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Private Set Union (PSU) protocol allows parties, each hold- ing an input set, to jointly compute the union of the sets without revealing anything else. In the literature, scalable PSU protocols follow the “split-execute-assemble” paradigm (Kolesnikov et al., ASIACRYPT 2019); in addition, those fast protocols often use Oblivious Transfer as building blocks. Kolesnikov et al. (ASIACRYPT 2019) and Jia et al. (USENIX Security 2022), pointed out that certain security issues can be introduced in the “split-execute-assemble” paradigm. In this work, surprisingly, we observe that the typical way of invoking Oblivious Transfer also causes unnecessary leakage, and only the PSU protocols based on additively homomor- phic encryption (AHE) can avoid the leakage. However, the AHE-based PSU protocols are far from being practical. To bridge the gap, we also design a new PSU protocol that can avoid the unnecessary leakage. Unlike the AHE- based PSU protocols, our new construction only relies on symmetric-key operations other than base OTs, thereby being much more scalable. The experimental results demonstrate that our protocol can obtain at least 873.74× speedup over the best-performing AHE-based scheme. Moreover, our per- formance is comparable to that of the state-of-the-art PSU protocol (Chen et al., USENIX Security 2023), which also suffers from the unnecessary leakage. 

Abstract The formation of magma‐poor continental rifts is an enigmatic process, as the weakening mechanism(s) for cratonic lithosphere remains uncertain in the absence of elevated lithospheric temperature. One view links weakening to melts hidden at depth, while another ascribes it to pre‐existing weaknesses. Long‐term extensional rates also influence lithospheric strength and rift evolution. We target the Linfen Basin (LB) in the magma‐poor Shanxi Rift System (SRS) in the North China Craton to understand these components. We apply cosmogenic²⁶Al/¹⁰Be burial dating on 14 core samples at different depths from three deep boreholes in the basin and obtain six valid burial ages ranging from 2.37^{+1.18/−1.21}to 5.86^+inf/−1.37 Ma. We further re‐interpret a seismic reflection profile and quantify the geometry and amount of extension by forward structural modeling with multiple constraints based on extensional fault‐bend folding theory. The timing of the basal sedimentation is estimated to be ∼6.1 and ∼4.2 Ma in the southern and northern portions, respectively, indicating diachronous, northward‐propagating rifting. The amount and mean rate of extension are ∼3.6 km and ∼0.9 km/Myr, respectively. The basin depths increasing northward indicates the clockwise rotation of the basin. We propose a basin‐scale non‐rigid transtensional bookshelf faulting model to explain the rotation patterns of the circum‐Ordos basins. We argue that the inherited structures weaken the cratonic lithosphere of the SRS, and the low extension rate contributes to its magma‐poor nature. We propose a lithospheric‐scale evolution model for the LB, invoking the inherited crustal weakness, low extension rate, and lower lithosphere counterflow. 

Private Set Union (PSU) allows two players, the sender and the receiver, to compute the union of their input datasets with- out revealing any more information than the result. While it has found numerous applications in practice, not much re- search has been carried out so far, especially for large datasets. In this work, we take shuffling technique as a key to de- sign PSU protocols for the first time. By shuffling receiver’s set, we put forward the first protocol, denoted as ΠRPSU, that eliminates the expensive operations in previous works, such as additive homomorphic encryption and repeated operations on the receiver’s set. It outperforms the state-of-the-art design by Kolesnikov et al. (ASIACRYPT 2019) in both efficiency and security; the unnecessary leakage in Kolesnikov et al.’s design, can be avoided in our design. We further extend our investigation to the application sce- narios in which both players may hold unbalanced input datasets. We propose our second protocol ΠSPSU, by shuffling the sender’s dataset. This design can be viewed as a dual ver- sion of our first protocol, and it is suitable in the cases where the sender’s input size is much smaller than the receiver’s. Finally, we implement our protocols ΠRPSU and ΠSPSU in C++ on big datasets, and perform a comprehensive evaluation in terms of both scalability and parallelizability. The results demonstrate that our design can obtain a 4-5× improvement over the state-of-the-art by Kolesnikov et al. with a single thread in WAN/LAN settings. 

Private Set Union (PSU) allows two players, the sender and the receiver, to compute the union of their input datasets with- out revealing any more information than the result. While it has found numerous applications in practice, not much research has been carried out so far, especially for large datasets. In this work, we take shuffling technique as a key to design PSU protocols for the first time. By shuffling receiver’s set, we put forward the first protocol, denoted as $$\Pi^R_{PSU}$$, that eliminates the expensive operations in previous works, such as additive homomorphic encryption and repeated operations on the receiver’s set. It outperforms the state-of-the-art design by Kolesnikov et al. (ASIACRYPT 2019) in both efficiency and security; the unnecessary leakage in Kolesnikov et al.’s design, can be avoided in our design. We further extend our investigation to the application scenarios in which both players may hold unbalanced input datasets. We propose our second protocol $$\Pi^S_{PSU}$$, by shuffling the sender’s dataset. This design can be viewed as a dual version of our first protocol, and it is suitable in the cases where the sender’s input size is much smaller than the receiver’s. Finally, we implement our protocols $$\Pi^R_{PSU}$$ and $$\Pi^S_{PSU}$$ in C++ on big datasets, and perform a comprehensive evaluation in terms of both scalability and parallelizability. The results demonstrate that our design can obtain a 4-5X improvement over the state-of-the-art by Kolesnikov et al. with a single thread in WAN/LAN settings. 

Significance The exothermic metamorphic reaction in orthopyroxene (Opx), a major component of oceanic lithospheric mantle, is shown to trigger brittle failure in laboratory deformation experiments under conditions where garnet exsolution takes place. The reaction product is an extremely fine-grained material, forming narrow reaction zones that are mechanically weak, thereby facilitating macroscopic faulting. Oceanic subduction zones are characterized by two separate bands of seismicity, known as the double seismic zone. The upper band of seismicity, located in the oceanic crust, is well explained by dehydration-induced mechanical instability. Our newly discovered metamorphism-induced mechanical instability provides an alternative physical mechanism for earthquakes in the lower band of seismicity (located in the oceanic lithospheric mantle), with no requirement of hydration/dehydration processes. 

Abstract It has been suggested that ion foreshock waves originating in the solar wind upstream of the quasi-parallel ( Q -||) shock can impact the planetary magnetosphere leading to standing shear Alfvén waves, i.e., the field line resonances (FLRs). In this paper, we carry out simulations of interaction between the solar wind and terrestrial magnetosphere under radial interplanetary magnetic field conditions by using a 3-D global hybrid model, and show the properties of self-consistently generated field line resonances through direct mode conversion in magnetospheric response to the foreshock disturbances for the first time. The simulation results show that the foreshock disturbances from the Q -|| shock can excite magnetospheric ultralow-frequency waves, among which the toroidal Alfvén waves are examined. It is found that the foreshock wave spectrum covers a wide frequency range and matches the band of FLR harmonics after excluding the Doppler shift effects. The fundamental harmonic of field line resonances dominates and has the strongest wave power, and the higher the harmonic order, the weaker the corresponding wave power. The nodes and anti-nodes of the odd and even harmonics in the equatorial plane are also presented. In addition, as the local Alfvén speed increases earthward, the corresponding frequency of each harmonic increases. The field-aligned current in the cusp region indicative of the possibly observable aurora is found to be a result of magnetopause perturbation which is caused by the foreshock disturbances, and a global view substantiating this scenario is given. Finally, it is found that when the solar wind Mach number decreases, the strength of both field line resonance and field-aligned current decreases accordingly.