Descriptions
of Salil Vadhan's Research
One of the main goals of the Theory of Computation, and complexity theory in
particular, is to quantify the resources needed to accomplish useful
computational tasks. The most traditional interpretation of this is to
determine the time and space needed to compute various functions.
Over time, the scope of complexity theory has broadened to consider a wider
range of computational tasks, ranging from secure multiparty computations
to explicit constructions of combinatorial objects, and additional
resources, such as interaction and randomness. Most
of my research focuses on these kinds of computational tasks and resources,
particularly as they relate to cryptography and randomized
computations.
Below there are descriptions of some more specific topics which I have
investigated.
Interactive Proofs & Zero-Knowledge Proofs
The notion of a proof is central to mathematics
and computer science. Indeed, it has been long understood that properties
of traditional mathematical proofs are intimately connected to the
fundamental questions of complexity theory (e.g., P vs. NP and NP
vs. co-NP). In the mid 80's, Goldwasser, Micali, and
Rackoff [GMR] and Babai [Bab], proposed generalizations of the traditional
notion of proof, known as interactive proofs, which have been at the
center of some very exciting developments in complexity theory and
cryptography. The two new ingredients in interactive proofs are randomization
--- verification of proofs is probabilistic and may err with some small
probability --- and interaction --- the traditional "written"
proof is replaced with a dynamic, all-powerful prover which tries to
convince a polynomial-time verifier that some assertion is true.
Zero-knowledge proofs are interactive proofs with the amazing
property that the verifier learns nothing from its interaction with the
prover, other than the fact that the assertion being proven is true.
Zero-knowledge proofs have vast applicability in constructing secure cryptographic
protocols. Much of my work has taken a complexity-theoretic approach to
developing our understanding of zero-knowledge proofs: characterizing the
classes of problems having various kinds of zero-knowledge proofs (e.g. via
complete problems), proving general theorems about zero-knowledge proofs, and
trying to minimize or eliminate the complexity assumptions used in the study of
zero knowledge.
For more background:
My papers on this topic:
- B. Barak, Y. Lindell, S. Vadhan.
Lower
Bounds for Non-Black-Box Zero Knowledge.
FOCS `03. Crypto ePrint `04, ECCC `04, JCSS `06.
- B. Barak, S. J. Ong, S. Vadhan.
Derandomization in
Cryptography.
CRYPTO `03. Crypto ePrint `05, ECCC `05, SICOMP `07.
- E. Birrell, S. Vadhan.
Composition of Zero-Knowledge Proofs with Efficient Provers.
Crypto ePrint `09, TCC `10.
- A. Chailloux, D. F. Ciocan,
I.
Kerenidis, S. Vadhan.
Interactive and Noninteractive Zero
Knowledge Are Equivalent in the Help Model.
Crypto ePrint `07. TCC `08.
- K.M. Chung, Y. Kalai, S. Vadhan.
Improved Delegation of Computation using Fully Homomorphic Encryption.
Crypto ePrint `10, CRYPTO `10.
- Z. Dvir, D. Gutfreund, G. Rothblum, S. Vadhan.
On Approximating the Entropy of Polynomial Mappings.
ICS `11.
- O. Goldreich, A. Sahai ,
S.Vadhan.
Honest
Verifier Statistical Zero-Knowledge Equals General Statistical
Zero-Knowledge.
STOC `98.
- O. Goldreich, A. Sahai,
S.Vadhan.
Can
Statistical Zero Knowledge be made Non-Interactive? or On the Relationship
of SZK and NISZK.
CRYPTO `99, ECCC `99.
- O. Goldreich, S. Vadhan.
Comparing
Entropies in Statistical Zero-Knowledge with Applications to the Structure
of SZK.
CCC `99.
- O. Goldreich, S.Vadhan,
A.Wigderson.
On
Interactive Proofs with a Laconic Prover.
ICALP `01, Computational Complexity `02.
- I. Haitner, M. Nguyen, S.J.
Ong, O. Reingold, S. Vadhan.
