All reports by Author Ron Rothblum:

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TR24-024
| 14th February 2024
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Changrui Mu, Shafik Nassar, Ron Rothblum, Prashant Nalini Vasudevan#### Strong Batching for Non-Interactive Statistical Zero-Knowledge

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TR23-113
| 8th August 2023
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Justin Holmgren, Ron Rothblum#### Linear-Size Boolean Circuits for Multiselection

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TR23-077
| 25th May 2023
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Nir Bitansky, Chethan Kamath, Omer Paneth, Ron Rothblum, Prashant Nalini Vasudevan#### Batch Proofs are Statistically Hiding

Revisions: 4

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TR21-180
| 21st December 2021
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Noga Ron-Zewi, Ron Rothblum#### Proving as Fast as Computing: Succinct Arguments with Constant Prover Overhead

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TR21-084
| 21st June 2021
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Liron Bronfman, Ron Rothblum#### PCPs and Instance Compression from a Cryptographic Lens

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TR21-032
| 5th March 2021
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Justin Holmgren, Alex Lombardi, Ron Rothblum#### Fiat-Shamir via List-Recoverable Codes (or: Parallel Repetition of GMW is not Zero-Knowledge)

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TR21-029
| 1st March 2021
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Inbar Kaslasi, Ron Rothblum, Prashant Nalini Vasudevan#### Public-Coin Statistical Zero-Knowledge Batch Verification against Malicious Verifiers

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TR20-157
| 21st October 2020
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Guy Rothblum, Ron Rothblum#### Batch Verification and Proofs of Proximity with Polylog Overhead

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TR20-147
| 24th September 2020
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Inbar Kaslasi, Prashant Nalini Vasudevan, Guy Rothblum, Ron Rothblum, Adam Sealfon#### Batch Verification for Statistical Zero Knowledge Proofs

Revisions: 1

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TR19-169
| 21st November 2019
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Lijie Chen, Ron Rothblum, Roei Tell, Eylon Yogev#### On Exponential-Time Hypotheses, Derandomization, and Circuit Lower Bounds

Revisions: 2

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TR19-127
| 19th September 2019
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Noga Ron-Zewi, Ron Rothblum#### Local Proofs Approaching the Witness Length

Revisions: 2

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TR18-161
| 13th September 2018
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Justin Holmgren, Ron Rothblum#### Delegating Computations with (almost) Minimal Time and Space Overhead

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TR18-022
| 1st February 2018
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Omer Reingold, Guy Rothblum, Ron Rothblum#### Efficient Batch Verification for UP

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TR17-172
| 3rd November 2017
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Itay Berman, Akshay Degwekar, Ron Rothblum, Prashant Nalini Vasudevan#### From Laconic Zero-Knowledge to Public-Key Cryptography

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TR17-143
| 26th September 2017
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Tom Gur, Govind Ramnarayan, Ron Rothblum#### Relaxed Locally Correctable Codes

Revisions: 1

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TR17-097
| 31st May 2017
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Itay Berman, Akshay Degwekar, Ron Rothblum, Prashant Nalini Vasudevan#### Multi Collision Resistant Hash Functions and their Applications

Revisions: 1

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TR16-061
| 17th April 2016
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Omer Reingold, Ron Rothblum, Guy Rothblum#### Constant-Round Interactive Proofs for Delegating Computation

Revisions: 2

Changrui Mu, Shafik Nassar, Ron Rothblum, Prashant Nalini Vasudevan

A zero-knowledge proof enables a prover to convince a verifier that $x \in S$, without revealing anything beyond this fact. By running a zero-knowledge proof $k$ times, it is possible to prove (still in zero-knowledge) that $k$ separate instances $x_1,\dots,x_k$ are all in $S$. However, this increases the communication by ... more >>>

Justin Holmgren, Ron Rothblum

We study the circuit complexity of the multiselection problem: given an input string $x \in \{0,1\}^n$ along with indices $i_1,\dots,i_q \in [n]$, output $(x_{i_1},\dots,x_{i_q})$. A trivial lower bound for the circuit size is the input length $n + q \cdot \log(n)$, but the straightforward construction has size $\Theta(q \cdot n)$.

... more >>>Nir Bitansky, Chethan Kamath, Omer Paneth, Ron Rothblum, Prashant Nalini Vasudevan

Batch proofs are proof systems that convince a verifier that $x_1,\dots, x_t \in L$, for some $NP$ language $L$, with communication that is much shorter than sending the $t$ witnesses. In the case of statistical soundness (where the cheating prover is unbounded but honest prover is efficient), interactive batch proofs ... more >>>

Noga Ron-Zewi, Ron Rothblum

Succinct arguments are proof systems that allow a powerful, but untrusted, prover to convince a weak verifier that an input $x$ belongs to a language $L \in NP$, with communication that is much shorter than the $NP$ witness. Such arguments, which grew out of the theory literature, are now drawing ... more >>>

