International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Salil P. Vadhan

Affiliation: Harvard University

Publications

Year
Venue
Title
2016
TCC
2016
TCC
2015
EPRINT
2013
CRYPTO
2013
EUROCRYPT
2012
TCC
2012
CRYPTO
2011
TCC
2011
CRYPTO
2010
TCC
2010
CRYPTO
2010
EUROCRYPT
2010
EPRINT
Universal One-Way Hash Functions via Inaccessible Entropy
This paper revisits the construction of Universally One-Way Hash Functions (UOWHFs) from any one-way function due to Rompel (STOC 1990). We give a simpler construction of UOWHFs which also obtains better efficiency and security. The construction exploits a strong connection to the recently introduced notion of *inaccessible entropy* (Haitner et al. STOC 2009). With this perspective, we observe that a small tweak of any one-way function f is already a weak form of a UOWHF: Consider F(x, i) that outputs the i-bit long prefix of f(x). If F were a UOWHF then given a random x and i it would be hard to come up with x' \neq x such that F(x, i) = F(x', i). While this may not be the case, we show (rather easily) that it is hard to sample x' with almost full entropy among all the possible such values of x'. The rest of our construction simply amplifies and exploits this basic property. With this and other recent works we have that the constructions of three fundamental cryptographic primitives (Pseudorandom Generators, Statistically Hiding Commitments and UOWHFs) out of one-way functions are to a large extent unified. In particular, all three constructions rely on and manipulate computational notions of entropy in similar ways. Pseudorandom Generators rely on the well-established notion of pseudoentropy, whereas Statistically Hiding Commitments and UOWHFs rely on the newer notion of inaccessible entropy.
2010
EPRINT
Improved Delegation of Computation using Fully Homomorphic Encryption
Kai-Min Chung Yael Kalai Salil P. Vadhan
Following Gennaro, Gentry, and Parno (Cryptology ePrint Archive 2009/547), we use fully homomorphic encryption to design improved schemes for delegating computation. In such schemes, a delegator outsources the computation of a function $F$ on many, dynamically chosen inputs $x_i$ to a worker in such a way that it is infeasible for the worker to make the delegator accept a result other than $F(x_i)$. The "online stage" of the Gennaro et al. scheme is very efficient: the parties exchange two messages, the delegator runs in time $poly(log T)$, and the worker runs in time $poly(T)$, where $T$ is the time complexity of $F$. However, the "offline stage" (which depends on the function $F$ but not the inputs to be delegated) is inefficient: the delegator runs in time $poly(T)$ and generates a public key of length $poly(T)$ that needs to be accessed by the worker during the online stage. Our first construction eliminates the large public key from the Gennaro et al. scheme. The delegator still invests $poly(T)$ time in the offline stage, but does not need to communicate or publish anything. Our second construction reduces the work of the delegator in the offline stage to $poly(log T)$ at the price of a 4-message (offline) interaction with a $poly(T)$-time worker (which need not be the same as the workers used in the online stage). Finally, we describe a "pipelined" implementation of the second construction that avoids the need to re-run the offline construction after errors are detected (assuming errors are not too frequent).
2009
TCC
2009
TCC
2009
CRYPTO
2009
EPRINT
Proofs of Retrievability via Hardness Amplification
Yevgeniy Dodis Salil P. Vadhan Daniel Wichs
Proofs of Retrievability (PoR), introduced by Juels and Kaliski, allow the client to store a file $F$ on an untrusted server, and later run an efficient audit protocol in which the server proves that it (still) possesses the client's data. Constructions of PoR schemes attempt to minimize the client and server storage, the communication complexity of an audit, and even the number of file-blocks accessed by the server during the audit. In this work, we identify several different variants of the problem (such as bounded-use vs. unbounded-use, knowledge-soundness vs. information-soundness), and giving nearly optimal PoR schemes for each of these variants. Our constructions either improve (and generalize) the prior PoR constructions, or give the first known PoR schemes with the required properties. In particular, we \begin{itemize} \item Formally prove the security of an (optimized) variant of the bounded-use scheme of Juels and Kaliski~\cite{JuelsK07}, without making any simplifying assumptions on the behavior of the adversary. \item Build the first unbounded-use PoR scheme where the communication complexity is linear in the security parameter and which does not rely on Random Oracles, resolving an open question of Shacham and Waters~\cite{ShachamW08}. \item Build the first bounded-use scheme with {\em information-theoretic} security. \end{itemize} The main insight of our work comes from a simple connection between PoR schemes and the notion of {\em hardness amplification}, extensively studied in complexity theory. In particular, our improvements come from first abstracting a purely information-theoretic notion of {\em PoR codes}, and then building nearly optimal PoR codes using state-of-the-art tools from coding and complexity theory.