Statistically Hiding Commitments and
Statistical Zero-Knowledge Arguments from Any One-Way Function.
SICOMP `09.
- D. Micciancio, S. J. Ong, A.
Sahai, S. Vadhan.
Concurrent Zero Knowledge without
Complexity Assumptions.
ECCC `05. TCC `06.
- D. Micciancio, S. Vadhan.
Statistical Zero-Knowledge Proofs
with Efficient Provers: Lattice Problems and More.
CRYPTO `03.
- M. Nguyen, S.J. Ong, S. Vadhan.
Statistical Zero-Knowledge
Arguments for NP from Any One-Way Function.
ECCC `06. FOCS `06.
- M. Nguyen, S. Vadhan.
Zero Knowledge with Efficient
Provers.
STOC `06.
- S. J. Ong, S. Vadhan.
An Equivalence between Zero
Knowledge and Commitments.
TCC `08.
- S. J. Ong, S. Vadhan.
Zero Knowledge and
Soundness are Symmetric.
EUROCRYPT `07.
- G. Rothblum, S. Vadhan.
Are PCPs Inherent in Efficient Arguments?
CCC `09, CC `10.
- A. Sahai, S. Vadhan.
A
Complete Problem for Statistical Zero Knowledge.
FOCS `97, JACM `03.
- A. Sahai, S. Vadhan.
Manipulating
Statistical Difference.
DIMACS Workshop `97.
- S. Vadhan.
The Complexity of Zero Knowledge.
FSTTCS `07.
- S. Vadhan.
Interactive
Proofs & Zero-Knowledge Proofs.
IAS/PCMI Summer School `00.
- S. Vadhan.
On
Transformations of Interactive Proofs that Preserve the Prover's Complexity.
STOC `00.
- S. Vadhan.
A
Study of Statistical Zero-Knowledge Proofs.
PhD Thesis, MIT `99. Revised 8/00.
- S. Vadhan.
An
Unconditional Study of Computational Zero Knowledge.
FOCS `04. ECCC `06. SICOMP `06.
Pseudorandomness
The surprising power of randomization is one of the most
fascinating phenomena in computer science. By allowing algorithms to ``flip
coins,'' we are able to efficiently solve many problems that we do not know how
to efficiently solve otherwise. Randomization is also a powerful tool for
proving the existence of useful combinatorial objects, such as error-correcting
codes and ``expander graphs'' (sparse graphs with very strong connectivity
properties), as one can often prove that a ``random'' object has the desired
properties. However, we still do not know to what extent the randomness
is really necessary in these settings, and understanding this is an
important goal. One reason is that it is unclear whether there exist
sufficiently good sources of randomness in nature to reliably run randomized
algorithms. Another is that, for the case of combinatorial constructions,
the ``random objects'' often require an exponentially large description are
hence infeasible to use. Thus, we ask: Can the need for
randomness in these settings be eliminated, or at least reduced? More
concretely: Can randomized algorithms be simulated using a defective
source of randomness, and how great a loss of efficiency must be incurred to do
so? Or can we even completely remove the use of randomness from a
randomized algorithm with only a small loss in efficiency? Can we
deterministically construct objects such as expander graphs that perform as
well as the random constructions? These questions are addressed by the
paradigm of pseudorandomness, which is concerned with efficiently
generating objects that ``look random'' despite being constructed using less or
defective randomness (or even deterministically).
For more background:
My papers on this topic:
- B. Barak, S. J. Ong, S. Vadhan.
Derandomization in
Cryptography.
CRYPTO `03. Crypto ePrint `05, ECCC `05, SICOMP `07.
- E. Ben-Sasson, M. Sudan, S. Vadhan, A.
Wigderson.
Randomness-efficient
low-degree tests and short PCPs via epsilon-biased sets.
STOC `03.
- M. Capalbo, O. Reingold, S.
Vadhan, A. Wigderson.
Randomness Conductors and
Constant-Degree Lossless Expanders.
STOC-CCC `02.
- K. M. Chung, O. Reingold, S.
Vadhan.
S-T Connectivity on Digraphs
with a Known Stationary Distribution.
