All reports by Author Benny Applebaum:

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TR23-136
| 14th September 2023
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Benny Applebaum, Oded Nir#### Advisor-Verifier-Prover Games and the Hardness of Information Theoretic Cryptography

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TR23-091
| 18th June 2023
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Benny Applebaum, Amos Beimel, Yuval Ishai, Eyal Kushilevitz, Tianren Liu, Vinod Vaikuntanathan#### Succinct Computational Secret Sharing

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TR23-087
| 9th June 2023
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Benny Applebaum, Oded Nir, Benny Pinkas#### How to Recover a Secret with $O(n)$ Additions

Revisions: 1

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TR23-062
| 2nd May 2023
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Benny Applebaum, Eliran Kachlon#### Conflict Checkable and Decodable Codes and Their Applications

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TR23-031
| 23rd March 2023
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Benny Applebaum, Eliran Kachlon, Arpita Patra#### The Round Complexity of Statistical MPC with Optimal Resiliency

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TR22-006
| 12th January 2022
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Benny Applebaum, Amos Beimel, Oded Nir, Naty Peter, Toniann Pitassi#### Secret Sharing, Slice Formulas, and Monotone Real Circuits

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TR21-052
| 12th April 2021
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Benny Applebaum, Oded Nir#### Upslices, Downslices, and Secret-Sharing with Complexity of $1.5^n$

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TR20-076
| 17th May 2020
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Benny Applebaum, Eliran Kachlon, Arpita Patra#### The Round Complexity of Perfect MPC with Active Security and Optimal Resiliency

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TR20-008
| 26th January 2020
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Benny Applebaum, Amos Beimel, Oded Nir, Naty Peter#### Better Secret-Sharing via Robust Conditional Disclosure of Secrets

Revisions: 2

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TR19-011
| 27th January 2019
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Benny Applebaum, Eliran Kachlon#### Sampling Graphs without Forbidden Subgraphs and Almost-Explicit Unbalanced Expanders

Revisions: 2

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TR18-208
| 27th November 2018
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Benny Applebaum, Prashant Nalini Vasudevan#### Placing Conditional Disclosure of Secrets in the Communication Complexity Universe

Revisions: 2

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TR18-033
| 16th February 2018
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Benny Applebaum, Thomas Holenstein, Manoj Mishra, Ofer Shayevitz#### The Communication Complexity of Private Simultaneous Messages, Revisited

Revisions: 2

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TR17-189
| 25th December 2017
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Benny Applebaum, Barak Arkis#### Conditional Disclosure of Secrets and $d$-Uniform Secret Sharing with Constant Information Rate

Revisions: 1

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TR17-067
| 21st April 2017
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Benny Applebaum#### Garbled Circuits as Randomized Encodings of Functions: a Primer

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TR17-063
| 10th April 2017
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Benny Applebaum#### Exponentially-Hard gap-CSP and local PRG via Local Hardcore Functions

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TR17-038
| 23rd February 2017
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Benny Applebaum, Barak Arkis, Pavel Raykov, Prashant Nalini Vasudevan#### Conditional Disclosure of Secrets: Amplification, Closure, Amortization, Lower-bounds, and Separations

Revisions: 1

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TR17-008
| 14th January 2017
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Benny Applebaum, Naama Haramaty, Yuval Ishai, Eyal Kushilevitz, Vinod Vaikuntanathan#### Low-Complexity Cryptographic Hash Functions

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TR16-082
| 22nd May 2016
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Benny Applebaum, Pavel Raykov#### Fast Pseudorandom Functions Based on Expander Graphs

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TR15-206
| 15th December 2015
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Benny Applebaum, Pavel Raykov#### From Private Simultaneous Messages to Zero-Information Arthur-Merlin Protocols and Back

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TR15-186
| 24th November 2015
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Benny Applebaum, Pavel Raykov#### On the Relationship between Statistical Zero-Knowledge and Statistical Randomized Encodings

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TR15-172
| 3rd November 2015
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Benny Applebaum, Shachar Lovett#### Algebraic Attacks against Random Local Functions and Their Countermeasures

Revisions: 1

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TR15-061
| 14th April 2015
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Benny Applebaum, Jonathan Avron, Christina Brzuska#### Arithmetic Cryptography

