اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn Probabilistic Checking in Perfect Zero Knowledge
143
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We present the first constructions of single-prover proof systems that achieve perfect zero knowledge (PZK) for languages beyond NP, under no intractability assumptions: 1. The complexity class #P has PZK proofs in the model of Interactive PCPs (IPCPs) [KR08], where the verifier first receives from the prover a PCP and then engages with the prover in an Interactive Proof (IP). 2. The complexity class NEXP has PZK proofs in the model of Interactive Oracle Proofs (IOPs) [BCS16,RRR16], where the verifier, in every round of interaction, receives a PCP from the prover. Our constructions rely on succinct simulators that enable us to simulate beyond NP, achieving exponential savings in efficiency over [BCGV16]. These simulators crucially rely on solving a problem that lies at the intersection of coding theory, linear algebra, and computational complexity, which we call the succinct constraint detection problem, and consists of detecting dual constraints with polynomial support size for codes of exponential block length. Our two results rely on solutions to this problem for fundamental classes of linear codes: * An algorithm to detect constraints for Reed--Muller codes of exponential length. * An algorithm to detect constraints for PCPs of Proximity of Reed--Solomon codes [BS08] of exponential degree. The first algorithm exploits the Raz--Shpilka [RS05] deterministic polynomial identity testing algorithm, and shows, to our knowledge, a first connection of algebraic complexity theory with zero knowledge. Along the way, we give a perfect zero knowledge analogue of the celebrated sumcheck protocol [LFKN92], by leveraging both succinct constraint detection and low-degree testing. The second algorithm exploits the recursive structure of the PCPs of Proximity to show that small-support constraints are locally spanned by a small number of small-support constraints.
قيم البحث
اقرأ أيضاً
In a recent seminal work, Bitansky and Shmueli (STOC 20) gave the first construction of a constant round zero-knowledge argument for NP secure against quantum attacks. However, their construction has several drawbacks compared to the classical counte
rparts. Specifically, their construction only achieves computational soundness, requires strong assumptions of quantum hardness of learning with errors (QLWE assumption) and the existence of quantum fully homomorphic encryption (QFHE), and relies on non-black-box simulation. In this paper, we resolve these issues at the cost of weakening the notion of zero-knowledge to what is called $epsilon$-zero-knowledge. Concretely, we construct the following protocols: - We construct a constant round interactive proof for NP that satisfies statistical soundness and black-box $epsilon$-zero-knowledge against quantum attacks assuming the existence of collapsing hash functions, which is a quantum counterpart of collision-resistant hash functions. Interestingly, this construction is just an adapted version of the classical protocol by Goldreich and Kahan (JoC 96) though the proof of $epsilon$-zero-knowledge property against quantum adversaries requires novel ideas. - We construct a constant round interactive argument for NP that satisfies computational soundness and black-box $epsilon$-zero-knowledge against quantum attacks only assuming the existence of post-quantum one-way functions. At the heart of our results is a new quantum rewinding technique that enables a simulator to extract a committed message of a malicious verifier while simulating verifiers internal state in an appropriate sense.
Using the probability theory-based approach, this paper reveals the equivalence of an arbitrary NP-complete problem to a problem of checking whether a level set of a specifically constructed harmonic cost function (with all diagonal entries of its He
ssian matrix equal to zero) intersects with a unit hypercube in many-dimensional Euclidean space. This connection suggests the possibility that methods of continuous mathematics can provide crucial insights into the most intriguing open questions in modern complexity theory.
In this paper we investigate the applicability of standard model checking approaches to verifying properties in probabilistic programming. As the operational model for a standard probabilistic program is a potentially infinite parametric Markov decis
ion process, no direct adaption of existing techniques is possible. Therefore, we propose an on-the-fly approach where the operational model is successively created and verified via a step-wise execution of the program. This approach enables to take key features of many probabilistic programs into account: nondeterminism and conditioning. We discuss the restrictions and demonstrate the scalability on several benchmarks.
We study the probabilistic degree over reals of the OR function on $n$ variables. For an error parameter $epsilon$ in (0,1/3), the $epsilon$-error probabilistic degree of any Boolean function $f$ over reals is the smallest non-negative integer $d$ su
ch that the following holds: there exists a distribution $D$ of polynomials entirely supported on polynomials of degree at most $d$ such that for all $z in {0,1}^n$, we have $Pr_{P sim D} [P(z) = f(z) ] geq 1- epsilon$. It is known from the works of Tarui ({Theoret. Comput. Sci.} 1993) and Beigel, Reingold, and Spielman ({ Proc. 6th CCC} 1991), that the $epsilon$-error probabilistic degree of the OR function is at most $O(log n.log 1/epsilon)$. Our first observation is that this can be improved to $O{log {{n}choose{leq log 1/epsilon}}}$, which is better for small values of $epsilon$. In all known constructions of probabilistic polynomials for the OR function (including the above improvement), the polynomials $P$ in the support of the distribution $D$ have the following special structure:$P = 1 - (1-L_1).(1-L_2)...(1-L_t)$, where each $L_i(x_1,..., x_n)$ is a linear form in the variables $x_1,...,x_n$, i.e., the polynomial $1-P(x_1,...,x_n)$ is a product of affine forms. We show that the $epsilon$-error probabilistic degree of OR when restricted to polynomials of the above form is $Omega ( log a/log^2 a )$ where $a = log {{n}choose{leq log 1/epsilon}}$. Thus matching the above upper bound (up to poly-logarithmic factors).
Traditional fact checking by expert journalists cannot keep up with the enormous volume of information that is now generated online. Computational fact checking may significantly enhance our ability to evaluate the veracity of dubious information. He
re we show that the complexities of human fact checking can be approximated quite well by finding the shortest path between concept nodes under properly defined semantic proximity metrics on knowledge graphs. Framed as a network problem this approach is feasible with efficient computational techniques. We evaluate this approach by examining tens of thousands of claims related to history, entertainment, geography, and biographical information using a public knowledge graph extracted from Wikipedia. Statements independently known to be true consistently receive higher support via our method than do false ones. These findings represent a significant step toward scalable computational fact-checking methods that may one day mitigate the spread of harmful misinformation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
