols. Proceedings of the 42nd Annual Symposium on Foundations of Computer Science, FOCS 2001, Las Vegas, NV, USA.","DOI":"10.1109\/SFCS.2001.959888"},{"key":"ref_15","first-page":"247","article-title":"Universally Composable Efficient Multiparty Computation from Threshold Homomorphic Encryption","volume":"Volume 2729","author":"Boneh","year":"2003","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014CRYPTO 2003, 23rd Annual International Cryptology Conference, Santa Barbara, CA, USA, 17\u201321 August 2003"},{"key":"ref_16","first-page":"645","article-title":"Secure Equality and Greater-Than Tests with Sublinear Online Complexity","volume":"Volume 7966","author":"Fomin","year":"2013","journal-title":"Lecture Notes in Computer Science, Proceedings of the Automata, Languages, and Programming\u201440th International Colloquium, ICALP 2013, Riga, Latvia, 8\u201312 July 2013"},{"key":"ref_17","first-page":"823","article-title":"Improved Primitives for MPC over Mixed Arithmetic-Binary Circuits","volume":"Volume 12171","author":"Micciancio","year":"2020","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014CRYPTO 2020\u201440th Annual International Cryptology Conference, CRYPTO 2020, Santa Barbara, CA, USA, 17\u201321 August 2020"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Damg\u00e5rd, I., Escudero, D., Frederiksen, T.K., Keller, M., Scholl, P., and Volgushev, N. (2019, January 19\u201323). New Primitives for Actively-Secure MPC over Rings with Applications to Private Machine Learning. Proceedings of the 2019 IEEE Symposium on Security and Privacy, SP 2019, San Francisco, CA, USA.","DOI":"10.1109\/SP.2019.00078"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1007\/s10207-014-0271-8","article-title":"Secure Floating-Point Arithmetic and Private Satellite Collision Analysis","volume":"14","author":"Kamm","year":"2015","journal-title":"Int. J. Inf. Secur."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"339","DOI":"10.2478\/popets-2021-0073","article-title":"Secure integer division with a private divisor","volume":"2021","author":"Veugen","year":"2021","journal-title":"Proc. Priv. Enhancing Technol."},{"key":"ref_21","first-page":"182","article-title":"Improved Primitives for Secure Multiparty Integer Computation","volume":"Volume 6280","author":"Garay","year":"2010","journal-title":"Lecture Notes in Computer Science, Proceedings of the Security and Cryptography for Networks, 7th International Conference, SCN 2010, Amalfi, Italy, 13\u201315 September 2010"},{"key":"ref_22","first-page":"343","article-title":"Multiparty Computation for Interval, Equality, and Comparison Without Bit-Decomposition Protocol","volume":"Volume 4450","author":"Okamoto","year":"2007","journal-title":"Lecture Notes in Computer Science, Proceedings of the Public Key Cryptography\u2014PKC 2007, 10th International Conference on Practice and Theory in Public-Key Cryptography, Beijing, China, 16\u201320 April 2007"},{"key":"ref_23","first-page":"285","article-title":"Unconditionally Secure Constant-Rounds Multi-party Computation for Equality, Comparison, Bits and Exponentiation","volume":"Volume 3876","author":"Halevi","year":"2006","journal-title":"Lecture Notes in Computer Science, Proceedings of the Theory of Cryptography, Third Theory of Cryptography Conference, TCC 2006, New York, NY, USA, 4\u20137 March 2006"},{"key":"ref_24","first-page":"265","article-title":"Universal Composition with Joint State","volume":"Volume 2729","author":"Boneh","year":"2003","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014CRYPTO 2003, 23rd Annual International Cryptology Conference, Santa Barbara, CA, USA, 17\u201321 August 2003"},{"key":"ref_25","unstructured":"Pfitzmann, B., and Waidner, M. (2001, January 14\u201316). A Model for Asynchronous Reactive Systems and its Application to Secure Message Transmission. Proceedings of the 2001 IEEE Symposium on Security and Privacy\u2014SP\u201901, Oakland, CA, USA."},{"key":"ref_26","first-page":"336","article-title":"A General Composition Theorem for Secure Reactive Systems","volume":"Volume 2951","author":"Naor","year":"2004","journal-title":"Lecture Notes in Computer Science, Proceedings of the Theory of Cryptography, First Theory of Cryptography Conference, TCC 2004, Cambridge, MA, USA, 19\u201321 February 2004"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1016\/j.ic.2007.05.002","article-title":"The reactive simulatability (RSIM) framework for asynchronous systems","volume":"205","author":"Backes","year":"2007","journal-title":"Inf. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Goldreich, O. (2004). The Foundations of Cryptography\u2014Volume 2: Basic Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511721656"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s001459910006","article-title":"Security and Composition of Multiparty Cryptographic Protocols","volume":"13","author":"Canetti","year":"2000","journal-title":"J. Cryptol."},{"key":"ref_30","first-page":"392","article-title":"Secure Computation (Abstract)","volume":"Volume 576","author":"Feigenbaum","year":"1991","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014CRYPTO\u201991, 11th Annual International Cryptology Conference, Santa Barbara, CA, USA, 11\u201315 August 1991"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/BF00196771","article-title":"Secure Multiparty Protocols and Zero-Knowledge Proof Systems Tolerating a Faulty Minority","volume":"4","author":"Beaver","year":"1991","journal-title":"J. Cryptol."},{"key":"ref_32","unstructured":"Miller, G.L. (1996, January 22\u201324). Adaptively Secure Multi-Party Computation. Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, Philadelphia, PA, USA."},{"key":"ref_33","first-page":"274","article-title":"Realistic Failures in Secure Multi-party Computation","volume":"Volume 5444","author":"Reingold","year":"2009","journal-title":"Lecture Notes in Computer Science, Proceedings of the Theory of Cryptography, 6th Theory of Cryptography Conference, TCC 2009, San Francisco, CA, USA, 15\u201317 March 2009"},{"key":"ref_34","first-page":"19","article-title":"Complete Fairness in Multi-party Computation without an Honest Majority","volume":"Volume 5444","author":"Reingold","year":"2009","journal-title":"Lecture Notes in Computer Science, Proceedings of the Theory of Cryptography, 6th Theory of Cryptography Conference, TCC 2009, San Francisco, CA, USA, 15\u201317 March 2009"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1007\/s00145-016-9245-5","article-title":"Fairness Versus Guaranteed Output Delivery in Secure Multiparty Computation","volume":"30","author":"Cohen","year":"2017","journal-title":"J. Cryptol."},{"key":"ref_36","unstructured":"Kiraz, M., and Schoenmakers, B. (2006, January 8\u20139). A protocol issue for the malicious case of Yao\u2019s garbled circuit construction. Proceedings of the 27th Symposium on Information Theory in the Benelux, Noordwijk, The Netherlands."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1007\/11745853_30","article-title":"Efficiency Tradeoffs for Malicious Two-Party Computation","volume":"Volume 3958","author":"Yung","year":"2006","journal-title":"Lecture Notes in Computer Science, Proceedings of the Public Key Cryptography\u2014PKC 2006, 9th International Conference on Theory and Practice of Public-Key Cryptography, New York, NY, USA, 24\u201326 April 2006"},{"key":"ref_38","first-page":"137","article-title":"Security Against Covert Adversaries: Efficient Protocols for Realistic Adversaries","volume":"Volume 4392","author":"Vadhan","year":"2007","journal-title":"Lecture Notes in Computer Science, Proceedings of the Theory of Cryptography, 4th Theory of Cryptography Conference, TCC 2007, Amsterdam, The Netherlands, 21\u201324 February 2007"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1007\/s00145-008-9019-9","article-title":"On the Relationships between Notions of Simulation-Based Security","volume":"21","author":"Datta","year":"2008","journal-title":"J. Cryptol."},{"key":"ref_40","first-page":"23","article-title":"Concurrent Secure Computation via Non-Black Box Simulation","volume":"Volume 9216","author":"Gennaro","year":"2015","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014CRYPTO 2015\u201435th Annual Cryptology Conference, Santa Barbara, CA, USA, 16\u201320 August 2015"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s00145-018-09309-5","article-title":"Non-black-box Simulation in the Fully Concurrent Setting, Revisited","volume":"32","author":"Kiyoshima","year":"2019","journal-title":"J. Cryptol."},{"key":"ref_42","first-page":"160","article-title":"Simulation in Quasi-Polynomial Time, and Its Application to Protocol Composition","volume":"Volume 2656","author":"Biham","year":"2003","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014EUROCRYPT 2003, International Conference on the Theory and Applications of Cryptographic Techniques, Warsaw, Poland, 4\u20138 May 2003"},{"key":"ref_43","unstructured":"Barak, B., and Sahai, A. (2005, January 23\u201325). How To Play Almost Any Mental Game Over The Net\u2014Concurrent Composition via Super-Polynomial Simulation. Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2005), Pittsburgh, PA, USA."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Oren, Y. (1987, January 27\u201329). On the Cunning Power of Cheating Verifiers: Some Observations about Zero Knowledge Proofs (Extended Abstract). Proceedings of the 28th Annual Symposium on Foundations of Computer Science, Los Angeles, CA, USA.","DOI":"10.1109\/SFCS.1987.43"},{"key":"ref_45","unstructured":"Canetti, R. (2021, August 20). Universally Composable Security: A New Paradigm for Cryptographic Protocols. Cryptology ePrint Archive, Report 2000\/067. Available online: https:\/\/eprint.iacr.org\/2000\/067."},{"key":"ref_46","unstructured":"Chazelle, B. (2011, January 7\u20139). Abstract Cryptography. Proceedings of the Innovations in Computer Science\u2014ICS 2011, Beijing, China."},{"key":"ref_47","unstructured":"K\u00fcsters, R. (2006, January 5\u20137). Simulation-Based Security with Inexhaustible Interactive Turing Machines. Proceedings of the 19th IEEE Computer Security Foundations Workshop, (CSFW-19 2006), Venice, Italy."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s00145-013-9160-y","article-title":"GNUC: A New Universal Composability Framework","volume":"28","author":"Hofheinz","year":"2015","journal-title":"J. Cryptol."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3233\/JCS-140523","article-title":"Symbolic universal composability","volume":"24","author":"Unruh","year":"2016","journal-title":"J. Comput. Secur."},{"key":"ref_50","first-page":"191","article-title":"iUC: Flexible Universal Composability Made Simple","volume":"Volume 11923","author":"Galbraith","year":"2019","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014ASIACRYPT 2019\u201425th International Conference on the Theory and Application of Cryptology and Information Security, Kobe, Japan, 8\u201312 December 2019"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/11535218_22","article-title":"Secure Computation Without Authentication","volume":"Volume 3621","author":"Shoup","year":"2005","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014CRYPTO 2005: 25th Annual International Cryptology Conference, Santa Barbara, CA, USA, 14\u201318 August 2005"},{"key":"ref_52","first-page":"3","article-title":"A Simpler Variant of Universally Composable Security for Standard Multiparty Computation","volume":"Volume 9216","author":"Gennaro","year":"2015","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014CRYPTO 2015\u201435th Annual Cryptology Conference, Santa Barbara, CA, USA, 16\u201320 August 2015"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Yao, A.C. (1982, January 3\u20135). Protocols for Secure Computations (Extended Abstract). Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, Chicago, IL, USA.","DOI":"10.1109\/SFCS.1982.38"},{"key":"ref_54","first-page":"377","article-title":"Foundations of Secure Interactive Computing","volume":"Volume 576","author":"Feigenbaum","year":"1991","journal-title":"Lecture Notes in Computer Science, Proceedings of the Advances in Cryptology\u2014CRYPTO\u201991, 11th Annual International Cryptology Conference, Santa Barbara, CA, USA, 11\u201315 August 1991"},{"key":"ref_55","unstructured":"Bellare, M., and Rogaway, P. (October, January 2). Robust Computational Secret Sharing and a Unified Account of Classical Secret-Sharing Goals. Proceedings of the 14th ACM Conference on Computer and Communications Security\u2014CCS\u201907, Alexandria, VA, USA."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Damg\u00e5rd, I., and Nielsen, J.B. (2014, January 9\u201310). Adaptive versus static security in the UC model. Proceedings of the International Conference on Provable Security, Hong Kong, China.","DOI":"10.1007\/978-3-319-12475-9_2"},{"key":"ref_57","unstructured":"Shmoys, D.B. (June, January 31). Circuits resilient to additive attacks with applications to secure computation. Proceedings of the Symposium on Theory of Computing, STOC 2014, New York, NY, USA."}],"container-title":["Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2410-387X\/5\/3\/22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:48:55Z","timestamp":1760165335000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2410-387X\/5\/3\/22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,21]]},"references-count":57,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["cryptography5030022"],"URL":"https:\/\/doi.org\/10.3390\/cryptography5030022","relation":{},"ISSN":["2410-387X"],"issn-type":[{"type":"electronic","value":"2410-387X"}],"subject":[],"published":{"date-parts":[[2021,8,21]]}}}