Public Coin Research Articles

Verifiable Quantum Advantage without Structure

We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: — There are NP search problems solvable by quantum polynomial-time (QPT) machines but not classical probabilistic polynomial-time (PPT) machines. — There exist functions that are one-way, and even collision resistant, against classical adversaries but are easily inverted quantumly. Similar counterexamples exist for digital signatures and CPA-secure public key encryption (the latter requiring the assumption of a classically CPA-secure encryption scheme). Interestingly, the counterexample does not necessarily extend to the case of other cryptographic objects such as PRGs. — There are unconditional publicly verifiable proofs of quantumness with the minimal rounds of interaction: for uniform adversaries, the proofs are non-interactive, whereas for non-uniform adversaries the proofs are two message public coin. — Our results do not appear to contradict the Aaronson-Ambanis conjecture. Assuming this conjecture, there exist publicly verifiable certifiable randomness, again with the minimal rounds of interaction. By replacing the random oracle with a concrete cryptographic hash function such as SHA2, we obtain plausible Minicrypt instantiations of the above results. Previous analogous results all required substantial structure, either in terms of highly structured oracles and/or algebraic assumptions in Cryptomania and beyond.

COVID-19 Cryptocurrency Investment: Wealth Disparities and Portfolio Diversification.

The introduction of cryptocurrency and blockchain technology has provided many investors the option to engage in the market, diversify their portfolios, and accumulate wealth. The high return on cryptocurrency during the pandemic has served as an incentive for all ethnic groups to participate in the market. Cryptocurrency is perceived as a hedging instrument for wealth prospects across races during COVID-19. Considering the return on investment, to what extent is blockchain a good hedging instrument for minority investors? Using weekly trade price data from Yahoo Finance, market valuations from coinranking.com, and asset/equity variables from the Federal Reserve Bank, this paper examines investment strategies of different racial/ethnic groups in cryptocurrency during the pandemic in a panel data model from 2019 to 2021. Should investors use public coins such as Bitcoin and Ethereum as part of their investment portfolio mix during the pandemic? We find that an increase in the price of Bitcoin and other cryptocurrencies during the pandemic may repress the investment strategy for marginalized groups.

Cost-Effective IoT Extensions for Existing Public Coin Operated Washing Machine Towards Smarter Apartment Complexes

Due to increasing urbanization in Bangkok, Thailand, it is observed that there are an increasing number of people who have moved into high-density apartment/condominium complexes. One common service that is provided at such complexes is the provision of public coin operated washing machines that allow tenants to do their laundry at a reasonable price. This has led to a new set of challenges, one of which is that the number of public coin operated washing machines is usually inadequate during peak hours, leading to long waits in queues for the tenants. The development of smart public coin operated washing machines has improved the quality of life of the tenants. This research proposes a smart public coin operated washing machine platform by extending the usefulness and convenience of existing washing machines using IoT applications. The infrastructure, the proposed application features, and the vacancy state detection of the new washing machine platform are discussed. Using the proposed platform, tenants using public coin operated washing machines can better plan when to do their laundry even during peak hours, improving their quality of life.

The role of randomness in the broadcast congested clique model

We study the role of randomness in the broadcast congested clique model. This is a message-passing model of distributed computation where the nodes of a network know their local neighborhoods and they broadcast, in synchronous rounds, messages that are visible to every other node.This works aims to separate three different settings: deterministic protocols, randomized protocols with private coins, and randomized protocols with public coins. We obtain the following results:•If more than one round is allowed, public randomness is as powerful as private randomness.•One-round public-coin algorithms can be exponentially more powerful than deterministic algorithms running in several rounds.•One-round public-coin algorithms can be exponentially more powerful than one-round private-coin algorithms.•One-round private-coin algorithms can be exponentially more powerful than one-round deterministic algorithms.

Winning Hearts and Minds, Losing the War: Public Opinion, COIN, and Rebel Strategy in Afghanistan, 2009-2014

Relying on survey and conflict data collected by the ISAF at the district level in Afghanistan from 2009-2014, this paper explores the causal relationships between public opinion, levels of insurgency, and counterinsurgent strategy. In order to overcome potential endogeneity problems, it relies on Bayesian Dynamical Systems Modelling, which makes minimal assumptions about how relevant variables relate to one another and is designed to uncover interactive and non-linear links between them. Consistent with COIN theory, the American surge increased support for the Afghan government, the most violent areas of the country saw reductions in attacks, and insurgent activity increased least in areas where support for the Afghan government was high. Nonetheless, the Taliban was able to expand the insurgency to more areas of the country, and, in districts where there was more counterinsurgent activity, higher support for the government was associated with increased Taliban activity. This is likely because, knowing it cannot take and hold territory due to the presence of ISAF forces, rebels seek to disrupt the successful implementation of hearts and minds and stretch the resources of the enemy. Moreover, this strategy appears to be somewhat effective, as more insurgent activity is associated with less legitimacy for the state. The results show that while hearts and minds can be won and public support for the government can benefit counterinsurgents, rebel forces can use strategy in order to disrupt this process.

