All reports by Author Nir Bitansky:

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TR24-114
| 12th July 2024
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Nir Bitansky, Ron D. Rothblum, Prahladh Harsha, Yuval Ishai, David Wu#### Dot-Product Proofs and Their Applications

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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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TR17-099
| 5th June 2017
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Nir Bitansky, Omer Paneth, Yael Tauman Kalai#### Multi-Collision Resistance: A Paradigm for Keyless Hash Functions

Revisions: 2

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TR17-005
| 10th January 2017
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Nir Bitansky#### Verifiable Random Functions from Non-Interactive Witness-Indistinguishable Proofs

Revisions: 3

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TR16-091
| 3rd June 2016
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Nir Bitansky, Akshay Degwekar, Vinod Vaikuntanathan#### Structure vs Hardness through the Obfuscation Lens

Revisions: 3

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TR15-187
| 24th November 2015
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Nir Bitansky, Vinod Vaikuntanathan#### A Note on Perfect Correctness by Derandomization

Revisions: 1

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TR15-001
| 2nd January 2015
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Nir Bitansky, Omer Paneth, Alon Rosen#### On the Cryptographic Hardness of Finding a Nash Equilibrium

Revisions: 1

Nir Bitansky, Ron D. Rothblum, Prahladh Harsha, Yuval Ishai, David Wu

A dot-product proof (DPP) is a simple probabilistic proof system in which the input statement $x$ and the proof ${\pi}$ are vectors over a finite field $\mathbb{F}$, and the proof is verified by making a single dot-product query $\langle {q},({x} \| {\pi})\rangle$ jointly to ${x}$ and ${\pi}$. A DPP can ... 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 >>>

Nir Bitansky, Omer Paneth, Yael Tauman Kalai

We study multi-collision-resistant hash functions --- a natural relaxation of collision-resistant hashing that only guarantees the intractability of finding many (rather than two) inputs that map to the same image. An appealing feature of such hash functions is that unlike their collision-resistant counterparts, they do not necessarily require a key. ... more >>>

Nir Bitansky

Verifiable random functions (VRFs) are pseudorandom functions where the owner of the seed, in addition to computing the function's value $y$ at any point $x$, can also generate a non-interactive proof $\pi$ that $y$ is correct (relative to so), without compromising pseudorandomness at other points. Being a natural primitive with ... more >>>

Nir Bitansky, Akshay Degwekar, Vinod Vaikuntanathan

Cryptography relies on the computational hardness of structured problems. While one-way functions, the most basic cryptographic object, do not seem to require much structure, as we advance up the ranks into public-key cryptography and beyond, we seem to require that certain structured problems are hard. For example, factoring, quadratic residuosity, ... more >>>

Nir Bitansky, Vinod Vaikuntanathan

In this note, we show how to transform a large class of erroneous cryptographic schemes into perfectly correct ones. The transformation works for schemes that are correct on every input with probability noticeably larger than half, and are secure under parallel repetition. We assume the existence of one-way functions ...
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Nir Bitansky, Omer Paneth, Alon Rosen

We prove that finding a Nash equilibrium of a game is hard, assuming the existence of indistinguishability obfuscation and injective one-way functions with sub-exponential hardness. We do so by showing how these cryptographic primitives give rise to a hard computational problem that lies in the complexity class PPAD, for which ... more >>>