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A private set membership (PSM) protocol allows a “receiver” to learn whether its input x is contained in a large database 𝖣𝖡 held by a “sender”. In this work, we define and construct credible private set membership (C-PSM) protocols: in addition to the conventional notions of privacy, C-PSM provides a soundness guarantee that it is hard for a sender (that does not know x) to convince the receiver that 𝑥∈𝖣𝖡. Furthermore, the communication complexity must be logarithmic in the size of 𝖣𝖡. We provide 2-round (i.e., round-optimal) C-PSM constructions based on standard assumptions: We present a black-box construction in the plain model based on DDH or LWE. Next, we consider protocols that support predicates f beyond string equality, i.e., the receiver can learn if there exists 𝑤∈𝖣𝖡 such that 𝑓(𝑥,𝑤)=1. We present two results with transparent setups: (1) A black-box protocol, based on DDH or LWE, for the class of NC1 functions f which are efficiently searchable. (2) An LWE-based construction for all bounded-depth circuits. The only non-black-box use of cryptography in this construction is through the bootstrapping procedure in fully homomorphic encryption. As an application, our protocols can be used to build enhanced round-optimal leaked password notification services, where unlike existing solutions, a dubious sender cannot fool a receiver into changing its password. https://doi.org/10.1007/978-3-031-31371-4_6 

Research into perovskite nanocrystals (PNCs) has uncovered interesting properties compared to their bulk counterparts, including tunable optical properties due to size‐dependent quantum confinement effect (QCE). More recently, smaller PNCs with even stronger QCE have been discovered, such as perovskite magic sized clusters (PMSCs) and ligand passivated PbX₂metal halide molecular clusters (MHMCs) analogous to perovskites.

This review aims to present recent data comparing and contrasting the optical and structural properties of PQDs, PMSCs, and MHMCs, where CsPbBr₃PQDs have first excitonic absorption around 520 nm, the corresponding PMSCS have absorption around 420 nm, and ligand passivated MHMCs absorb around 400 nm.

Compared to normal perovskite quantum dots (PQDs), these clusters exhibit both a much bluer optical absorption and emission and larger surface‐to‐volume (S/V) ratio. Due to their larger S/V ratio, the clusters tend to have more surface defects that require more effective passivation for stability.

Recent study of novel clusters has led to better understanding of their properties. The sharper optical bands of clusters indicate relatively narrow or single size distribution, which, in conjunction with their blue absorption and emission, makes them potentially attractive for applications in fields such as blue single photon emission.

 

Recent progress has been made on the synthesis and characterization of metal halide perovskite magic-sized clusters (PMSCs) with ABX 3 composition ( A = C H 3 N H 3 + or Cs + , B = P b 2 + , and X = C l − , Br - , or I - ). However, their mechanism of growth and structure is still not well understood. In our effort to understand their structure and growth, we discovered that a new species can be formed without the CH 3 NH 3 + component, which we name as molecular clusters (MCs). Specifically, CH 3 NH 3 PbBr 3 PMSCs, with a characteristic absorption peak at 424 nm, are synthesized using PbBr 2 and CH 3 NH 3 Br as precursors and butylamine (BTYA) and valeric acid (VA) as ligands, while MCs, with an absorption peak at 402 nm, are synthesized using solely PbBr 2 and BTYA, without CH 3 NH 3 Br. Interestingly, PMSCs are converted spontaneously overtime into MCs. An isosbestic point in their electronic absorption spectra indicates a direct interplay between the PMSCs and MCs. Therefore, we suggest that the MCs are precursors to the PMSCs. From spectroscopic and extended X-ray absorption fine structure (EXAFS) results, we propose some tentative structural models for the MCs. The discovery of the MCs is critical to understanding the growth of PMSCs as well as larger perovskite quantum dots (PQDs) or nanocrystals (PNCs).