Optimal Coding for Streaming Authentication and Interactive Communication

Franklin, Matthew K.; Gelles, Ran; Ostrovsky, Rafail; Schulman, Leonard J.

doi:10.1007/978-3-642-40084-1_15

Cited by 28 publications

(62 citation statements)

References 23 publications

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“…Later, Braverman and Rao [5] showed that an adversarial error rate of up to ǫ < 1/4 could be tolerated with a constant overhead α = Θ (1). Lastly, [4,6,7,10,11] determined the full error rate region in which a non-zero communication rate is possible in a variety of settings. While the initial coding schemes were not computationally efficient, because they relied on powerful but hard to construct tree codes, later results [1,2,9,10] provided polynomial time schemes using randomization.…”

Section: Prior Workmentioning

confidence: 99%

Interactive Channel Capacity Revisited

Haeupler

2014

2014 IEEE 55th Annual Symposium on Foundations of Computer Science

183

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We provide the first capacity approaching coding schemes that robustly simulate any interactive protocol over an adversarial channel that corrupts any ǫ fraction of the transmitted symbols. Our coding schemes achieve a communication rate of 1 − O( ǫ log log 1/ǫ) over any adversarial channel. This can be improved to 1 − O( √ ǫ) for random, oblivious, and computationally bounded channels, or if parties have shared randomness unknown to the channel. Surprisingly, these rates exceed 1 the 1 − Ω( H(ǫ)) = 1 − Ω( ǫ log 1/ǫ) interactive channel capacity bound which [Kol and Raz; STOC'13] recently proved for random errors. We conjecture 1 − Θ( ǫ log log 1/ǫ) and 1 − Θ( √ ǫ) to be the optimal rates for their respective settings and therefore to capture the interactive channel capacity for random and adversarial errors.In addition to being very communication efficient, our randomized coding schemes have multiple other advantages. They are computationally efficient, extremely natural, and significantly simpler than prior (non-capacity approaching) schemes. In particular, our protocols do not employ any coding but allow the original protocol to be performed as-is, interspersed only by short exchanges of hash values. When hash values do not match, the parties backtrack. Our approach is, as we feel, by far the simplest and most natural explanation for why and how robust interactive communication in a noisy environment is possible.1 Our protocols work for the standard setting in which the input protocol is alternating and the simulation has an alternating or non-adaptive, i.e., fixed, communication order. The impossibility result of [12] does not hold for alternating input protocols. Instead, an input protocol with a more complex communication order is assumed while the simulations are restricted to be non-adaptive. We point out that insisting on non-adaptive simulations is too restrictive for general input protocols: Independently of the amount of noise most (non-alternating) input protocols cannot be simulated robustly in a non-adaptive manner, i.e., a rate of 1 − o(1) is impossible even if the channel introduces merely a single random error. The 1 − O( H(ǫ))-rate coding scheme of [12] avoids this barrier by restricting the input protocols that can be simulated. Our coding scheme naturally works for any input protocol by allowing adaptive coding schemes as introduced in [11].

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Section: Prior Workmentioning

confidence: 99%

Interactive Channel Capacity Revisited

Haeupler

2014

2014 IEEE 55th Annual Symposium on Foundations of Computer Science

183

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“…Other computationally efficient encoding schemes have been developed [BK12, BN13, BKN14, GMS11, GMS14, GH14]. The communication rates under various scenarios have also been studied [BE17,GHS14,EGH15,FGOS15]. However, the rates do not approach the capacity expected of the noise rate.…”

