## CryptoDB

### Eyal Kushilevitz

#### Publications

**Year**

**Venue**

**Title**

2022

PKC

CNF-FSS and its Applications
Abstract

Function Secret Sharing (FSS), introduced by Boyle, Gilboa and Ishai~\cite{BGI15}, extends the classical notion of secret-sharing a \textit{value} to secret sharing a \textit{function}. Namely, for a secret function $f$ (from a class $\cal F$), FSS provides a sharing of $f$ whereby {\em succinct} shares (``keys'') are distributed to a set of parties, so that later the parties can non-interactively compute an additive sharing of $f(x)$, for any input $x$ in the domain of $f$.
Previous work on FSS concentrated mostly on the two-party case, where highly efficient schemes are obtained for some simple, yet extremely useful, classes $\cal F$ (in particular, FSS for the class of point functions, a task referred to as DPF~--~Distributed Point Functions~\cite{GI14,BGI15}).
In this paper, we concentrate on the multi-party case, with $p\ge 3$ parties and $t$-security ($1\le t<p$). First, we introduce the notion of \textsf{CNF-DPF} (or, more generally, \textsf{CNF-FSS}), where the scheme uses the CNF version of secret sharing (rather than additive sharing) to share each value $f(x)$. We then demonstrate the utility of CNF-DPF by providing several applications. Our main result shows how CNF-DPF can be used to achieve substantial asymptotic improvement in communication complexity when using it as a building block for constructing {\em standard} $(t,p)$-DPF protocols that tolerate $t>1$ (semi-honest) corruptions (of the $p$ parties). For example, we build a 2-out-of-5 secure (standard) DPF scheme of communication complexity $O(N^{1/4})$, where $N$ is the domain size of $f$ (compared with the current best-known of $O(N^{1/2})$ for $(2,5)$-DPF). More generally, with $p>dt$ parties, we give a $(t,p)$-DPF whose communication grows as $O(N^{1/2d})$ (rather than $O(\sqrt{N})$ that follows from the $(p-1,p)$-DPF scheme of \cite{BGI15}).
We also present a 1-out-of-3 secure CNF-DPF scheme, in which each party holds two of the three keys, with poly-logarithmic communication complexity. These results have immediate implications to scenarios where (multi-server) DPF was shown to be applicable. For example, we show how to use such a scheme to obtain asymptotic improvement ($O(\log^2N)$ versus $O(\sqrt{N})$) in communication complexity over the 3-party protocol of~\cite{BKKO20}.

2021

CRYPTO

Secure Computation from One-Way Noisy Communication, or: Anti-Correlation via Anti-Concentration
📺
Abstract

Can a sender encode a pair of messages (m_0,m_1) jointly, and send their encoding over (say) a binary erasure channel, so that the receiver can decode exactly one of the two messages and the sender does not know which one?
Garg et al. (Crypto 2015) showed that this is information-theoretically impossible.
We show how to circumvent this impossibility by assuming that the receiver is computationally bounded, settling for an inverse-polynomial security error (which is provably necessary), and relying on ideal obfuscation.
Our solution creates a ``computational anti-correlation'' between the events of receiving m_0 and receiving m_1 by exploiting the anti-concentration of the binomial distribution.
The ideal obfuscation primitive in our construction can either be directly realized using (stateless) tamper-proof hardware, yielding an unconditional result, or heuristically instantiated using existing indistinguishability obfuscation schemes. We put forward a new notion of obfuscation that suffices to securely instantiate our construction.
As a corollary, we get similar feasibility results for general secure computation of sender-receiver functionalities by leveraging the completeness of the above ``random oblivious transfer'' functionality.

