Slide 1Complexity Theory Lecture 6 Lecturer: Moni Naor Slide 2 Recap Last week: Probabilistic Complexity 1.Schwatz-Zippel 2.Approximating Counting Problems Plus Alternation…

Slide 1Complexity Theory Lecture 10 Lecturer: Moni Naor Slide 2 Recap Last week: IP=PSPACE Start with #P in PSPACE Public vs. Private Coins IP[k]=AM Mechanism for showing…

Slide 1Complexity Theory Lecture 8 Lecturer: Moni Naor Slide 2 Recap Last week: –Randomized Reductions –Low memory verifiers –#P Completeness of Permanent This Week:…

Slide 1How to Carpool Fairly Moni Naor Slide 2 The carpool problem A group of n people form a carpool. – Each day a subset arrives to a (fixed) gathering point and one…

Slide 1Complexity Theory Lecture 7 Lecturer: Moni Naor Slide 2 Recap Last week: Non-Uniform Complexity Classes Polynomial Time Hierarchy –BPP in hierarchy –If NP µ P/Poly…

Slide 1Complexity Theory Lecture 9 Lecturer: Moni Naor Slide 2 Recap Last week: –Toda’s Theorem: PH  P #P. –Program checking and hardness on the average of the permanent…

Slide 1Foundations of Cryptography Lecture 10 Lecturer: Moni Naor Slide 2 Recap of Lecture 9 Hardcore predicates with public randomness The inner product bit: Goldreich-Levin…

Slide 1Complexity Theory Lecture 1 Lecturer: Moni Naor Slide 2 Computational Complexity Theory Study the resources needed to solve computational problems –Computer time…

Slide 1 Foundations of Cryptography Lecture 13 Lecturer: Moni Naor Slide 2 Recap of Lecture 12 Pseudo-Random Permutations Feistal Permutations Proof of the construction Semantic…

Slide 1 Topics in Cryptography Lecture 7 Topic: Side Channels Lecturer: Moni Naor Slide 2 Recap: chosen ciphertext security Why chosen ciphertext/malleability matters Taxonomy…