Revisions: 1

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TR15-051
| 5th April 2015
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Benny Applebaum, Sergei Artemenko, Ronen Shaltiel, Guang Yang#### Incompressible Functions, Relative-Error Extractors, and the Power of Nondeterminsitic Reductions

Revisions: 2

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TR15-045
| 1st April 2015
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Benny Applebaum, Yuval Ishai, Eyal Kushilevitz#### Minimizing Locality of One-Way Functions via Semi-Private Randomized Encodings

Revisions: 1

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TR15-027
| 25th February 2015
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Benny Applebaum#### Cryptographic Hardness of Random Local Functions -- Survey

Revisions: 1

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TR13-098
| 28th June 2013
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Benny Applebaum, Yoni Moses#### Locally Computable UOWHF with Linear Shrinkage

Revisions: 2

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TR12-058
| 5th May 2012
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Benny Applebaum, Yuval Ishai, Eyal Kushilevitz#### How to Garble Arithmetic Circuits

Revisions: 1

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TR11-126
| 17th September 2011
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Benny Applebaum, Andrej Bogdanov, Alon Rosen#### A Dichotomy for Local Small-Bias Generators

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TR11-007
| 17th January 2011
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Benny Applebaum#### Pseudorandom Generators with Long Stretch and Low locality from Random Local One-Way Functions

Revisions: 3

Benny Applebaum, Oded Nir

A major open problem in information-theoretic cryptography is to obtain a super-polynomial lower bound for the communication complexity of basic cryptographic tasks. This question is wide open even for very powerful non-interactive primitives such as private information retrieval (or locally-decodable codes), general secret sharing schemes, conditional disclosure of secrets, and ... more >>>

Benny Applebaum, Amos Beimel, Yuval Ishai, Eyal Kushilevitz, Tianren Liu, Vinod Vaikuntanathan

A secret-sharing scheme enables a dealer to share a secret $s$ among $n$ parties such that only authorized subsets of parties, specified by a monotone access structure $f:\{0,1\}^n\to\{0,1\}$, can reconstruct $s$ from their shares. Other subsets of parties learn nothing about $s$.

The question of minimizing the (largest) share size ... more >>>

Benny Applebaum, Oded Nir, Benny Pinkas

Threshold cryptography is typically based on the idea of secret-sharing a private-key $s\in F$ ``in the exponent'' of some cryptographic group $G$, or more generally, encoding $s$ in some linearly homomorphic domain. In each invocation of the threshold system (e.g., for signing or decrypting) an ``encoding'' of the secret is ... more >>>

Benny Applebaum, Eliran Kachlon

Let $C$ be an error-correcting code over a large alphabet $q$ of block length $n$, and assume that, a possibly corrupted, codeword $c$ is distributively stored among $n$ servers where the $i$th entry is being held by the $i$th server. Suppose that every pair of servers publicly announce whether the ... more >>>

Benny Applebaum, Eliran Kachlon, Arpita Patra

In STOC 1989, Rabin and Ben-Or (RB) established an important milestone in the fields of cryptography and distributed computing by showing that every functionality can be computed with statistical (information-theoretic) security in the presence of an active (aka Byzantine) rushing adversary that controls up to half of the parties. We ... more >>>

Benny Applebaum, Amos Beimel, Oded Nir, Naty Peter, Toniann Pitassi

A secret-sharing scheme allows to distribute a secret $s$ among $n$ parties such that only some predefined ``authorized'' sets of parties can reconstruct the secret, and all other ``unauthorized'' sets learn nothing about $s$. For over 30 years, it was known that any (monotone) collection of authorized sets can be ... more >>>

Benny Applebaum, Oded Nir

A secret-sharing scheme allows to distribute a secret $s$ among $n$ parties such that only some predefined ``authorized'' sets of parties can reconstruct the secret, and all other ``unauthorized'' sets learn nothing about $s$.