Liron Bronfman, Ron Rothblum

Modern cryptography fundamentally relies on the assumption that the adversary trying to break the scheme is computationally bounded. This assumption lets us construct cryptographic protocols and primitives that are known to be impossible otherwise. In this work we explore the effect of bounding the adversary's power in other information theoretic ... more >>>

Justin Holmgren, Alex Lombardi, Ron Rothblum

Shortly after the introduction of zero-knowledge proofs, Goldreich, Micali and Wigderson (CRYPTO '86) demonstrated their wide applicability by constructing zero-knowledge proofs for the NP-complete problem of graph 3-coloring. A long-standing open question has been whether parallel repetition of their protocol preserves zero knowledge. In this work, we answer this question ... more >>>

Inbar Kaslasi, Ron Rothblum, Prashant Nalini Vasudevan

Suppose that a problem $\Pi$ has a statistical zero-knowledge (SZK) proof with communication complexity $m$. The question of batch verification for SZK asks whether one can prove that $k$ instances $x_1,\ldots,x_k$ all belong to $\Pi$ with a statistical zero-knowledge proof whose communication complexity is better than $k \cdot m$ (which ... more >>>

Guy Rothblum, Ron Rothblum

Suppose Alice wants to convince Bob of the correctness of k NP statements. Alice could send k witnesses to Bob, but as k grows the communication becomes prohibitive. Is it possible to convince Bob using smaller communication (without making cryptographic assumptions or bounding the computational power of a malicious Alice)? ... more >>>

Inbar Kaslasi, Prashant Nalini Vasudevan, Guy Rothblum, Ron Rothblum, Adam Sealfon

A statistical zero-knowledge proof (SZK) for a problem $\Pi$ enables a computationally unbounded prover to convince a polynomial-time verifier that $x \in \Pi$ without revealing any additional information about $x$ to the verifier, in a strong information-theoretic sense.

Suppose, however, that the prover wishes to convince the verifier that $k$ ... more >>>

Lijie Chen, Ron Rothblum, Roei Tell, Eylon Yogev

The Exponential-Time Hypothesis ($ETH$) is a strengthening of the $\mathcal{P} \neq \mathcal{NP}$ conjecture, stating that $3\text{-}SAT$ on $n$ variables cannot be solved in time $2^{\epsilon\cdot n}$, for some $\epsilon>0$. In recent years, analogous hypotheses that are ``exponentially-strong'' forms of other classical complexity conjectures (such as $\mathcal{NP}\not\subseteq\mathcal{BPP}$ or $co\text{-}\mathcal{NP}\not\subseteq \mathcal{NP}$) have ... more >>>

Noga Ron-Zewi, Ron Rothblum

Interactive oracle proofs (IOPs) are a hybrid between interactive proofs and PCPs. In an IOP the prover is allowed to interact with a verifier (like in an interactive proof) by sending relatively long messages to the verifier, who in turn is only allowed to query a few of the bits ... more >>>

Justin Holmgren, Ron Rothblum

The problem of verifiable delegation of computation considers a setting in which a client wishes to outsource an expensive computation to a powerful, but untrusted, server. Since the client does not trust the server, we would like the server to certify the correctness of the result. Delegation has emerged as ... more >>>

Omer Reingold, Guy Rothblum, Ron Rothblum

Consider a setting in which a prover wants to convince a verifier of the correctness of k NP statements. For example, the prover wants to convince the verifier that k given integers N_1,...,N_k are all RSA moduli (i.e., products of equal length primes). Clearly this problem can be solved by ... more >>>

Itay Berman, Akshay Degwekar, Ron Rothblum, Prashant Nalini Vasudevan

Since its inception, public-key encryption (PKE) has been one of the main cornerstones of cryptography. A central goal in cryptographic research is to understand the foundations of public-key encryption and in particular, base its existence on a natural and generic complexity-theoretic assumption. An intriguing candidate for such an assumption is ... more >>>

Tom Gur, Govind Ramnarayan, Ron Rothblum

Locally decodable codes (LDCs) and locally correctable codes (LCCs) are error-correcting codes in which individual bits of the message and codeword, respectively, can be recovered by querying only few bits from a noisy codeword. These codes have found numerous applications both in theory and in practice.

A natural relaxation of ... more >>>

Itay Berman, Akshay Degwekar, Ron Rothblum, Prashant Nalini Vasudevan

Collision resistant hash functions are functions that shrink their input, but for which it is computationally infeasible to find a collision, namely two strings that hash to the same value (although collisions are abundant).

In this work we study multi-collision resistant hash functions (MCRH) a natural relaxation of collision resistant ... more >>>

Omer Reingold, Ron Rothblum, Guy Rothblum

The celebrated IP=PSPACE Theorem [LFKN92,Shamir92] allows an all-powerful but untrusted prover to convince a polynomial-time verifier of the validity of extremely complicated statements (as long as they can be evaluated using polynomial space). The interactive proof system designed for this purpose requires a polynomial number of communication rounds and an ... more >>>