2008
TCC
2008
TCC
2008
JOFC
2008
TCC
2008
EPRINT
Fairness with an Honest Minority and a Rational Majority
We provide a simple protocol for secret reconstruction in any threshold secret sharing scheme, and prove that it is fair when executed with many rational parties together with a small minority of honest parties. That is, all parties will learn the secret with high probability when the honest parties follow the protocol and the rational parties act in their own self-interest (as captured by the notion of a Bayesian subgame perfect equilibrium). The protocol only requires a standard (synchronous) broadcast channel, and tolerates fail-stop deviations (i.e. early stopping, but not incorrectly computed messages). Previous protocols for this problem in the cryptographic or economic models have either required an honest majority, used strong communication channels that enable simultaneous exchange of information, or settled for approximate notions of security/equilibria.
2007
CRYPTO
2007
EUROCRYPT
2007
EPRINT
Interactive and Noninteractive Zero Knowledge Coincide in the Help Model
Dragos Florin Ciocan Salil P. Vadhan
We show that a problem in $\AM$ has a interactive zero-knowledge proof system {\em if and only if} it has a noninteractive zero knowledge proof system in the `help model' of Ben-Or and Gutfreund ({\em J. Cryptology}, 2003). In this model, the shared reference string is generated by a probabilistic polynomial-time dealer who is given access to the statement to be proven. Our result holds for both computational zero knowledge and statistical zero knowledge, and does not rely on any unproven complexity assumptions. We also show that help does not add power to interactive computational zero-knowledge proofs, paralleling a result of Ben-Or and Gutfreund for the case of statistical zero knowledge.
2007
EPRINT
Interactive and Noninteractive Zero Knowledge are Equivalent in the Help Model
We show that interactive and noninteractive zero-knowledge are equivalent in the `help model' of Ben-Or and Gutfreund ({\em J. Cryptology}, 2003). In this model, the shared reference string is generated by a probabilistic polynomial-time dealer who is given access to the statement to be proven. Our results do not rely on any unproven complexity assumptions and hold for statistical zero knowledge, for computational zero knowledge restricted to AM, and for quantum zero knowledge when the help is a pure quantum state.
2006
CRYPTO
2006
TCC
2006
EPRINT
Statistical Zero-Knowledge Arguments for NP from Any One-Way Function
We show that every language in NP has a *statistical* zero-knowledge argument system under the (minimal) complexity assumption that one-way functions exist. In such protocols, even a computationally unbounded verifier cannot learn anything other than the fact that the assertion being proven is true, whereas a polynomial-time prover cannot convince the verifier to accept a false assertion except with negligible probability. This resolves an open question posed by Naor, Ostrovsky, Venkatesan, and Yung (CRYPTO `92, J. Cryptology `98). Departing from previous works on this problem, we do not construct standard statistically hiding commitments from any one-way function. Instead, we construct a relaxed variant of commitment schemes called "1-out-of-2-binding commitments," recently introduced by Nguyen and Vadhan (STOC `06).
2006
EPRINT
Zero Knowledge and Soundness are Symmetric
Shien Jin Ong Salil P. Vadhan
We give a complexity-theoretic characterization of the class of problems in NP having zero-knowledge argument systems. This characterization is symmetric in its treatment of the zero knowledge and the soundness conditions, and thus we deduce that the class of problems in NP intersect coNP having zero-knowledge arguments is closed under complement. Furthermore, we show that a problem in NP has a *statistical* zero-knowledge argument system if and only if its complement has a computational zero-knowledge *proof* system. What is novel about these results is that they are *unconditional*, i.e., do not rely on unproven complexity assumptions such as the existence of one-way functions. Our characterization of zero-knowledge arguments also enables us to prove a variety of other unconditional results about the class of problems in NP having zero-knowledge arguments, such as equivalences between honest-verifier and malicious-verifier zero knowledge, private coins and public coins, inefficient provers and efficient provers, and non-black-box simulation and black-box simulation. Previously, such results were only known unconditionally for zero-knowledge *proof systems*, or under the assumption that one-way functions exist for zero-knowledge argument systems.
