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Demystifying the Master Thesis and Research in General

Join Oded Goldreich, a professor at the Weizmann Institute of Science, as he shares the story of his own master thesis and explores various topics in research. From permutation groups to secure multi-party protocols and property testing, this talk covers it all. Discover the challenges, breakthroughs, and lessons learned from some fascinating master theses.

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Demystifying the Master Thesis and Research in General

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  1. Demystifying the Master Thesis and Research in General: The Story of Some Master Theses Oded Goldreich Weizmann Institute of Science

  2. My own thesis (1981) : A permutation group over D is represented by a set of generators S. The group is denoted <S>. <S> = {g1○g2 ○∙ ∙ ∙ ○gt : g1,g2,…,gtS} Given S and a permutation π, does p belong to <S>? Given S, π, and t, can π be expressed by a sequence of up to t elements of S?

  3. My first MSc student: Ronen Vainish (1988) Background: A general construction of secure multi-party protocols by reduction to the two-party case. Suffices to compute the inner product mod 2 of two input vectors held by the two parties. 1st2nd Inputs: x1,…,xn y1,…,yn Outputs: rr+∑ixiyi Study it 1st2nd Inputs: x,z y Outputs: -z+xy SenderReceiver Inputs: s0,s1c Outputs: -sc

  4. Eyal Kushilevitz (1989) Background: Few sets known to have perfect zero-knowledge proof systems. E.g., Graph-Iso, Quad-Res. Can we provide stronger evidence to PZK not in BPP? Solve it YES: A promise problem based on DLP.

  5. Invent your own... (inspired by a course) Ran Canetti (1992) Background: communication complexity, gap between the complexity of randomized and deterministic protocols. Is there a randomness-communication trade-off? YES: Presents a trade-off. The ID function: two parties, each holds an n-bit long string. Deterministic lower bound: need n bits of communication. Randomized protocols: (1) via error-correcting codes: send a random position. (2) via the CRT: send integer modulo a random prime

  6. SenderReceiver Inputs: s0,s1c Outputs: -sc Iftach Haitner (2004) Background: assuming a collection of TDP {fi:Di→Di} SenderReceiver Inputs: s0,s1c desired outputs: -sc selects an indexi yc=fi(xc) , y1-c find the fi-preimages of both: z0 , z1b(z0)+s0 , b(z1)+s1 The problem: what is assumed about sampling Di? Can we relax?

  7. Lidor Avigad (2009) Background: property testing, the dense graph model, lowest level of query complexity. Specifically, c-CC is in that low level. Extend this result The work: TestingGraph blow-up in minimum query complexity (i.e., linear in 1/proximity, non-adaptively)

  8. The End The slides of this talk are available at http://www.wisdom.weizmann.ac.il/~oded/T/de-mysti.ppt

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