Generalized Quantum Arthur--Merlin Games

This paper investigates the role of interaction and coins in public-coin quantum interactive proof systems (also called quantum Arthur-Merlin games). While prior works focused on classical public coins even in the quantum setting, the present work introduces a generalized version of quantum Arthur-Merlin games where the public coins can be quantum as well: the verifier can send not only random bits, but also halves of EPR pairs. First, it is proved that the class of two-turn quantum Arthur-Merlin games with quantum public coins, denoted qq-QAM in this paper, does not change by adding a constant number of turns of classical interactions prior to the communications of the qq-QAM proof systems. This can be viewed as a quantum analogue of the celebrated collapse theorem for AM due to Babai. To prove this collapse theorem, this paper provides a natural complete problem for qq-QAM: deciding whether the output of a given quantum circuit is close to a totally mixed state. This complete problem is on the very line of the previous studies investigating the hardness of checking the properties related to quantum circuits, and is of independent interest. It is further proved that the class qq-QAM_1 of two-turn quantum-public-coin quantum Arthur-Merlin proof systems with perfect completeness gives new bounds for standard well-studied classes of two-turn interactive proof systems. Finally, the collapse theorem above is extended to comprehensively classify the role of interaction and public coins in quantum Arthur-Merlin games: it is proved that, for any constant m>1, the class of problems having an m-turn quantum Arthur-Merlin proof system is either equal to PSPACE or equal to the class of problems having a two-turn quantum Arthur-Merlin game of a specific type, which provides a complete set of quantum analogues of Babai's collapse theorem.

Delegating Computation

In this work we study interactive proofs for tractable languages. The (honest) prover should be efficient and run in polynomial time or, in other words, a “muggle”.1 The verifier should be super-efficient and run in nearly linear time. These proof systems can be used for delegating computation: a server can run a computation for a client and interactively prove the correctness of the result. The client can verify the result’s correctness in nearly linear time (instead of running the entire computation itself). Previously, related questions were considered in the holographic proof setting by Babai et al. [1991b] in the argument setting under computational assumptions by Kilian, and in the random oracle model by Micali [1994]. Our focus, however, is on the original interactive proof model where no assumptions are made on the computational power or adaptiveness of dishonest provers. Our main technical theorem gives a public coin interactive proof for any language computable by a log-space uniform boolean circuit with depth d and input length n . The verifier runs in time n · poly( d , log( n )) and space O (log( n )), the communication complexity is poly( d , log( n )), and the prover runs in time poly( n ). In particular, for languages computable by log-space uniform NC (circuits of polylog( n ) depth), the prover is efficient, the verifier runs in time n · polylog( n ) and space O (log( n )), and the communication complexity is polylog( n ). Using this theorem we make progress on several questions. --- We show how to construct 1-round computationally sound arguments with polylog communication for any log-space uniform NC computation. The verifier runs in quasi-linear time. This result uses a recent transformation of Kalai and Raz from public coin interactive proofs to 1-round arguments . The soundness of the argument system is based on the existence of a PIR scheme with polylog communication. --- We construct interactive proofs with public coin, log-space, poly-time verifiers for all of P are given. This settles an open question regarding the expressive power of proof systems with such verifiers. --- We construct zero-knowledge interactive proofs are given with communication complexity quasi-linear in the witness length for any NP language verifiable in NC , based on the existence of 1-way functions. --- We construct probabilistically checkable arguments (a model due to Kalai and Raz) of size polynomial in the witness length (rather than instance length) for any NP language verifiable in NC , under computational assumptions, are provided.

