The spectacular success of Bitcoin and Blockchain Technology in recent years has provided enough evidence that a widespread adoption of a common cryptocurrency system is not merely a distant vision, but a scenario that might come true in the near future. However, the presence of Bitcoin's obvious shortcomings such as excessive electricity consumption, unsatisfying transaction throughput, and large validation time (latency) makes it clear that a new, more efficient system is needed. We propose a protocol in which a set of nodes maintains and updates a linear ordering of transactions that are being submitted by users. Virtually every cryptocurrency system has such a protocol at its core, and it is the efficiency of this protocol that determines the overall throughput and latency of the system. We develop our protocol on the grounds of the well-established field of Asynchronous Byzantine Fault Tolerant (ABFT) systems. This allows us to formally reason about correctness, efficiency, and security in the strictest possible model, and thus convincingly prove the overall robustness of our solution. Our protocol improves upon the state-of-the-art HoneyBadgerBFT by by reducing the asymptotic latency while matching the optimal communication complexity. Furthermore, in contrast to the above, our protocol does not require a trusted dealer thanks to a novel implementation of a trustless ABFT Randomness Beacon.
In this paper we propose a different assumption on the transaction buffers that allows us to better demonstrate the capabilities of our protocol when it comes to latency. We assume that at every round the ratio between lengths of transaction buffers of any two honest nodes is at most a fixed constant. In this model, our protocol achieves @math latency, while a natural adaptation of HBBFT would achieve latency @math , thus again a factor- @math improvement. A qualitative improvement over HBBFT that we achieve in this paper is that we completely get rid of the trusted dealer assumption. We also note that the definitions of Atomic Broadcast slightly differ between this paper and @cite_5 : we achieve Censorship Resilience assuming that it was input to even a single honest node, while in @cite_5 it has to be input to @math nodes.
@cite_5
2517585112 2043868537 2591036807 2047805348
We study a noiseless broadcast link serving @math users whose requests arise from a library of @math files. Every user is equipped with a cache of size @math files each. It has been shown that by splitting all the files into packets and placing individual packets in a random independent manner across all the caches prior to any transmission, at most @math file transmissions are required for any set of demands from the library. The achievable delivery scheme involves linearly combining packets of different files following a greedy clique cover solution to the underlying index coding problem. This remarkable multiplicative gain of random placement and coded delivery has been established in the asymptotic regime when the number of packets per file @math scales to infinity. The asymptotic coding gain obtained is roughly @math . In this paper, we initiate the finite-length analysis of random caching schemes when the number of packets @math is a function of the system parameters @math , and @math . Specifically, we show that the existing random placement and clique cover delivery schemes that achieve optimality in the asymptotic regime can have at most a multiplicative gain of 2 even if the number of packets is exponential in the asymptotic gain @math . Furthermore, for any clique cover-based coded delivery and a large class of random placement schemes that include the existing ones, we show that the number of packets required to get a multiplicative gain of @math is at least @math . We design a new random placement and an efficient clique cover-based delivery scheme that achieves this lower bound approximately. We also provide tight concentration results that show that the average (over the random placement involved) number of transmissions concentrates very well requiring only a polynomial number of packets in the rest of the system parameters. Consider two parties Alice and Bob, who hold private inputs x and y, and wish to compute a function f(x, y) privately in the information theoretic sense; that is, each party should learn nothing beyond f(x, y). However, the communication channel available to them is noisy. This means that the channel can introduce errors in the transmission between the two parties. Moreover, the channel is adversarial in the sense that it knows the protocol that Alice and Bob are running, and maliciously introduces errors to disrupt the communication, subject to some bound on the total number of errors. A fundamental question in this setting is to design a protocol that remains private in the presence of large number of errors. If Alice and Bob are only interested in computing f(x, y) correctly, and not privately, then quite robust protocols are known that can tolerate a constant fraction of errors. However, none of these solutions is applicable in the setting of privacy, as they inherently leak information about the parties' inputs. This leads to the question whether we can simultaneously achieve privacy and error-resilience against a constant fraction of errors. We show that privacy and error-resilience are contradictory goals. In particular, we show that for every constant c > 0, there exists a function f which is privately computable in the error-less setting, but for which no private and correct protocol is resilient against a c-fraction of errors. The same impossibility holds also for sub-constant noise rate, e.g., when c is exponentially small (as a function of the input size). We consider distributed plurality consensus in a complete graph of size @math with @math initial opinions. We design an efficient and simple protocol in the asynchronous communication model that ensures that all nodes eventually agree on the initially most frequent opinion. In this model, each node is equipped with a random Poisson clock with parameter @math . Whenever a node's clock ticks, it samples some neighbors, uniformly at random and with replacement, and adjusts its opinion according to the sample. A prominent example is the so-called two-choices algorithm in the synchronous model, where in each round, every node chooses two neighbors uniformly at random, and if the two sampled opinions coincide, then that opinion is adopted. This protocol is very efficient and well-studied when @math . If @math for some small @math , we show that it converges to the initial plurality opinion within @math rounds, w.h.p., as long as the initial difference between the largest and second largest opinion is @math . On the other side, we show that there are cases in which @math rounds are needed, w.h.p. One can beat this lower bound in the synchronous model by combining the two-choices protocol with randomized broadcasting. Our main contribution is a non-trivial adaptation of this approach to the asynchronous model. If the support of the most frequent opinion is at least @math times that of the second-most frequent one and @math , then our protocol achieves the best possible run time of @math , w.h.p. We relax full synchronicity by allowing @math nodes to be poorly synchronized, and the well synchronized nodes are only required to be within a certain time difference from one another. We enforce this synchronicity by introducing a novel gadget into the protocol. We prove the first nontrivial (superlinear) lower bound in the noisy broadcast model, defined by El Gamal in [Open problems presented at the @math workshop on Specific Problems in Communication and Computation sponsored by Bell Communication Research, in Open Problems in Communication and Computation, T. M. Cover and B. Gopinath, eds., Springer-Verlag, New York, 1987, pp. 60-62]. In this model there are @math processors @math , each of which is initially given a private input bit @math . The goal is for @math to learn the value of @math , for some specified function @math , using a series of noisy broadcasts. At each step a designated processor broadcasts one bit to all of the other processors, and the bit received by each processor is flipped with fixed probability (independently for each recipient). In 1988, Gallager [IEEE Trans. Inform. Theory, 34 (1988), pp. 176-180] gave a noise-resistant protocol that allows @math to learn the entire input with constant probability in @math broadcasts. We prove that Gallager's protocol is optimal, up to a constant factor. Our lower bound follows by reduction from a lower bound for generalized noisy decision trees, a new model which may be of independent interest. For this new model we show a lower bound of @math on the depth of a tree that learns the entire input. While the above lower bound is for an @math -bit function, we also show an @math lower bound for the number of broadcasts required to compute certain explicit boolean-valued functions, when the correct output must be attained with probability at least @math for a constant parameter @math (this bound applies to all threshold functions as well as any other boolean-valued function with linear sensitivity). This bound also follows by reduction from a lower bound of @math on the depth of generalized noisy decision trees that compute the same functions with the same error. We also show a (nontrivial) @math lower bound on the depth of generalized noisy decision trees that compute such functions with small constant error. Finally, we show the first protocol in the noisy broadcast model that computes the Hamming weight of the input using a linear number of broadcasts.