PPT-Secure Computation Lecture 17-18

Arpita Patra Recap gtThree orthogonal problems nt sharing reconstruction multiplication protocol gt Verifiable Secret Sharing VSS will take care first two problems gtgt . 2.1TheArithmeticBlack-boxThearithmeticblack-boxallowsnparties,P1;:::;Pn,tosecurelystoreandretrieveelementsofaringZM.Here,MwillbeeitheraprimeoranRSA-modulus,i.e.theproductoftwooddprimes.Thesecurestorag (Lecture 2). Arpita. . Patra. Vishwaroop. of MPC. Expanding the scope of MPC. Dimension 1:. Any . polynomially. computable function can be computed securely.. >> So far you have seen how to compute addition and bit multiplication securely. (Lecture 1). Arpita. . Patra. Welcome to an exciting Journey .  . >> . Course Homepage. : . http://. drona.csa.iisc.ernet.in. /~. arpita. /SecureComputation15. .html . >> References:. Professor, Computer Science, UMD. Director, Maryland Cybersecurity Center. . Secure . Computation. Mathematics. Complexity . theory. C. ryptography. Cybersecurity. Science of . Cybersecurity. C. ryptography. Ranjit . Kumaresan. (MIT). Based on joint works with . Iddo. . Bentov. (. Technion. ), Tal Moran (IDC), Guy . Zyskind. (MIT). x. f. . (. x,y. ). y. f. . (. x,y. ). Secure Computation. Most general problem in cryptography. . Kartik . Nayak. With Xiao . Shaun . Wang, . Stratis. Ioannidis, Udi . Weinsberg. , Nina Taft, Elaine Shi. 1. 2. Users. Data. Data. Privacy concern!. Data Mining Engine. Data Model. Data Mining on User Data. Prediction markets & real-world data feeds. Assertions about the outside world . Idea. : add a mechanism to assert facts. election outcomes. sports results. commodity prices. Bet or hedge results using smart contracts. Tore Frederiksen. , . Thomas . Jakobsen. , . Jesper. Nielsen, Peter . Nordholt. , Claudio . Orlandi. 27-08-2016. The LEGO Approach for. Maliciously Secure Two-Party Computation. 1. What we will present. 1. Computation. In general, a . partial function. f on a set S. m. is a function whose domain is a subset of S. m. .. If a partial function on S. m. has the domain S. m. , then it is called . total. Payman. . Mohassel. Yahoo Labs. 1. Do We Have the Same Person. in Mind?. Alice. Bob. Jack. . Joe. o. nly reveal . Yes/No. Solutions?. You have access to a trusted computer. You can use an airline reservation service. Prediction markets & real-world data feeds. Assertions about the outside world . Idea. : add a mechanism to assert facts. election outcomes. sports results. commodity prices. Bet or hedge results using smart contracts. Chongwon Cho. . (HRL Laboratories). Sanjam. . Garg. (IBM T.J. Watson). . Rafail. . Ostrovsky. (UCLA). 2. Secure . Computation [Yao, GMW]. Alice and Bob. Alice holds input . x. .. Bob holds input . Arpita. . Patra. Recap . >> Scope of MPC . . . . > models of computation . . > network models . . > . modelling. distrust (centralized/decentralized adversary). Arpita. . Patra. In PK setting, . privacy . is provided by . PKE. Digital Signatures. . I. ntegrity/authenticity. is provided by digital signatures (counterpart of MACs in PK world). Definition:. A Digital signature scheme  consists of three PPT algorithms (Gen, Sign, .