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Hard properties with (very) short PCPPs and their applications
[article]
2019
arXiv
pre-print
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We show that there exist properties that are maximally hard for testing, while still admitting PCPPs with a proof size very close to linear. ...
The best previously known upper bound on the PCPP proof size for a maximally hard to test property was O(n ·polylogn). ...
Beyond demonstrating that PCPPs with extremely short proofs exist for some hard properties, we use Theorem 1.1 to derive several applications. We proceed to describe these applications next. ...
arXiv:1909.03255v2
fatcat:hfkyuaaeu5bjdhleu2w6bf2r7a
Hard Properties with (Very) Short PCPPs and Their Applications
2020
Innovations in Theoretical Computer Science
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We show that there exist properties that are maximally hard for testing, while still admitting PCPPs with a proof size very close to linear. ...
The best previously known upper bound on the PCPP proof size for a maximally hard to test property was O(n • polylog n). ...
I T C S 2 0 2 0 9:14 Hard Properties with (Very) Short PCPPs and Their Applications Next, suppose that dist(v, C(w)) > ε, and observe that this implies that v is at least ε/3far from C eq . ...
doi:10.4230/lipics.itcs.2020.9
dblp:conf/innovations/Ben-EliezerFLR20
fatcat:5dpgdossibgktdldiqfzmq5b5i
Combinatorial PCPs with Short Proofs
2012
2012 IEEE 27th Conference on Computational Complexity
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However, our use of polynomials is confined to the construction of error correcting codes with a certain simple multiplication property, and it is conceivable that such codes can be constructed without ...
ACM 45 (1,3) ) asserts the existence of proofs that can be verified by reading a very small part of the proof. ...
However, our use of polynomials is a very restricted one, and is confined to the construction of error correcting codes with a certain simple property. ...
doi:10.1109/ccc.2012.14
dblp:conf/coco/Meir12
fatcat:pti4s37q6nd7rht6hsspeiy44y
Combinatorial PCPs with Short Proofs
2016
Computational Complexity
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However, our use of polynomials is a very restricted one, and is confined to the construction of error correcting codes with a certain simple property. ...
However, our use of polynomials is confined to the construction of error correcting codes with a certain simple multiplication property, and it is conceivable that such codes can be constructed without ...
However, their construction is signicantly more complicated than ours, and relies heavily on algebraic machinery. We also note that other works in this area (e.g. ...
doi:10.1007/s00037-015-0111-x
fatcat:3zvai4wa5rcbpflqhq67mibvrm
Smooth and Strong PCPs
2020
Innovations in Theoretical Computer Science
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This improves on the recent construction of Dinur, Gur and Goldreich (ITCS, 2019) of PCPPs that are strong canonical but inherently non-smooth. ...
This proves a hypothesis used in the work of Friggstad, Khodamoradi and Salavatipour (SODA, 2019), suggesting a connection between the hardness of these instances and other stable optimization problems ...
high probability, and assuming g L is the closest low-degree polynomial to f [L], rejection occurs with this very probability. ...
doi:10.4230/lipics.itcs.2020.2
dblp:conf/innovations/Paradise20
fatcat:2w4fsfevungyrpb2cc3yruf43y
Probabilistically Checkable Proofs of Proximity with Zero-Knowledge
[chapter]
2014
Lecture Notes in Computer Science
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Motivated by their usefulness for sublinear-communication cryptography, we initiate the study of a natural zero-knowledge variant of PCPP (ZKPCPP), where the view of any verifier making a bounded number ...
We obtain the first constructions of query-efficient ZKPCPPs via a general transformation which combines standard query-efficient PCPPs with protocols for secure multiparty computation. ...
Before describing our main results, we first give a short overview of probabilistic proof systems. ...
doi:10.1007/978-3-642-54242-8_6
fatcat:3qsw45nw2zco3bo2gz4lx3lbm4
Sound 3-Query PCPPs Are Long
[chapter]
2008
Lecture Notes in Computer Science
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To prove the exponential trade-off for inspective verifiers, we show a connection between PCPP proof length and property-testing query complexity that may be of independent interest. ...
We initiate the study of the trade-off between the length of a probabilistically checkable proof of proximity (PCPP) and the maximal soundness that can be guaranteed by a 3-query verifier with oracle access ...
We will refer to linear properties and their duals in all our results. Definition 2.7. Let F be a finite field and n ∈ Z + . ...
doi:10.1007/978-3-540-70575-8_56
fatcat:ngkwkzba6re3xdhdg2vs4u3duy
Sound 3-Query PCPPs Are Long
2009
ACM Transactions on Computation Theory
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To prove the exponential trade-off for inspective verifiers, we show a connection between PCPP proof length and property-testing query complexity that may be of independent interest. ...
We initiate the study of the trade-off between the length of a probabilistically checkable proof of proximity (PCPP) and the maximal soundness that can be guaranteed by a 3-query verifier with oracle access ...