2005
EPRINT
Concurrent Zero Knowledge without Complexity Assumptions
We provide unconditional constructions of concurrent statistical zero-knowledge proofs for a variety of non-trivial problems (not known to have probabilistic polynomial-time algorithms). The problems include Graph Isomorphism, Graph Nonisomorphism, Quadratic Residuosity, Quadratic Nonresiduosity, a restricted version of Statistical Difference, and approximate versions of the (coNP forms of the) Shortest Vector Problem and Closest Vector Problem in lattices. For some of the problems, such as Graph Isomorphism and Quadratic Residuosity, the proof systems have provers that can be implemented in polynomial time (given an NP witness) and have \tilde{O}(log n) rounds, which is known to be essentially optimal for black-box simulation. To our best of knowledge, these are the first constructions of concurrent zero-knowledge protocols in the asynchronous model (without timing assumptions) that do not require complexity assumptions (such as the existence of one-way functions).
2005
EPRINT
Derandomization in Cryptography
Boaz Barak Shien Jin Ong Salil P. Vadhan
We give two applications of Nisan--Wigderson-type ("non-cryptographic") pseudorandom generators in cryptography. Specifically, assuming the existence of an appropriate NW-type generator, we construct: A one-message witness-indistinguishable proof system for every language in NP, based on any trapdoor permutation. This proof system does not assume a shared random string or any setup assumption, so it is actually an "NP proof system." A noninteractive bit commitment scheme based on any one-way function. The specific NW-type generator we need is a hitting set generator fooling nondeterministic circuits. It is known how to construct such a generator if ETIME = DTIME(2^O(n)) has a function of nondeterministic circuit complexity 2^\Omega(n) (Miltersen and Vinodchandran, FOCS `99). Our witness-indistinguishable proofs are obtained by using the NW-type generator to derandomize the ZAPs of Dwork and Naor (FOCS `00). To our knowledge, this is the first construction of an NP proof system achieving a secrecy property. Our commitment scheme is obtained by derandomizing the interactive commitment scheme of Naor (J. Cryptology, 1991). Previous constructions of noninteractive commitment schemes were only known under incomparable assumptions.
2004
TCC
2004
TCC
2004
JOFC
2004
EPRINT
Simpler Session-Key Generation from Short Random Passwords
Minh-Huyen Nguyen Salil P. Vadhan
Goldreich and Lindell (CRYPTO `01) recently presented the first protocol for password-authenticated key exchange in the standard model (with no common reference string or set-up assumptions other than the shared password). However, their protocol uses several heavy tools and has a complicated analysis. We present a simplification of the Goldreich--Lindell (GL) protocol and analysis for the special case when the dictionary is of the form $D=\{0,1\}^d$, i.e. the password is a short random string (like an ATM PIN number). Our protocol can be converted into one for arbitrary dictionaries using a common reference string of logarithmic length. The security bound achieved by our protocol is somewhat worse than the GL protocol. Roughly speaking, our protocol guarantees that the adversary can ``break'' the scheme with probability at most $O(\mathrm{poly}(n)/|D|)^{\Omega(1)}$, whereas the GL protocol guarantees a bound of $O(1/|D|)$. We also present an alternative, more natural definition of security than the ``augmented definition'' of Goldreich and Lindell, and prove that the two definitions are equivalent.
