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'''Secure two-party computation''' (2PC) is sub-problem of [[secure multi-party computation]] (MPC) that has received special attention by researchers because of its close relation to many [[cryptographic]] tasks. The goal of 2PC is to create a generic protocol that allows two parties to jointly compute an arbitrary function on their inputs without sharing the value of their inputs with the opposing party. One of the most well known examples of 2PC is [[Yao's Millionaires' Problem|Yao's millionaire problem]], in which two parties, Alice and Bob, are millionaires who wish to determine who is wealthier without revealing their wealth. Formally, Alice has wealth <math>a</math>, Bob has wealth <math>b</math>, and they wish to compute <math>a \geq b</math> without revealing the values <math>a</math> or <math>b</math>.
[[Andrew Yao|Yao]]'s [[garbled circuit protocol]] for two-party computation <ref>{{Cite book | last1 = Yao | first1 = A. C. | title = 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982) | doi = 10.1109/SFCS.1982.38 | pages = 160–164 | year = 1982 | chapter = Protocols for secure computations | s2cid = 206558698 }}</ref> only provided security against passive adversaries. One of the first general solutions for achieving security against active adversary was introduced by Goldreich, Micali and Wigderson<ref>{{Cite journal|lastlast1=Goldreich|firstfirst1=O.|last2=Micali|first2=S.|last3=Wigderson|first3=A.|date=1987-01-01|title=How to play ANY mental game|url=https://doi.org/10.1145/28395.28420|journal=Proceedings of the nineteenthNineteenth annualAnnual ACM symposiumSymposium on Theory of computingComputing|series=STOC '87|___location=New York, New York, USA|publisher=Association for Computing Machinery|pages=218–229|doi=10.1145/28395.28420|isbn=978-0-89791-221-1}}</ref> by applying Zero-Knowledge Proof<ref>{{Cite journal|lastlast1=Goldwasser|firstfirst1=S|last2=Micali|first2=S|last3=Rackoff|first3=C|date=1985-12-01|title=The knowledge complexity of interactive proof-systems|url=https://doi.org/10.1145/22145.22178|journal=Proceedings of the seventeenthSeventeenth annualAnnual ACM symposiumSymposium on Theory of computingComputing|series=STOC '85|___location=Providence, Rhode Island, USA|publisher=Association for Computing Machinery|pages=291–304|doi=10.1145/22145.22178|isbn=978-0-89791-151-1}}</ref> to enforce semi-honest behavior. This approach was known to be impractical for years due to high complexity overheads. However, significant improvements have been made toward applying this method in 2PC and Abascal, Faghihi Sereshgi, Hazay, Ishai and Venkitasubramaniam gave the first efficient protocol based on this approach.<ref>{{Cite journal|lastlast1=Abascal|firstfirst1=Jackson|last2=Faghihi Sereshgi|first2=Mohammad Hossein|last3=Hazay|first3=Carmit|last4=Ishai|first4=Yuval|last5=Venkitasubramaniam|first5=Muthuramakrishnan|date=2020-10-30|title=Is the Classical GMW Paradigm Practical? The Case of Non-Interactive Actively Secure 2PC|url=https://doi.org/10.1145/3372297.3423366|journal=Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security|series=CCS '20|___location=Virtual Event, USA|publisher=Association for Computing Machinery|pages=1591–1605|doi=10.1145/3372297.3423366|isbn=978-1-4503-7089-9}}</ref> Another type of 2PC protocols that are secure against active adversaries were proposed by Lindell and Pinkas,<ref>{{Cite book | last1 = Lindell | first1 = Y. | title = Advances in Cryptology - EUROCRYPT 2007 | last2 = Pinkas | first2 = B. | doi = 10.1007/978-3-540-72540-4_4 | volume = 4515 | pages = 52–78 | year = 2007 | series = Lecture Notes in Computer Science | isbn = 978-3-540-72539-8 }}</ref> Ishai, Prabhakaran and Sahai <ref>{{Cite book | last1 = Ishai | first1 = Y. | title = Advances in Cryptology – CRYPTO 2008 | last2 = Prabhakaran | first2 = M. | last3 = Sahai | first3 = A. | doi = 10.1007/978-3-540-85174-5_32 | volume = 5157 | pages = 572–591 | year = 2008 | series = Lecture Notes in Computer Science | isbn = 978-3-540-85173-8 }}</ref> and Nielsen and Orlandi.<ref>{{Cite book | last1 = Nielsen | first1 = J. B. | last2 = Orlandi | first2 = C. | doi = 10.1007/978-3-642-00457-5_22 | chapter = LEGO for Two-Party Secure Computation | title = Theory of Cryptography | series = Lecture Notes in Computer Science | volume = 5444 | pages = 368–386 | year = 2009 | isbn = 978-3-642-00456-8 | citeseerx = 10.1.1.215.4422 }}</ref>
Another solution for this problem, that explicitly works with committed input was proposed by Jarecki and Shmatikov.<ref>{{Cite book | last1 = Jarecki | first1 = S. | title = Advances in Cryptology - EUROCRYPT 2007 | last2 = Shmatikov | first2 = V. | doi = 10.1007/978-3-540-72540-4_6 | volume = 4515 | pages = 97–114 | year = 2007 | series = Lecture Notes in Computer Science | isbn = 978-3-540-72539-8 }}</ref>