The collection of authorized/unauthorized sets can be captured by a monotone function $f:\{0,1\}^n\rightarrow \{0,1\}$.

more >>>

Benny Applebaum, Eliran Kachlon, Arpita Patra

In STOC 1988, Ben-Or, Goldwasser, and Wigderson (BGW) established an important milestone in the fields of cryptography and distributed computing by showing that every functionality can be computed with perfect (information-theoretic and error-free) security at the presence of an active (aka Byzantine) rushing adversary that controls up to $n/3$ of ... more >>>

Benny Applebaum, Amos Beimel, Oded Nir, Naty Peter

A secret-sharing scheme allows to distribute a secret $s$ among $n$ parties such that only some predefined ``authorized'' sets of parties can reconstruct the secret, and all other ``unauthorized'' sets learn nothing about $s$. The collection of authorized sets is called the access structure. For over 30 years, it was ... more >>>

Benny Applebaum, Eliran Kachlon

We initiate the study of the following hypergraph sampling problem: Sample a $d$-uniform hypergraph over $n$ vertices and $m$ hyperedges from some pseudorandom distribution $\mathcal{G}$ conditioned on not having some small predefined $t$-size hypergraph $H$ as a subgraph. The algorithm should run in $\mathrm{poly}(n)$-time even when the size of the ... more >>>

Benny Applebaum, Prashant Nalini Vasudevan

In the *Conditional Disclosure of Secrets* (CDS) problem (Gertner et al., J. Comput. Syst. Sci., 2000) Alice and Bob, who hold $n$-bit inputs $x$ and $y$ respectively, wish to release a common secret $z$ to Carol (who knows both $x$ and $y$) if and only if the input $(x,y)$ satisfies ... more >>>

Benny Applebaum, Thomas Holenstein, Manoj Mishra, Ofer Shayevitz

Private Simultaneous Message (PSM) protocols were introduced by Feige, Kilian and Naor (STOC '94) as a minimal non-interactive model for information-theoretic three-party secure computation. While it is known that every function $f:\{0,1\}^k\times \{0,1\}^k \rightarrow \{0,1\}$ admits a PSM protocol with exponential communication of $2^{k/2}$ (Beimel et al., TCC '14), the ... more >>>

Benny Applebaum, Barak Arkis

Consider the following secret-sharing problem. Your goal is to distribute a long file $s$ between $n$ servers such that $(d-1)$-subsets cannot recover the file, $(d+1)$-subsets can recover the file, and $d$-subsets should be able to recover $s$ if and only if they appear in some predefined list $L$. How small ... more >>>

Benny Applebaum

Yao's garbled circuit construction is a central cryptographic tool with numerous applications. In this tutorial, we study garbled circuits from a foundational point of view under the framework of \emph{randomized encoding} (RE) of functions. We review old and new constructions of REs, present some lower bounds, and describe some applications. ... more >>>

Benny Applebaum

The gap-ETH assumption (Dinur 2016; Manurangsi and Raghavendra 2016) asserts that it is exponentially-hard to distinguish between a satisfiable 3-CNF formula and a 3-CNF formula which is at most 0.99-satisfiable. We show that this assumption follows from the exponential hardness of finding a satisfying assignment for *smooth* 3-CNFs. Here smoothness ... more >>>

Benny Applebaum, Barak Arkis, Pavel Raykov, Prashant Nalini Vasudevan

In the \emph{conditional disclosure of secrets} problem (Gertner et al., J. Comput. Syst. Sci., 2000) Alice and Bob, who hold inputs $x$ and $y$ respectively, wish to release a common secret $s$ to Carol (who knows both $x$ and $y$) if only if the input $(x,y)$ satisfies some predefined predicate ... more >>>

Benny Applebaum, Naama Haramaty, Yuval Ishai, Eyal Kushilevitz, Vinod Vaikuntanathan

Cryptographic hash functions are efficiently computable functions that shrink a long input into a shorter output while achieving some of the useful security properties of a random function. The most common type of such hash functions is {\em collision resistant} hash functions (CRH), which prevent an efficient attacker from finding ... more >>>

Benny Applebaum, Pavel Raykov

We present direct constructions of pseudorandom function (PRF) families based on Goldreich's one-way function. Roughly speaking, we assume that non-trivial local mappings $f:\{0,1\}^n\rightarrow \{0,1\}^m$ whose input-output dependencies graph form an expander are hard to invert. We show that this one-wayness assumption yields PRFs with relatively low complexity. This includes weak ... more >>>

