Slide 1Fully Homomorphic Encryption over the Integers Marten van Dijk 1, Craig Gentry 2, Shai Halevi 2, Vinod Vaikuntanathan 2 1 – MIT, 2 – IBM Research Many slides borrowed…

F. R. Schleif Engineering and Research Center Bureau of Reclamation February 1971 Governor Characteristics for Large Hydraulic Turbines -- -- - - - -E. 114198 71A C- 1 F.…

Slide 1 1 L is in NP means: There is a language L’ in P and a polynomial p so that L 1 · L 2 means: For some polynomial time computable map r : 8 x: x 2 L 1 iff r(x) 2…

Slide 1 CS151 Complexity Theory Lecture 11 May 4, 2004 Slide 2 CS151 Lecture 112 Outline Extractors Trevisan’s extractor RL and undirected STCONN Slide 3 May 4, 2004CS151…

Slide 1 Case Study #2 Background You have selected your sub-contractors using your criteria in Case Study #1 and work will now begin The land has to be cleared and surveyed…

1 How to establish NP-hardness Lemma: If L1 is NP-hard and L1 ≤ L2 then L2 is NP-hard. 2 SAT SAT is in NP. Cook’s theorem (1972): SAT is NP-hard. 3 SAT SAT: Given a Boolean…

1 SAT SAT: Given a Boolean function in CNF representation, is there a way to assign truth values to the variables so that the function evaluates to true? SAT: Given a CNF,…

1 How to establish NP-hardness Lemma: If L1 is NP-hard and L1 ≤ L2 then L2 is NP-hard. 2 SAT SAT is in NP. Cook’s theorem (1972): SAT is NP-hard. 3 SAT SAT: Given a Boolean…

CS151 Complexity Theory Lecture 11 May 4, 2004 CS151 Lecture 11 Outline Extractors Trevisan’s extractor RL and undirected STCONN CS151 Lecture 11 Extractors PRGs: can remove…