CCC `07, TALG `09.
- K. M. Chung, S. Vadhan.
Tight Bounds for Hashing Block Sources.
RANDOM `08, arXiv `08.
- N. Dedic, L. Reyzin, S.
Vadhan.
An Improved Pseudorandom
Generator Based on Hardness of Factoring.
SCN `02. Crypto ePrint `02.
- Y. Dodis, S. Vadhan, D. Wichs.
Proofs of Retrievability via Hardness Amplification.
TCC `09, Crypto ePrint `09.
- O. Goldreich, S.Vadhan,
A.Wigderson.
Simplified
Derandomization of BPP using a Hitting Set Generator.
ECCC `00.
- R. Gradwohl, S. Vadhan, D. Zuckerman.
Random Selection with an
Adversarial Majority.
ECCC `06. CRYPTO `06.
- V. Guruswami, C. Umans, S. Vadhan.
Unbalanced Expanders and Randomness
Extractors from Parvaresh-Vardy Codes.
ECCC `06, CCC `07, JACM `09.
- V. Guruswami,
S. Vadhan.
A Lower Bound on List Size for List
Decoding.
RANDOM `05, IEEE TIT `10.
- D. Gutfreund, S. Vadhan.
Limitations
of Hardness vs. Randomness under Uniform Reductions.
ECCC `08, RANDOM `08.
- I. Haitner, O. Reingold, S. Vadhan.
Efficiency Improvements in Constructing Pseudorandom Generators from One-Way Functions.
STOC `10. ECCC `10.
- I. Haitner, O. Reingold, S. Vadhan, H. Wee.
Inaccessible Entropy.
STOC `09. ECCC `09.
- I. Haitner, T. Holenstein, O. Reingold, S. Vadhan, H. Wee.
Universal One-Way Hash Functions via Inaccessible Entropy.
EUROCRYPT `10. ePrint `10.
- A. Healy, S. Vadhan, E.
Viola.
Using
Nondeterminism to Amplify Hardness.
STOC `04. SICOMP `05.
- J. Kamp, A. Rao, S. Vadhan, D. Zuckerman.
Deterministic Extractors for
Small-Space Sources.
STOC `06. JCSS `10.
- D. Lewin, S. Vadhan.
Checking
Polynomial Identities over any Field: Towards a Derandomization?
STOC `98.
- S. Lovett, O. Reingold, L. Trevisan, S. Vadhan.
Pseudorandom Bit Generators that Fool Modular Sums.
RANDOM `09.
- C.-J. Lu, O. Reingold, S.
Vadhan, A. Wigderson.
Extractors:
Optimal up to Constant Factors.
STOC `03.
- S. Micali, M. Rabin, S. Vadhan.
Verifiable
Random Functions.
FOCS `99.
- M. Mitzenmacher, S. Vadhan.
Why
Simple Hash Functions Work: Exploiting the Entropy in a Data Stream.
SODA `08.
- R. Raz, O. Reingold, S.
Vadhan.
Extracting
all the Randomness and Reducing the Error in Trevisan's Extractors.
STOC `99, JCSS `02.
- R. Raz, O. Reingold,
S.Vadhan.
Error
Reduction for Extractors.
FOCS `99.
- O. Reingold, L. Trevisan, M.
Tulsiani, S. Vadhan.
Dense Subsets of Pseudorandom Sets.
ECCC `08, FOCS `08.
- O. Reingold, L. Trevisan, S. Vadhan.
Pseudorandom Walks on Regular
Digraphs and the RL vs. L Problem.
ECCC `05. STOC `06.
- O. Reingold, S. Vadhan, A.
Wigderson.
Entropy
Waves, The Zig-Zag Graph Product, and New Constant-Degree Expanders and
Extractors.
FOCS `00, ECCC `01, DIMACS TR `01, Annals of Math `02.
- Y. Reshef, S. Vadhan.
On Extractors and Exposure-Resilient Functions for Sublogarithmic Entropy.
arXiv `10.
- E. Rozenman, S. Vadhan.
