1. Oded Goldreich Weizmann Institute of Science
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.
1st nd
Inputs: x1,…,xn y1,…,yn
Outputs: r r+∑ixiyi
Study it
1st nd
Inputs: x,z y
Outputs: z+xy
The $i$th invocation uses inputs $(x_i,r_i)$ and $y_i$, where $r_i\rnd\bitset$.
The final output is the sum of $r_i$’s and sum of $r_i+x_iy_i$’s.
Sender Receiver
Inputs: s0,s c
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. Ran Canetti (1992) Invent your own... (inspired by a course)
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. Iftach Haitner (2004) Sender Receiver
Inputs: s0,s c
Outputs: sc
Background: assuming a collection of TDP {fi:Di→Di}
Sender Receiver
Inputs: s0,s c
desired outputs: sc
selects an index i
yc=fi(xc) , y1-c
find the fi-preimages
of both: z0 , z b(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: Testing Graph 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