Benny Applebaum, Pavel Raykov

Goos, Pitassi and Watson (ITCS, 2015) have recently introduced the notion of Zero-Information Arthur-Merlin Protocols (ZAM). In this model, which can be viewed as a private version of the standard Arthur-Merlin communication complexity game, Alice and Bob are holding a pair of inputs $x$ and $y$ respectively, and Merlin, the ... more >>>

Benny Applebaum, Pavel Raykov

\emph{Statistical Zero-knowledge proofs} (Goldwasser, Micali and Rackoff, SICOMP 1989) allow a computationally-unbounded server to convince a computationally-limited client that an input $x$ is in a language $\Pi$ without revealing any additional information about $x$ that the client cannot compute by herself. \emph{Randomized encoding} (RE) of functions (Ishai and Kushilevitz, FOCS ... more >>>

Benny Applebaum, Shachar Lovett

Suppose that you have $n$ truly random bits $x=(x_1,\ldots,x_n)$ and you wish to use them to generate $m\gg n$ pseudorandom bits $y=(y_1,\ldots, y_m)$ using a local mapping, i.e., each $y_i$ should depend on at most $d=O(1)$ bits of $x$. In the polynomial regime of $m=n^s$, $s>1$, the only known solution, ... more >>>

Benny Applebaum, Jonathan Avron, Christina Brzuska

We study the possibility of computing cryptographic primitives in a fully-black-box arithmetic model over a finite field F. In this model, the input to a cryptographic primitive (e.g., encryption scheme) is given as a sequence of field elements, the honest parties are implemented by arithmetic circuits which make only a ... more >>>

Benny Applebaum, Sergei Artemenko, Ronen Shaltiel, Guang Yang

A circuit $C$ \emph{compresses} a function $f:\{0,1\}^n\rightarrow \{0,1\}^m$ if given an input $x\in \{0,1\}^n$ the circuit $C$ can shrink $x$ to a shorter $\ell$-bit string $x'$ such that later, a computationally-unbounded solver $D$ will be able to compute $f(x)$ based on $x'$. In this paper we study the existence of ... more >>>

Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

A one-way function is $d$-local if each of its outputs depends on at most $d$ input bits. In (Applebaum, Ishai, and Kushilevitz, FOCS 2004) it was shown that, under relatively mild assumptions, there exist $4$-local one-way functions (OWFs). This result is not far from optimal as it is not hard ... more >>>

Benny Applebaum

Constant parallel-time cryptography allows to perform complex cryptographic tasks at an ultimate level of parallelism, namely, by local functions that each of their output bits depend on a constant number of input bits. A natural way to obtain local cryptographic constructions is to use \emph{random local functions} in which each ... more >>>

Benny Applebaum, Yoni Moses

We study the problem of constructing locally computable Universal One-Way Hash Functions (UOWHFs) $H:\{0,1\}^n \rightarrow \{0,1\}^m$. A construction with constant \emph{output locality}, where every bit of the output depends only on a constant number of bits of the input, was established by [Applebaum, Ishai, and Kushilevitz, SICOMP 2006]. However, this ... more >>>

Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

Yao's garbled circuit construction transforms a boolean circuit $C:\{0,1\}^n\to\{0,1\}^m$

into a ``garbled circuit'' $\hat{C}$ along with $n$ pairs of $k$-bit keys, one for each

input bit, such that $\hat{C}$ together with the $n$ keys

corresponding to an input $x$ reveal $C(x)$ and no additional information about $x$.

The garbled circuit ...
more >>>

Benny Applebaum, Andrej Bogdanov, Alon Rosen

We consider pseudorandom generators in which each output bit depends on a constant number of input bits. Such generators have appealingly simple structure: they can be described by a sparse input-output dependency graph and a small predicate that is applied at each output. Following the works of Cryan and Miltersen ... more >>>

Benny Applebaum

We continue the study of pseudorandom generators (PRG) $G:\{0,1\}^n \rightarrow \{0,1\}^m$ in NC0. While it is known that such generators are likely to exist for the case of small sub-linear stretch $m=n+n^{1-\epsilon}$, it remains unclear whether achieving larger stretch such as $m=2n$ or even $m=n+n^2$ is possible. The existence of ... more >>>