Derandomized Squaring of
Graphs.
RANDOM `05. ECCC `05.
- M. Sudan, L. Trevisan, S. Vadhan.
Pseudorandom
Generators without the XOR Lemma.
STOC-CCC `99 joint session, JCSS `01 (Special Issue on CCC `99).
- L. Trevisan, M. Tulsiani, S. Vadhan.
Regularity, Boosting, and Efficiently Simulating Every High-Entropy Distribution.
ECCC `08, CCC `09.
- L. Trevisan, S. Vadhan.
Pseudorandomness
and Average-Case Complexity via Uniform Reductions.
CCC `02. CC `07.
- L. Trevisan, S. Vadhan.
Extracting
Randomness from Samplable Distributions.
FOCS `00.
- L. Trevisan, S. Vadhan, D. Zuckerman.
Compression of Samplable
Sources.
CCC `04, ECCC `05, CC `07.
- S. Vadhan.
Constructing
Locally Computable Extractors and Cryptosystems in the Bounded-Storage
Model.
CRYPTO `03, J. Cryptology `04.
- S. Vadhan.
The Unified Theory of
Pseudorandomness.
SIGACT News `07. ICM `10.
Data Privacy
The enormous amount of data being collected by researchers, governments, and companies on individuals contains information that, on one hand, can be used for great societal benefit, but on the other hand, poses a severe threat to privacy. Computer science research on data privacy seeks to provide algorithms that enable sharing useful information computed on such data sets while protecting privacy of the individuals whose data is used. A particularly appealing model for privacy guarantees is the recent notion of differential privacy, which requires releasing information in a randomized ("noisy") way so that the output distribution is insensitive to the presence or absence of any one individual. (See the surveys on the Microsoft Research page below for more about differential privacy.) I have been particularly interested in the effect of computational complexity on differential privacy --- constraining the computational resources of either the privacy mechanism/curator (making privacy harder) or the adversary (making privacy easier). My interest in data privacy was sparked by and continues to be influenced by my involvement with the Harvard Center for Research on Computation and Society.
For more background:
My papers on this topic:
- C. Dwork, M. Naor, O. Reingold, G. Rothblum, S. Vadhan.
On the Complexity of Differentially Private Data Release: Efficient Algorithms and Hardness Results.
STOC `09.
- C. Dwork, G. Rothblum, S. Vadhan.
Boosting and Differential Privacy.
FOCS `10.
- A. McGregor, I. Mironov, T. Pitassi, O. Reingold, K. Talwar, S. Vadhan.
The Limits of Two-Party Differential Privacy.
FOCS `10.
- I. Mironov, O. Pandey, O. Reingold, S. Vadhan.
Computational Differential Privacy.
CRYPTO `09.
- J. Ullman, S. Vadhan.
PCPs and the Hardness of Generating Synthetic Data.
ECCC `10.
Other Computational Complexity
My interests extend to many other topics in computational
complexity theory (and indeed the Theory of Computation at large). Some
particular topics I have focused on include the complexity of Counting
Problems and the design of efficient probabilistically checkable proof
systems (PCPs).
For more background:
My papers on the complexity of counting:
- A. Bogdanov, E. Mossel, S. Vadhan.
The Complexity of Distinguishing Markov
Random Fields.
RANDOM `08.
- D. Ron, A. Rosenfeld, S.
Vadhan.
The
Hardness of the Expected Decision Depth Problem.
IPL `08.
- G. Schoenebeck,
S. Vadhan.
The Computational Complexity of Nash Equilibria in Concisely Represented Games.
ECCC `05. EC `06.
- L. Trevisan, S. Vadhan, D. Zuckerman.
Compression of Samplable
Sources.
CCC `04, ECCC `05, Computational Complexity `05.
- S. Vadhan.
The
Complexity of Counting.
Undergraduate Thesis, Harvard `95.
- S. Vadhan.
The
Complexity of Counting in Sparse, Regular, and Planar Graphs.
SICOMP `01.
- S. Vadhan.
Rapidly
Mixing Markov Chains and their Applications.
