PPT-Homomorphic Encryption:

WHAT WHY and HOW Vinod Vaikuntanathan University of Toronto A Brief History of Cryptography Julius Ceasar 10044 BC In the beginning there was symmetric encryption Message . tXi=0g2iandkg(x)k1=maxi=0;:::;tjgij:Forapositivevaluer,wedenetwocorrespondingtypesof\ball"centeredattheorigin:B2;N(r)=(N1Xi=0aixi:N1Xi=0a2ir2);B1;N(r)=(N1Xi=0aixi:rair):Wehavetheusualinclusion 0368-4474-01, . Winter 2011. Lecture 14:. More on vulnerability and exploits,. Fully . homomorphic. encryption. Eran. . Tromer. Slides credit: . Vinod. . Vaikuntanathan. (U. Toronto). More on vulnerability exploitation. CSE 5351: Introduction to Cryptography. Reading assignment:. Chapter 2. Chapter 3 (sections 3.1-3.4). You may skip proofs, but are encouraged to read some of them.. 2. Computational Difficulty (One-Way Functions). . Really. Be Run . Josh Benaloh. Senior Cryptographer. Microsoft Research. Disclaimer. Any opinions presented in this talk are my own and do not necessary represent those of the Microsoft Corporation or any subsidiary or partner thereof.. Computing on Private Data. Ten H Lai. Ohio State University. Agenda. Computing on private data. Fully . homomorphic. encryption . (FHE). Gentry’s bootstrapping theorem. Our result. FHE: The Holy Grail of Cryptography. Arvind Arasu, Ken Eguro, . Ravi Ramamurthy, Raghav Kaushik. Microsoft Research. Cloud Computing . 2. Well-documented benefits. Trend to move computation and data to cloud. Database functionality. Amazon RDS. Schemes and Parameters. Joppe W. Bos. Microsoft Research. Contains joint work with Kristin . Lauter, . Jake Loftus and Michael Naehrig. Computing on Encrypted Data. Motivation. Outsource data and computation. usna. . si110. Symmetric Encryption Limitations. Symmetric encryption algorithms use the . same key for encryption and decryption. Both parties must agree to a secret key. Fundamental limitation. How do you exchange a secret key?. Election. Technologies. How Elections . Should . Be Run. Josh . Benaloh. Senior Cryptographer. Microsoft Research. Traditional Voting Methods. Traditional Voting Methods. Hand-Counted Paper. Traditional Voting Methods. Computing on Private Data. Ten H Lai. Ohio State University. Agenda. Computing on private data. Fully . homomorphic. encryption . (FHE). Gentry’s bootstrapping theorem. Our result. FHE: The Holy Grail of Cryptography. Schemes and Parameters. Joppe W. Bos. Microsoft Research. Contains joint work with Kristin . Lauter, . Jake Loftus and Michael Naehrig. Computing on Encrypted Data. Motivation. Outsource data and computation. Crypto Concepts Symmetric encryption, Public key encryption, and TLS Cryptography Is: A tremendous tool The basis for many security mechanisms Is not: The solution to all security problems Reliable unless implemented and used properly Student: Q.D. MCGAW. Supervisors: . Dr.. Wei Dai and . Dr.. Cong Ling. Second marker: Professor . Athanassios. . Manikas. 20 June 2016. Provide a general purpose C++ API for homomorphic encryption and cloud computing. Ravi Ramamurthy, Raghav Kaushik. Microsoft Research. 1. Cloud Computing . 2. Well-documented benefits. Trend to move computation and data to cloud. Database functionality. Amazon RDS. Microsoft SQL Azure.