arXiv subjects
Publications and source records attributed to Diksha Gupta.
We present a foraging algorithm, GoldenFA, in which search direction is chosen based on the Golden Ratio. We show both theoretically and empirically that GoldenFA is more efficient for a single searcher than a comparable algorithm where search direction is chosen uniformly at random. Moreover, we give a variant of our algorithm that parallelizes linearly with the number of searchers.
Proof-of-work(PoW) is an algorithmic tool used to secure networks by imposing a computational cost on participating devices. Unfortunately, traditional PoW schemes require that correct devices perform significant computational work in perpetuity, even when the system is not under attack. We address this issue by designing general PoW protocols that ensure two properties. First, the fraction of identities in the system that are controlled by an attacker is a minority. Second, the computational cost of our protocol is comparable to the cost of an attacker. In particular, we present an efficient algorithm, GMCOM, which guarantees that the average computational cost to the good ID per unit time is O(J + sqrt(T(J+1))), where J is the average number of joins by the good IDs and T is the average computational spending of the adversary. Additionally, we discuss a precursor to this algorithm, CCOM, which guarantees an average computational cost to good IDs per unit time of O(J+T). We prove a lower bound showing that GMCOM's spending rate is asymptotically optimal among a large family of algorithms. Finally, we provide empirical evidence that our algorithms can be significantly more efficient than previous defenses under various attack scenarios.
Proof-of-work (PoW) is an algorithmic tool used to secure networks by imposing a computational cost on participating devices. Unfortunately, traditional PoW schemes require that correct devices perform computational work perpetually, even when the system is not under attack. We address this issue by designing a general PoW protocol that ensures two properties. First, the network stays secure. In particular, the fraction of identities in the system that are controlled by an attacker is always less than 1/2. Second, our protocol's computational cost is commensurate with the cost of an attacker. In particular, the total computational cost of correct devices is a linear function of the attacker's computational cost plus the number of correct devices that have joined the system. Consequently, if the network is attacked, we ensure security with cost that grows linearly with the attacker's cost; and, in the absence of attack, our computational cost remains small. We prove similar guarantees for bandwidth cost. Our results hold in a dynamic, decentralized system where participants join and depart over time, and where the total computational power of the attacker is up to a constant fraction of the total computational power of correct devices. We demonstrate how to leverage our results to address important security problems in distributed computing including: Sybil attacks, Byzantine consensus, and Committee election.
Multiplicative weights update algorithms have been used extensively in designing iterative algorithms for many computational tasks. The core idea is to maintain a distribution over a set of experts and update this distribution in an online fashion based on the parameters of the underlying optimization problem. In this report, we study the behavior of a special MWU algorithm used for generating a global coin flip in the presence of an adversary that tampers the experts' advice. Specifically, we focus our attention on two adversarial strategies: (1) non-adaptive, in which the adversary chooses a fixed set of experts a priori and corrupts their advice in each round; and (2) adaptive, in which this set is chosen as the rounds of the algorithm progress. We formulate these adversarial strategies as being greedy in terms of trying to maximize the share of the corrupted experts in the final weighted advice the MWU computes and provide the underlying optimization problem that needs to be solved to achieve this goal. We provide empirical results to show that in the presence of either of the above adversaries, the MWU algorithm takes $\mathcal{O}(n)$ rounds in expectation to produce the desired output. This result compares well with the current state of the art of $\mathcal{O}(n^3)$ for the general Byzantine consensus problem. Finally, we briefly discuss the extension of these adversarial strategies for a general MWU algorithm and provide an outline for the framework in that setting.