WITHDRAWN: Quantum cryptography: Public key distribution and coin tossing

WITHDRAWN: Quantum cryptography: Public key distribution and coin tossing

Separating Deterministic from Randomized Multiparty Communication Complexity

We solve some fundamental problems in the number-on-forehead (NOF) $k$-player communication model. We show that there exists a function which has at most logarithmic communication complexity for randomized protocols with one-sided false-positives error probability of 1/3, but which has linear communication complexity for deterministic protocols, and in fact, even for the more powerful nondeterministic protocols. The result holds for every $\epsilon > 0$ and every $k \le 2^{(1-\epsilon)n}$ players, where $n$ is the number of bits on each player's forehead. As a consequence, we obtain the NOF communication class separation $\mathsf{coRP} \not\subset \mathsf{NP}$. This in particular implies that $\mathsf{P} \neq \mathsf{RP}$ and $\mathsf{NP} \neq \mathsf{coNP}$. We also show that for every $\epsilon > 0$ and every $k \le n^{1-\epsilon}$, there exists a function which has constant randomized complexity for public coin protocols but at least logarithmic complexity for private coin protocols. No larger gap between private and public coin protocols is possible. Our lower bounds are existential; no explicit function is known to satisfy nontrivial lower bounds for $k \ge \log n$ players. However, for every $\epsilon > 0$ and every $k \le (1-\epsilon) \cdot \log n$ players, the $\mathsf{NP} \ne \mathsf{coNP}$ separation (and even the $\mathsf{coNP} \not\subset \mathsf{MA}$ separation) was obtained independently by Gavinsky and Sherstov (2010) using an explicit construction. In this work, for $k \le (1/9) \cdot \log n$ players, we exhibit an explicit function which has communication complexity $O(1)$ for public coin protocols and $\Omega(\log n)$ for deterministic protocols. This improves the best previously known deterministic lower bound for a function with efficient randomized protocols, which was $\Omega(\log \log n)$, given by Beigel, Gasarch, and Glenn (2006). It follows from our existential result that any function that is complete for the class of functions with polylogarithmic nondeterministic $k$-player communication complexity does not have polylogarithmic deterministic complexity. We show that the set intersection function, which is complete in the number-in-hand model, is not complete in the NOF model under cylindrical reductions.

Exponential Separation of Quantum and Classical One-Way Communication Complexity

We give the first exponential separation between quantum and bounded-error randomized one-way communication complexity. Specifically, we define the Hidden Matching Problem HM$_n$: Alice gets as input a string ${\bf x}\in\{0, 1\}^n$, and Bob gets a perfect matching $M$ on the $n$ coordinates. Bob's goal is to output a tuple $\langle i,j,b \rangle$ such that the edge $(i,j)$ belongs to the matching $M$ and $b=x_i\oplus x_j$. We prove that the quantum one-way communication complexity of HM$_n$ is $O(\log n)$, yet any randomized one-way protocol with bounded error must use $\Omega({\sqrt{n}})$ bits of communication. No asymptotic gap for one-way communication was previously known. Our bounds also hold in the model of Simultaneous Messages (SM), and hence we provide the first exponential separation between quantum SM and randomized SM with public coins. For a Boolean decision version of HM$_n$, we show that the quantum one-way communication complexity remains $O(\log n)$ and that the 0-error randomized one-way communication complexity is $\Omega(n)$. We prove that any randomized linear one-way protocol with bounded error for this problem requires $\Omega(\sqrt[3]{n \log n})$ bits of communication.

Zaps and Their Applications

A zap is a 2‐round, public coin witness‐indistinguishable protocol in which the first round, consisting of a message from the verifier to the prover, can be fixed “once and for all” and applied to any instance. We present a zap for every language in NP, based on the existence of noninteractive zero‐knowledge proofs in the shared random string model. The zap is in the standard model and hence requires no common guaranteed random string. We present several applications for zaps, including 3‐round concurrent zero‐knowledge and 2‐round concurrent deniable authentication, in the timing model of Dwork, Naor, and Sahai [J. ACM, 51 (2004), pp. 851–898], using moderately hard functions. We also characterize the existence of zaps in terms of a primitive called verifiable pseudorandom bit generators.

A characterization of average case communication complexity

It is well known that the average case deterministic communication complexity is bounded below by an entropic quantity, which one would now call deterministic information complexity. In this paper we show a corresponding upper bound. We also improve known lower bounds for the public coin Las Vegas communication complexity by a constant factor.

The communication complexity of the Hamming distance problem

We investigate the randomized and quantum communication complexity of the Hamming Distance problem, which is to determine if the Hamming distance between two n-bit strings is no less than a threshold d. We prove a quantum lower bound of Ω ( d ) qubits in the general interactive model with shared prior entanglement. We also construct a classical protocol of O ( d log d ) bits in the restricted Simultaneous Message Passing model with public random coins, improving previous protocols of O ( d 2 ) bits [A.C.-C. Yao, On the power of quantum fingerprinting, in: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, 2003, pp. 77–81], and O ( d log n ) bits [D. Gavinsky, J. Kempe, R. de Wolf, Quantum communication cannot simulate a public coin, quant-ph/0411051, 2004].

On small space complexity classes of stochastic Turing machines and Arthur-Merlin-games

A Stochastic Turing machine (STM) is a Turing machine that can perform nondeterministic and probabilistic moves and alternate between both types. Such devices are also called games against nature, Arthur-Merlin-games, or interactive proof systems with public coins. We investigate stochastic machines with space resources between constant and logarithmic size, and, in addition, constant or sublinear bounds on the number of alternations between nondeterministic and probabilistic moves. Lower space bounds are shown for a specific family of languages by exploiting combinatorial properties. These results imply an infinite hierarchy with respect to the number of alternations of STMs, and nonclosure properties of certain classes.