2020

ASIACRYPT

Cryptography from One-Way Communication: On Completeness of Finite Channels
📺
Abstract

Garg et al. (Crypto 2015) initiated the study of cryptographic protocols over noisy channels in the non-interactive setting, namely when only one party speaks. A major question left open by this work is the completeness of {\em finite} channels, whose input and output alphabets do not grow with the desired level of security. In this work, we address this question by obtaining the following results:
Completeness of Bit-ROT with Inverse Polynomial Error: We show that bit-ROT (i.e., Randomized Oblivious Transfer channel, where each of the two messages is a single bit) can be used to realize general randomized functionalities with inverse polynomial error. Towards this, we provide a construction of string-ROT from bit-ROT with inverse polynomial error.
No Finite Channel is Complete with Negligible Error: To complement the above, we show that {\it no} finite channel can be used to realize string-ROT with negligible error, implying that the inverse polynomial error in the completeness of bit-ROT is inherent. This holds even with semi-honest parties and for computational security, and is contrasted with the (negligible-error) completeness of string-ROT shown by Garg et al.
Characterization of Finite Channels Enabling Zero-Knowledge Proofs: An important instance of secure computation is zero-knowledge proofs.
Noisy channels can potentially be used to realize truly non-interactive zero-knowledge proofs, without trusted common randomness, and with non-transferability and deniability features that cannot be realized in the plain model. Garg et al. obtain such zero-knowledge proofs from the binary erasure channel (BEC) and the binary symmetric channel (BSC). We complete the picture by showing that in fact any non-trivial channel suffices.

2019

PKC

Sub-logarithmic Distributed Oblivious RAM with Small Block Size
Abstract

Oblivious RAM (ORAM) is a cryptographic primitive that allows a client to securely execute RAM programs over data that is stored in an untrusted server. Distributed Oblivious RAM is a variant of ORAM, where the data is stored in $$m>1$$ servers. Extensive research over the last few decades have succeeded to reduce the bandwidth overhead of ORAM schemes, both in the single-server and the multi-server setting, from $$O(\sqrt{N})$$ to O(1). However, all known protocols that achieve a sub-logarithmic overhead either require heavy server-side computation (e.g. homomorphic encryption), or a large block size of at least $$\varOmega (\log ^3 N)$$.In this paper, we present a family of distributed ORAM constructions that follow the hierarchical approach of Goldreich and Ostrovsky [17]. We enhance known techniques, and develop new ones, to take better advantage of the existence of multiple servers. By plugging efficient known hashing schemes in our constructions, we get the following results:1.For any number $$m\ge 2$$ of servers, we show an m-server ORAM scheme with $$O(\log N/\log \log N)$$ overhead, and block size $$\varOmega (\log ^2 N)$$. This scheme is private even against an $$(m-1)$$-server collusion.2.A three-server ORAM construction with $$O(\omega (1)\cdot \log N/\log \log N)$$ overhead and a block size almost logarithmic, i.e. $$\varOmega (\log ^{1+\epsilon }N)$$.
We also investigate a model where the servers are allowed to perform a linear amount of light local computations, and show that constant overhead is achievable in this model, through a simple four-server ORAM protocol. From theoretical viewpoint, this is the first ORAM scheme with asymptotic constant overhead, and polylogarithmic block size, that does not use homomorphic encryption. Practically speaking, although we do not provide an implementation of the suggested construction, evidence from related work (e.g. [12]) confirms that despite the linear computational overhead, our construction is practical, in particular when applied to secure computation.

2019

CRYPTO

Cryptographic Sensing
📺
Abstract

Is it possible to measure a physical object in a way that makes the measurement signals unintelligible to an external observer? Alternatively, can one learn a natural concept by using a contrived training set that makes the labeled examples useless without the line of thought that has led to their choice? We initiate a study of “cryptographic sensing” problems of this type, presenting definitions, positive and negative results, and directions for further research.

2019

TCC

On Fully Secure MPC with Solitary Output
Abstract

We study the possibility of achieving full security, with guaranteed output delivery, for secure multiparty computation of functionalities where only one party receives output, to which we refer as solitary functionalities. In the standard setting where all parties receive an output, full security typically requires an honest majority; otherwise even just achieving fairness is impossible. However, for solitary functionalities, fairness is clearly not an issue. This raises the following question: Is full security with no honest majority possible for all solitary functionalities?We give a negative answer to this question, by showing the existence of solitary functionalities that cannot be computed with full security. While such a result cannot be proved using fairness-based arguments, our proof builds on the classical proof technique of Cleve (STOC 1986) for ruling out fair coin-tossing and extends it in a nontrivial way.On the positive side, we show that full security against any number of malicious parties is achievable for many natural and useful solitary functionalities, including ones for which the multi-output version cannot be realized with full security.

