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

Design of singlet fission chromophores with cyclic (alkyl)(amino) carbene building blocks

We use MRSF-TDDFT and NEVPT2 methods to design singlet fission chromophores with the building blocks of cyclic (alkyl)(amino)carbenes (CAACs). CAAC dimers with C2, C4, and p-phenylene spacers are considered. The substitutions with trifluoromethyls and fluorine atoms at the α C position are investigated. The electronegative substituents enhance the π accepting capability of the α C, while maintaining it as a quaternary C atom. The phenylene-connected dimers with the two substitutions are identified as promising candidates for singlet fission chromophores. The cylindrically symmetric C2 and C4 spacers allow for substantial structural reorganizations in the S0-to-S1 and S0-to-T1 excitations. Although the two substituted dimers with the C4 spacer satisfy (or very close to satisfy) the primary thermodynamics criterion for singlet fission, the significant structural reorganizations result in high barriers so that the fission is kinetically unfavorable

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

Tsanet: Temporal and Scale Alignment for Unsupervised Video Object Segmentation

Unsupervised Video Object Segmentation (UVOS) refers to the challenging task of segmenting the prominent object in videos without manual guidance. In recent works, two approaches for UVOS have been discussed that can be divided into: appearance and appearance-motion-based methods, which have limitations respectively. Appearance-based methods do not consider the motion of the target object due to exploiting the correlation information between randomly paired frames. Appearance-motion-based methods have the limitation that the dependency on optical flow is dominant due to fusing the appearance with motion. In this paper, we propose a novel framework for UVOS that can address the aforementioned limitations of the two approaches in terms of both time and scale. Temporal Alignment Fusion aligns the saliency information of adjacent frames with the target frame to leverage the information of adjacent frames. Scale Alignment Decoder predicts the target object mask by aggregating multi-scale feature maps via continuous mapping with implicit neural representation. We present experimental results on public benchmark datasets, DAVIS 2016 and FBMS, which demonstrate the effectiveness of our method. Furthermore, we outperform the state-of-the-art methods on DAVIS 2016.Comment: Accepted to ICIP 202