2004
EPRINT
Lower Bounds for Non-Black-Box Zero Knowledge
Boaz Barak Yehuda Lindell Salil P. Vadhan
We show new lower bounds and impossibility results for general (possibly *non-black-box*) zero-knowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions: 1. There does not exist a two-round zero-knowledge *proof* system with perfect completeness for an NP-complete language. The previous impossibility result for two-round zero knowledge, by Goldreich and Oren (J. Cryptology, 1994) was only for the case of *auxiliary-input* zero-knowledge proofs and arguments. 2. There does not exist a constant-round zero-knowledge *strong* proof or argument of knowledge (as defined by Goldreich (2001)) for a nontrivial language. 3. There does not exist a constant-round public-coin *proof* system for a nontrivial language that is *resettable zero knowledge*. This result also extends to "bounded-resettable" zero knowledge, in which the number of resets is a priori bounded by a polynomial in the input length and prover-to-verifier communication. In contrast, we show that under reasonable assumptions, there does exist such a (computationally sound) *argument* system that is bounded-resettable zero knowledge. The complexity assumptions we use are not commonly used in cryptography. However, in all cases, we show that assumptions similar to ours are necessary for the above results. Most previously known lower bounds, such as those of Goldreich and Krawczyk (SIAM J. Computing, 1996), were only for *black-box* zero knowledge. However, a result of Barak (FOCS 2001) shows that many (or even most) of these black-box lower bounds do *not* extend to the case of general zero knowledge.
2003
CRYPTO
2003
CRYPTO
2003
CRYPTO
2002
EPRINT
An Improved Pseudorandom Generator Based on Hardness of Factoring
Nenad Dedic Leonid Reyzin Salil P. Vadhan
We present a simple to implement and efficient pseudorandom generator based on the factoring assumption. It outputs more than pn/2 pseudorandom bits per p exponentiations, each with the same base and an exponent shorter than n/2 bits. Our generator is based on results by Hastad, Schrift and Shamir [HSS93], but unlike their generator and its improvement by Goldreich and Rosen [GR00], it does not use hashing or extractors, and is thus simpler and somewhat more efficient. In addition, we present a general technique that can be used to speed up pseudorandom generators based on iterating one-way permutations. We construct our generator by applying this technique to results of [HSS93]. We also show how the generator given by Gennaro [Gen00] can be simply derived from results of Patel and Sundaram [PS98] using our technique.
2002
EPRINT
On Constructing Locally Computable Extractors and Cryptosystems in the Bounded Storage Model
Salil P. Vadhan
We consider the problem of constructing randomness extractors which are {\em locally computable}, i.e. only read a small number of bits from their input. As recently shown by Lu (CRYPTO `02), locally computable extractors directly yield secure private-key cryptosystems in Maurer's bounded storage model (J. Cryptology, 1992). In this note, we observe that a fundamental lemma of Nisan and Zuckerman (J. Computer and System Sciences, 1996) yields a general technique for constructing locally computable extractors. Specifically, we obtain a locally computable extractor by combining any extractor with any randomness-efficient (averaging) sampler. Plugging in known extractor and sampler constructions, we obtain locally computable extractors, and hence cryptosystems in the bounded storage model, whose parameters improve upon previous constructions and come quite close to the lower bounds. Along the way, we also present a refinement of the Nisan--Zuckerman lemma, showing that random sampling bits from a weak random source preserves the min-entropy rate up to an arbitrarily small additive loss (whereas the original lemma loses a logarithmic factor).
2001
CRYPTO
2001
EPRINT
On the (Im)possibility of Obfuscating Programs
Informally, an {\em obfuscator} $O$ is an (efficient, probabilistic) ``compiler'' that takes as input a program (or circuit) $P$ and produces a new program $O(P)$ that has the same functionality as $P$ yet is ``unintelligible'' in some sense. Obfuscators, if they exist, would have a wide variety of cryptographic and complexity-theoretic applications, ranging from software protection to homomorphic encryption to complexity-theoretic analogues of Rice's theorem. Most of these applications are based on an interpretation of the ``unintelligibility'' condition in obfuscation as meaning that $O(P)$ is a ``virtual black box,'' in the sense that anything one can efficiently compute given $O(P)$, one could also efficiently compute given oracle access to $P$. In this work, we initiate a theoretical investigation of obfuscation. Our main result is that, even under very weak formalizations of the above intuition, obfuscation is impossible. We prove this by constructing a family of functions $F$ that are {\em \inherently unobfuscatable} in the following sense: there is a property $\pi : F \rightarrow \{0,1\}$ such that (a) given {\em any program} that computes a function $f\in F$, the value $\pi(f)$ can be efficiently computed, yet (b) given {\em oracle access} to a (randomly selected) function $f\in F$, no efficient algorithm can compute $\pi(f)$ much better than random guessing. We extend our impossibility result in a number of ways, including even obfuscators that (a) are not necessarily computable in polynomial time, (b) only {\em approximately} preserve the functionality, and (c) only need to work for very restricted models of computation ($TC_0$). We also rule out several potential applications of obfuscators, by constructing ``unobfuscatable'' signature schemes, encryption schemes, and pseudorandom function families.