2019

TCC

Lower and Upper Bounds on the Randomness Complexity of Private Computations of AND
Abstract

We consider multi-party information-theoretic private protocols, and specifically their randomness complexity. The randomness complexity of private protocols is of interest both because random bits are considered a scarce resource, and because of the relation between that complexity measure and other complexity measures of boolean functions such as the circuit size or the sensitivity of the function being computed [12, 17].More concretely, we consider the randomness complexity of the basic boolean function and, that serves as a building block in the design of many private protocols. We show that and cannot be privately computed using a single random bit, thus giving the first non-trivial lower bound on the 1-private randomness complexity of an explicit boolean function, $$f: \{0,1\}^n \rightarrow \{0,1\}$$. We further show that the function and, on any number of inputs n (one input bit per player), can be privately computed using 8 random bits (and 7 random bits in the special case of $$n=3$$ players), improving the upper bound of 73 random bits implicit in [17]. Together with our lower bound, we thus approach the exact determination of the randomness complexity of and. To the best of our knowledge, the exact randomness complexity of private computation is not known for any explicit function (except for xor, which is trivially 1-random, and for several degenerate functions).

2018

TCC

Best Possible Information-Theoretic MPC
Abstract

We reconsider the security guarantee that can be achieved by general protocols for secure multiparty computation in the most basic of settings: information-theoretic security against a semi-honest adversary. Since the 1980s, we have elegant solutions to this problem that offer full security, as long as the adversary controls a minority of the parties, but fail completely when that threshold is crossed. In this work, we revisit this problem, questioning the optimality of the standard notion of security. We put forward a new notion of information-theoretic security which is strictly stronger than the standard one, and which we argue to be “best possible.” This notion still requires full security against dishonest minority in the usual sense, and adds a meaningful notion of information-theoretic security even against dishonest majority.We present protocols for useful classes of functions that satisfy this new notion of security. Our protocols have the unique feature of combining the efficiency benefits of protocols for an honest majority and (most of) the security benefits of protocols for dishonest majority. We further extend some of the solutions to the malicious setting.

2006

JOFC

2003

EUROCRYPT

2000

EUROCRYPT

#### Program Committees

- Eurocrypt 2020
- TCC 2018
- Eurocrypt 2017
- TCC 2016 (Program chair)
- TCC 2014
- Crypto 2013
- Crypto 2010
- TCC 2008
- TCC 2006
- Eurocrypt 2005
- Crypto 2003
- PKC 2002

#### Coauthors

- Shweta Agrawal (2)
- Benny Applebaum (4)
- Amos Beimel (4)
- Alex Biryukov (2)
- Dan Boneh (1)
- Paul Bunn (1)
- Ran Canetti (4)
- Benny Chor (3)
- Ronald Cramer (1)
- Yevgeniy Dodis (1)
- Serge Fehr (1)
- Ariel Gabizon (1)
- Sanjam Garg (1)
- Rosario Gennaro (1)
- Mihály Geréb-Graus (1)
- Oded Goldreich (2)
- Shai Halevi (3)
- Danny Harnik (2)
- William E. Skeith III (1)
- Yuval Ishai (26)
- Ranjit Kumaresan (2)
- Yehuda Lindell (3)
- Nikolaos Makriyannis (1)
- Sigurd Meldgaard (2)
- Tamer Mour (1)
- Varun Narayanan (2)
- Jesper Buus Nielsen (1)
- Pnina Nissim (1)
- Claudio Orlandi (1)
- Rafail Ostrovsky (10)
- Anat Paskin (1)
- Anat Paskin-Cherniavsky (3)
- Erez Petrank (1)
- Vinod Prabhakaran (1)
- Manoj Prabhakaran (5)
- Vinod M. Prabhakaran (1)
- Emmanuel Prouff (1)
- Tal Rabin (3)
- Alon Rosen (2)
- Adi Rosén (3)
- Amit Sahai (6)
- Adrian Thillard (1)
- Damien Vergnaud (1)
- Brent Waters (1)
- Jürg Wullschleger (1)
- Ching-Hua Yu (1)