Introduction to Special Section on Probabilistic Proof Systems

The study of probabilistically verifiable proofs originated in the mid 1980s with the introduction of Interactive Proof Systems (IPs). The primary focus of research in this area in the '80s has been twofold: the role of zero-knowledge interactive proofs within cryptographic protocols, and characterizing which languages are efficiently interactively provable. In the 1990s, the focus of research on the topic shifted. Extensions of the interactive proof model, such as Multiprover Interactive Proofs (MIPs) and Probabilistically Checkable Proofs (PCPs), were considered with the intention of expanding our notion of what should be considered efficiently verifiable. In addition, researchers have taken a closer look at the exact resources (and tradeoffs amongst them) needed to verify a proof using various proof systems. This culminated in the important discovery that it is possible to verify NP statements (with a constant error probability) by only examining a constant number of bits of a PCP and using logarithmic amount of randomness. Perhaps, however, the most dramatic development has been the connection which was found between probabilistically verifiable proofs and proving hardness of approximation for optimization problems. It has been shown that a large variety of optimization versions of NP-hard problems (e.g., the maximum size of a clique in a graph, the minimum number of colors necessary to color a graph, and the maximum number of clauses satisfiable in a CNF formula) are not only NP-hard to solve exactly but also NP-hard to approximate in a very strong sense. The tools to establish hardness of approximation came directly from results on MIPs and PCPs. Indeed, almost every improvement in the efficiency of these proof systems translates directly into showing larger factors within which these optimization problems are hard to approximate. In 1994--1995 two exciting workshops were held at the Weizmann Institute in Israel on the new developments in probabilistically verifiable proofs and their applications to approximation problems, cryptography, program checking, and complexity theory at large. Over 60 papers were presented in the workshop series, and we are proud to include three of them in this special section. "On the Power of Finite Automata with Both Nondeterministic and Probabilistic States" by Anne Condon, Lisa Hellerstein, Samuel Pottle, and Avi Wigderson, considers constant round interactive proof systems where the verifier is restricted to use constant space and public coins. An equivalent characterization is finite automata with both nondeterministic and random states (npfa's), which accept their languages with a small probability of error. The paper shows that npfa's restricted to run in polynomial expected time accept only the regular languages in the case of npfa with 1-way input head, and that if Lis a nonregular language, then either L or its complement is not accepted by any npfa with a 2-way input head. "A Parallel Repetition Theorem" by Ran Raz, addresses and resolves the Parallel Repetition Conjecture which has eluded researchers for some time. The broader topic is what happens to the error probability of proof systems when they are composed. It has been known for awhile that sequential composition of proof systems (both single and multiprover interactive proofs) reduces the error exponentially, but this increases the number of rounds. For interactive proof systems, parallel repetition is known to reduce the error exponentially, and the Parallel Repetition Conjecture asserts that the same holds in a one-round two-prover proof system. Raz proves a constructive bound on the probability of error which indeed reduces at an exponential rate. The constant in the exponent is logarithmic in the total number of possible answers of the two provers, which means one can achieve two-prover one-round MIPs for NP statements with arbitrarily small constant error probability. This, in turn, has played a crucial role in further developments in the area and in particular in those reported in the next paper. "Free Bits, PCPs, and Nonapproximability---Towards Tight Results" by Mihir Bellare, Oded Goldreich, and Madhu Sudan, continues the investigation of PCPs and nonapproximability with emphasis on trying to get closer to tight results. The work consists of three parts. The first part presents several PCP proof systems for NP, based on a new error-correcting code called the Long Code. The second part shows that the connection between PCPs and hardness of approximation is not accidental. In particular, it shows that the transformation of a PCP for NP into hardness results for MaxClique can be reversed. Finally, the third part initiates a systematic investigation of the properties of PCPs as a function of the various parameters: randomness, query complexity, free-bit complexity, amortized free-bit complexity, proof size, etc. Two more papers submitted for this special section were not ready at this time for publication. They will appear in future issues of the SIAM Journal on Computing.

Proving properties of interactive proofs by a generalized counting technique

The problem of proving membership in languages accepted by interactive proof protocols is reduced to the problem of estimating the number of leaves in certain trees. Using this reduction, we present a direct proof that every language accepted by an interactive protocol whithin g ( n ) rounds is also accepted by an Arthur Merlin game within ⌈ g(n) 2 ⌉ rounds. This unifies the proofs of the two main positive results on the IP Hierarchy, namely: that private coin tossing can be replaced by public coin tossing, and that the numer of interactions can be reduced by a constant factor.