Section: Classical Results With Efficient Encoding and Decodingmentioning

confidence: 99%

Capacity approaching coding for low noise interactive quantum communication

Leung

Nayak

Shayeghi

et al. 2018

Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

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We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with n messages, designed for a noiseless qudit channel over a poly (n) size alphabet, our main result is a simulation method that fails with probability less than 2 −Θ(n ) and uses a qudit channel over the same alphabet n(1 + Θ( √ )) times, of which an fraction can be corrupted adversarially. The simulation is thus capacity achieving to leading order, and we conjecture that it is optimal up to a constant factor in the √ term. Furthermore, the simulation is in a model that does not require pre-shared resources such as randomness or entanglement between the communicating parties. Our work improves over the best previously known quantum result where the overhead is a non-explicit large constant [Brassard et al., FOCS'14] for low . Introduction Motivation The main questions.Quantum communication offers the possibility of distributed computation with extraordinary provable savings in communication as compared with classical communication (see, e.g., [RK11] and the references therein). Most often, if not always, the savings are achieved by protocols that assume access to noiseless communication channels. In practice, though, imperfection in channels is inevitable. Is it possible to make the protocols robust to noise while maintaining the advantages offered by quantum communication? If so, what is the cost of making the protocols robust, and how much noise can be tolerated? In this article, we address these questions in the context of quantum communication protocols involving two parties, in the low noise regime. Following convention, we call the two parties Alice and Bob. 1.1.2 Channel coding theory as a special case. Proposition 2.3. The Bell states φ j,k 0≤j,k≤d−1 form an orthonormal basis in A ⊗ B. Proposition 2.4. For any unitary operator U on register A, it holds that Quantum Communication ModelThe definitions for the noiseless and noisy quantum communication models are copied from Ref.[BNT + 19]. We refer the reader there for a more formal definition of the noisy quantum communication model, as well as the relationship of the noiseless quantum communication model to well-studied quantum communication complexity models such a Yao's model and the Cleve-Buhrman model. 6 Noiseless Communication ModelIn the noiseless quantum communication model that we want to simulate, there are five quantum registers: the A register held by Alice, the B register held by Bob, the C register, which is the communication register exchanged back-and-forth between Alice and Bob and initially held by Alice, the E register held by a potential adversary Eve, and finally the R register, a reference system which purifies the state of the ABCE registers throughout the protocol. The initial stateis chosen arbitrarily from the set of possible inputs, and is fixed at the outset of the protocol, but possibly unknown (totally or partial...

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“…Later, Braverman and Rao [6] improved the tolerated error rate to < 1/4. Franklin et al [10] showed that constant rate cannot be achieved if the error rate is above 1 2 . As mentioned in [15], the initial interactive coding schemes are not computationally efficient because the involved tree codes are complicated to construct.…”

Section: Related Workmentioning

confidence: 99%

Small Memory Robust Simulation of Client-Server Interactive Protocols over Oblivious Noisy Channels

Chan¹,

Liang²,

Polychroniadou³

et al. 2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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We revisit the problem of low-memory robust simulation of interactive protocols over noisy channels. Haeupler [FOCS 2014] considered robust simulation of two-party interactive protocols over oblivious, as well as adaptive, noisy channels. Since the simulation does not need to have fixed communication pattern, the achieved communication rates can circumvent the lower bound proved by Kol and Raz [STOC 2013]. However, a drawback of this approach is that each party needs to remember the whole history of the simulated transcript. In a subsequent manuscript, Haeupler and Resch considered low-memory simulation. The idea was to view the original protocol as a computational DAG and only the identities of the nodes are saved (as opposed to the whole transcript history) for backtracking to reduce memory usage.In this paper, we consider low-memory robust simulation of more general client-server interactive protocols, in which a leader communicates with other members/servers, who do not communicate among themselves; this setting can be applied to information-theoretic multi-server Private Information Retrieval (PIR) schemes. We propose an information-theoretic technique that converts any correct PIR protocol that assumes reliable channels, into a protocol which is both correct and private in the presence of a noisy channel while keeping the space complexity to a minimum. Despite the huge attention that PIR protocols have received in the literature, the existing works assume that the parties communicate using noiseless channels.Moreover, we observe that the approach of Haeupler and Resch to just save the nodes in the aforementioned DAG without taking the transcript history into account will lead to a correctness issue even for oblivious corruptions. We resolve this issue by saving hashes of prefixes of past transcripts. Departing from the DAG representation also allows us to accommodate scenarios where a party can simulate its part of the protocol without any extra knowledge (such as the DAG representation of the whole protocol). In the the two-party setting, our simulation has the same dependence on the error rate as in the work of Haeupler, and in the client-server setting it also depends on the number of servers. Furthermore, since our approach does not remember the complete transcript history, our current technique can defend only against oblivious corruptions.1. If protocol Π is run where the communication channel between Alice and each Bob has oblivious error rate , then, except with probability δ, Π correctly simulates Π.2. In Π , for each (noisy) communication channel, the number of bits transmitted is at most3. If party X has a memory usage of M X bits and is involved in κ (= 1 for each Bob, or m for Alice) communication channels in Π, then its memory usage (in bits) in Π is at mostPaper Organization. While we are trying to give the precise results of this paper in the above description as soon as possible, readers unfamiliar with the formal definitions and settings can first refer to Section 2. The research backgroun...

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Optimal Coding for Streaming Authentication and Interactive Communication

Cited by 28 publications

References 23 publications

Interactive Channel Capacity Revisited

Interactive Channel Capacity Revisited

Capacity approaching coding for low noise interactive quantum communication

Small Memory Robust Simulation of Client-Server Interactive Protocols over Oblivious Noisy Channels

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