2000
EPRINT
A Complete Problem for Statistical Zero Knowledge
Amit Sahai Salil P. Vadhan
We present the first complete problem for SZK, the class of (promise) problems possessing statistical zero-knowledge proofs (against an honest verifier). The problem, called STATISTICAL DIFFERENCE, is to decide whether two efficiently samplable distributions are either statistically close or far apart. This gives a new characterization of SZK that makes no reference to interaction or zero knowledge. We propose the use of complete problems to unify and extend the study of statistical zero knowledge. To this end, we examine several consequences of our Completeness Theorem and its proof, such as: (1) A way to make every (honest-verifier) statistical zero-knowledge proof very communication efficient, with the prover sending only one bit to the verifier (to achieve soundness error 1/2). (2) Simpler proofs of many of the previously known results about statistical zero knowledge, such as the Fortnow and Aiello--Håstad upper bounds on the complexity of SZK and Okamoto's result that SZK is closed under complement. (3) Strong closure properties of SZK which amount to constructing statistical zero-knowledge proofs for complex assertions built out of simpler assertions already shown to be in SZK. (4) New results about the various measures of "knowledge complexity," including a collapse in the hierarchy corresponding to knowledge complexity in the "hint" sense. (5) Algorithms for manipulating the statistical difference between efficiently samplable distributions, including transformations which "polarize" and "reverse" the statistical relationship between a pair of distributions.
1999
CRYPTO
1998
CRYPTO
1998
EPRINT
Many-to-one Trapdoor Functions and their Relation to Public-key Cryptosystems
The heart of the task of building public key cryptosystems is viewed as that of ``making trapdoors;'' in fact, public key cryptosystems and trapdoor functions are often discussed as synonymous. How accurate is this view? In this paper we endeavor to get a better understanding of the nature of ``trapdoorness'' and its relation to public key cryptosystems, by broadening the scope of the investigation: we look at general trapdoor functions; that is, functions that are not necessarily injective (ie., one-to-one). Our first result is somewhat surprising: we show that non-injective trapdoor functions (with super-polynomial pre-image size) can be constructed {from} any one-way function (and hence it is unlikely that they suffice for public key encryption). On the other hand, we show that trapdoor functions with polynomial pre-image size are sufficient for public key encryption. Together, these two results indicate that the pre-image size is a fundamental parameter of trapdoor functions. We then turn our attention to the converse, asking what kinds of trapdoor functions can be constructed from public key cryptosystems. We take a first step by showing that in the random-oracle model one can construct injective trapdoor functions from any public key cryptosystem.
1998
EPRINT
Comparing Entropies in Statistical Zero-Knowledge with Applications to the Structure of SZK
Oded Goldreich Salil P. Vadhan
We consider the following (promise) problem, denoted ED (for Entropy Difference): The input is a pairs of circuits, and YES instances (resp., NO instances) are such pairs in which the first (resp., second) circuit generates a distribution with noticeably higher entropy. On one hand we show that any language having a (honest-verifier) statistical zero-knowledge proof is Karp-reducible to ED. On the other hand, we present a public-coin (honest-verifier) statistical zero-knowledge proof for ED. Thus, we obtain an alternative proof of Okamoto's result by which HVSZK (i.e., Honest-Verifier Statistical Zero-Knowledge) equals public-coin HVSZK. The new proof is much simpler than the original one. The above also yields a trivial proof that HVSZK is closed under complementation (since ED easily reduces to its complement). Among the new results obtained is an equivalence of a weak notion of statistical zero-knowledge to the standard one.

Program Committees

TCC 2017
TCC 2014
Crypto 2009
TCC 2007
Crypto 2006
Eurocrypt 2005
TCC 2004
Crypto 2000