We will refer to linear properties and their duals in all our results. Definition 2.7. Let F be a finite field and n ∈ Z + . ...
doi:10.1145/1595391.1595394
fatcat:ahubtjhgn5dk5lqcuefvwmw6qe
Simple PCPs with poly-log rate and query complexity
2005
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing - STOC '05
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Previous constructions of short PCPs (from [5] to [9]) relied extensively on properties of low degree multi-variate polynomials. ...
We also give constructions of locally testable codes (LTCs) with similar parameters. ...
In addition to the inherent motivation mentioned above, the length of PCPs also plays an important role in their use in cryptography (e.g., CS-proofs [22, 26] and their applications [6, 12] ) and is ...
doi:10.1145/1060590.1060631
dblp:conf/stoc/Ben-SassonS05
fatcat:o5wz74j6vzfc3o2jejt62adolm
Executable Proofs, Input-Size Hiding Secure Computation and a New Ideal World
[chapter]
2015
Lecture Notes in Computer Science
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Their security formulation consisted of transforming a real-world adversary into an ideal-world one and became a de facto standard for assessing security of protocols. ...
Such an input-size hiding property is not implied by the standard denitions for two-party computation and is not satised by known constructions for secure computation. ...
Very roughly, the PCPP properties allow the functionality to verify that e is correct given only this circuit representation of the PCPP and the implicit representation of x 0 that we extracted in step ...
doi:10.1007/978-3-662-46803-6_18
fatcat:xzybcvdey5h3xbm2s5bcykrl2e
Short PCPs with Polylog Query Complexity
2008
SIAM journal on computing (Print)
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In contrast, previous constructions of short PCPs, beginning with [5] and until the recent [9], relied extensively on properties of low-degree polynomials in many variables. ...
In addition to the inherent motivation mentioned above, the length of PCPs also plays an important role in their use in cryptography (e.g., 35] and their applications [6, 13] ) and is closely related to ...
The PCPPs for the RS-code described earlier allow us to tolerate this and verify proximity to high-degree polynomials with very small query complexity -logarithmic in the degree. ...
doi:10.1137/050646445
fatcat:qoemxaexdvff5dwf4apsv4vrwi
Securing Circuits against Constant-Rate Tampering
[chapter]
2012
Lecture Notes in Computer Science
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(Eurocrypt 2006), we consider adversaries who may choose an arbitrary set of wires to corrupt, and may set each such wire to 0 or to 1, or may toggle with the wire. ...
We present a compiler that converts any circuit into one that remains secure even if a constant fraction of its wires are tampered with. Following the seminal work of Ishai et. al. ...
We note that the tampering allowed in [37] is very local: To be resilient against tampering with t wires per run, they blow up the size of the circuit by a factor of at least t; thus their overall tampering ...
doi:10.1007/978-3-642-32009-5_31
fatcat:ndliuuctsvf6zlhicgbx2irb7e
Hybrid nano‐ and microgels doped with photoacoustic contrast agents for cancer theranostics
2021
View
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Their applications in multimodal cancer theranostics and cancer hallmark imaging are presented, highlighting their merits and potential in treatment and diagnosis. ...
, and stimuliresponsive properties. ...
[11] Nevertheless, it remains a great challenge to efficiently deliver PA contrast agent to their targets, owing to their unstable chemical properties and short circulation lifetime. ...
doi:10.1002/viw.20200176
fatcat:j4decxm3zvdsdjvf3piy5yifuu
Rigid Matrices From Rectangular PCPs
[article]
2020
arXiv
pre-print
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2020 pre-print arXiv:2005.03123v3 fatcat:pyakkxmybfalbk3zb2i7xffyeyOther Versions
As a key application, we show that proofs for hard languages in NTIME(2^n), when viewed as matrices, are rigid infinitely often. ...
We construct PCPs that are efficient, short, smooth and (almost-)rectangular. ...
Acknowledgements We thank Lijie Chen and Emanuele Viola for their helpful comments on Section 1.5, and an anonymous reviewer for pointing out Remark 2.10. ...
arXiv:2005.03123v4
fatcat:7icnjyt7fzfovixm5puja3fxui
Arguments of Proximity
[chapter]
2015
Lecture Notes in Computer Science
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As our second result, assuming sufficiently hard cryptographic PRGs, we give a lower bound, showing that the parameters obtained both in the IPPs of Rothblum et al., and in our arguments of proximity, ...
Since the verifier runs in sublinear-time, following the property testing literature, the verifier is only required to reject inputs that are far from L. ...
As pointed out by [RVW13] , their transformation can be also used to convert any PCPP into a 2-round argument of proximity. ...
doi:10.1007/978-3-662-48000-7_21
fatcat:5kuidvuiibcmjlmtv75r6oztsa
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