Approximating Cumulative Pebbling Cost Is Unique Games Hard

The cumulative pebbling complexity of a directed acyclic graph $G$ is defined as $\mathsf{cc}(G) = \min_P \sum_i |P_i|$, where the minimum is taken over all legal (parallel) black pebblings of $G$ and $|P_i|$ denotes the number of pebbles on the graph during round $i$. Intuitively, $\mathsf{cc}(G)$ captures the amortized Space-Time complexity of pebbling $m$ copies of $G$ in parallel. The cumulative pebbling complexity of a graph $G$ is of particular interest in the field of cryptography as $\mathsf{cc}(G)$ is tightly related to the amortized Area-Time complexity of the Data-Independent Memory-Hard Function (iMHF) $f_{G,H}$ [AS15] defined using a constant indegree directed acyclic graph (DAG) $G$ and a random oracle $H(\cdot)$. A secure iMHF should have amortized Space-Time complexity as high as possible, e.g., to deter brute-force password attacker who wants to find $x$ such that $f_{G,H}(x) = h$. Thus, to analyze the (in)security of a candidate iMHF $f_{G,H}$, it is crucial to estimate the value $\mathsf{cc}(G)$ but currently, upper and lower bounds for leading iMHF candidates differ by several orders of magnitude. Blocki and Zhou recently showed that it is $\mathsf{NP}$-Hard to compute $\mathsf{cc}(G)$, but their techniques do not even rule out an efficient $(1+\varepsilon)$-approximation algorithm for any constant $\varepsilon>0$. We show that for any constant $c > 0$, it is Unique Games hard to approximate $\mathsf{cc}(G)$ to within a factor of $c$. (See the paper for the full abstract.)Comment: 28 pages, updated figures and corrected typo

Domain Alignment and Temporal Aggregation for Unsupervised Video Object Segmentation

Unsupervised video object segmentation aims at detecting and segmenting the most salient object in videos. In recent times, two-stream approaches that collaboratively leverage appearance cues and motion cues have attracted extensive attention thanks to their powerful performance. However, there are two limitations faced by those methods: 1) the domain gap between appearance and motion information is not well considered; and 2) long-term temporal coherence within a video sequence is not exploited. To overcome these limitations, we propose a domain alignment module (DAM) and a temporal aggregation module (TAM). DAM resolves the domain gap between two modalities by forcing the values to be in the same range using a cross-correlation mechanism. TAM captures long-term coherence by extracting and leveraging global cues of a video. On public benchmark datasets, our proposed approach demonstrates its effectiveness, outperforming all existing methods by a substantial margin

On the Security of Proofs of Sequential Work in a Post-Quantum World

A Proof of Sequential Work (PoSW) allows a prover to convince a resource-bounded verifier that the prover invested a substantial amount of sequential time to perform some underlying computation. PoSWs have many applications including time-stamping, blockchain design, and universally verifiable CPU benchmarks. Mahmoody, Moran, and Vadhan (ITCS 2013) gave the first construction of a PoSW in the random oracle model though the construction relied on expensive depth-robust graphs. In a recent breakthrough, Cohen and Pietrzak (EUROCRYPT 2018) gave an efficient PoSW construction that does not require expensive depth-robust graphs. In the classical parallel random oracle model, it is straightforward to argue that any successful PoSW attacker must produce a long $\mathcal{H}$-sequence and that any malicious party running in sequential time $T-1$ will fail to produce an $\mathcal{H}$-sequence of length $T$ except with negligible probability. In this paper, we prove that any quantum attacker running in sequential time $T-1$ will fail to produce an $\mathcal{H}$-sequence except with negligible probability -- even if the attacker submits a large batch of quantum queries in each round. The proof is substantially more challenging and highlights the power of Zhandry's recent compressed oracle technique (CRYPTO 2019). We further extend this result to establish post-quantum security of a non-interactive PoSW obtained by applying the Fiat-Shamir transform to Cohen and Pietrzak's efficient construction (EUROCRYPT 2018).Comment: 44 pages, 4 figure

Dynamic human resource selection for business process exceptions

A key capability of today's organizations is to flexibly and effectively react to unexpected events. A critical case of an unexpected event is sudden unavailability of human resources, which was not properly addressed by existing resource allocation approaches. This paper proposes a systematic approach that analyzes event logs to select suitable substitutes if the initial human resources become unavailable. The approach uses process mining and social network analysis to derive a metric called degree of substitution, which measures how much the work experiences of the human resources overlap, from the two perspectives: task execution and transfer of work. Along with the metric, suitable substitutes are also identified. A simulation demonstrates that the approach identifies suitable substitutes more effectively and accurately than existing allocation methods such as role‐based allocation or random allocation. The proposed approach will increase the effectiveness of dynamic allocation of human resources, especially in an exceptional situation.11Yscopu