1 / 11

Demystifying the Master Thesis and Research in General: The Story of Some Master Theses

Join Oded Goldreich as he shares the stories of his master theses and their research topics, ranging from permutation groups to secure multi-party protocols and beyond.

salazard
Download Presentation

Demystifying the Master Thesis and Research in General: The Story of Some Master Theses

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


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

  2. Out of an accident 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(n=2 suffices) Inputs: x1,…,xn y1,…,yn Outputs: rr+∑ixiyi (N.B.: rnd) Study it Out of general interest. No concrete goal. 1st2nd Inputs: x,z y Outputs: -z+xy From a randomized functionality to a deterministic one (OT) 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 Known open problem communicated through the advisor. 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. OT 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? Problem suggested by the adviser

  7. Or Meir (2007) Background: Constructions of PCP and LTC, which mostly rely on algebraic machinery. Specifically, best LTCs are constructed based on PCPs, whereas LTCs seem simpler constructs. Initiate a research program The work: A combinatorial construction of LTCs (wo PCPs).The project continued to a PhD, which consists of several combinatorial constructions of PCPs (and also an IP). Definitely NOT the expectation, but the unexpected may happen

  8. Lidor Avigad (2009) Background: property testing, the dense graph model, lowest level of query complexity. Specifically, c-CC is in that low level. For a start: Extend this result to any blow-up A blow-up of a 3-star The work: TestingGraph blow-up in minimum query complexity (i.e., linear in 1/proximity, non-adaptively)

  9. Roei Tell (2015) Context: Property testing (i.e. super-fast approximate decision algorithms). Question: Characterize properties (of strings) that are close under far-from-far operator. Take the question elsewhere The work: Initiates a systematic study of testing “Dual problems” (i.e., testing the set of objects that are far from a given set). (After refuting my conjecture re the characterization…)

  10. Maya Leshkowitz (2017) Background: Interactive proof systems. Seeking a more intuitive transformation of general interactive proofs to public-coin ones. Solve it, and continue to a question that “arises” The work: 1. Resolves the original problem (by presenting lower and upper bound on how well this can be done). 2. Shows that any interactive proof that uses $r(n)$ coins can be transformed into one that uses $r/log n$ rounds (and $O(r)$ public coins).

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

More Related