Essay, Cambridge U. `96.
My papers on PCPs:
- E. Ben-Sasson, O. Goldreich, P. Harsha, M.
Sudan, S. Vadhan.
Robust
PCPs of Proximity, Short PCPs, and Applications to Coding.
STOC `04. ECCC `04. SICOMP `06.
- E. Ben-Sasson, O. Goldreich, P. Harsha, M.
Sudan, S. Vadhan.
Short
PCPs Verifiable in Polylogarithmic Time
CCC `05.
- E. Ben-Sasson, M. Sudan, S. Vadhan, A.
Wigderson.
Randomness-efficient
low-degree tests and short PCPs via epsilon-biased sets.
STOC `03.
- G. Rothblum, S. Vadhan.
Are PCPs Inherent in Efficient Arguments?
CCC `09, CC `10.
- J. Ullman, S. Vadhan.
PCPs and the Hardness of Generating Synthetic Data.
ECCC `10.
Other Cryptography
Over the past 25 years, research has made it possible to develop
cryptographic systems that are provably secure based on precise assumptions about
the hardness of various computational problems, such as factoring.
Between the hard problems and the final applications lie the primitives, which
accomplish basic cryptographic tasks (such as encryption and authentication)
that are useful in a wide variety of cryptographic protocols. My research
interests in this area is centered around these primitives --- designing new
primitives to solve natural cryptographic problems, obtaining more efficient
constructions of existing primitives, determining the minimal assumptions
needed for them, and exploring the relationships among them.
For more background:
My papers on this topic:
- B. Barak, O. Goldreich, R.
Impagliazzo, S. Rudich, A. Sahai, S. Vadhan, K. Yang.
On the (Im)possibility of Obfuscating Programs.
CRYPTO `01, ECCC `01, Crypto ePrint `01.
- M. Bellare, S. Halevi , A. Sahai , S.
Vadhan.
Many-to-one Trapdoor Functions and their Relation to Public-Key
Cryptosystems.
CRYPTO `98, Crypto ePrint `98.
- R. Canetti, R. Rivest, M. Sudan, L. Trevisan,
S. Vadhan, H. Wee.
Amplifying collision-resistance: A
complexity-theoretic treatment.
CRYPTO `07.
- N. Dedic, L. Reyzin, S.
Vadhan.
An Improved Pseudorandom
Generator Based on Hardness of Factoring.
SCN `02. Crypto ePrint `02.
- Y. Dodis, S. Vadhan, D. Wichs.
Proofs of Retrievability via Hardness Amplification.
TCC `09, Crypto ePrint `09.
- R. Gradwohl, S. Vadhan, D. Zuckerman.
Random Selection with an
Adversarial Majority.
ECCC `06. CRYPTO `06.
- M.Mahmoody, T. Moran, S. Vadhan.
Time-Lock Puzzles in the Random Oracle Model.
CRYPTO `11.
- S. Micali, M. Rabin, S. Vadhan.
Verifiable
Random Functions.
FOCS `99.
- I. Mironov, O. Pandey, O. Reingold, S. Vadhan.
Computational Differential Privacy.
CRYPTO `09.
- M. Nguyen, S. Vadhan.
Simpler Session-Key Generation from
Short Random Passwords.
TCC `04. JCrypt `08.
- S. J. Ong, D. Parkes, A. Rosen,
S. Vadhan.
Fairness
with an Honest Minority and a Rational Majority.
ePrint `08. TCC `09.
- O. Reingold, L. Trevisan, S. Vadhan.
Notions of Reducibility
between Cryptographic Primitives.
TCC `04.
- S. Sanghvi, S. Vadhan.
The Round Complexity of Two-Party
Random Selection.
STOC `05. ECCC `05. SICOMP `08.
- S. Vadhan.
Computational
Complexity.
Encyclopedia of Cryptography and Security `05.
- S. Vadhan.
Constructing
Locally Computable Extractors and Cryptosystems in the Bounded-Storage
Model.
CRYPTO `03, J. Cryptology `04.
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This page was last updated 11/4/10.