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Abstract Zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) are cryptographic protocols that offer efficient and privacy-preserving means of verifying NP language relations and have drawn considerable attention for their appealing applications, e.g., verifiable computation and anonymous payment protocol. Compared with the pre-quantum case, the practicability of this primitive in the post-quantum setting is still unsatisfactory, especially for the space complexity. To tackle this issue, this work seeks to enhance the efficiency and compactness of lattice-based zk-SNARKs, including proof length and common reference string (CRS) length. In this paper, we develop the framework of square span program-based SNARKs and design new zk-SNARKs over cyclotomic rings. Compared with previous works, our construction is without parallel repetition and achieves shorter proof and CRS lengths than previous lattice-based zk-SNARK schemes. Particularly, the proof length of our scheme is around$$23.3\%$$ $23.3\%$smaller than the recent shortest lattice-based zk-SNARKs by Ishai et al. (in: Proceedings of the 2021 ACM SIGSAC conference on computer and communications security, pp 212–234, 2021), and the CRS length is$$3.6\times$$ $3.6\times$smaller. Our constructions follow the framework of Gennaro et al. (in: Proceedings of the 2018 ACM SIGSAC conference on computer and communications security, pp 556–573, 2018), and adapt it to the ring setting by slightly modifying the knowledge assumptions. We develop concretely small constructions by using module-switching and key-switching procedures in a novel way. 

Leveraging the accuracy and consistency of vehicle motion control enabled by the connected and automated vehicle technology, we propose the rhythmic control (RC) scheme that allows vehicles to pass through an intersection in a conflict-free manner with a preset rhythm. The rhythm enables vehicles to proceed at a constant speed without any stop. The RC is capable of breaking the limitation that right-of-way can only be allocated to nonconflicting movements at a time. It significantly improves the performance of intersection control for automated traffic. Moreover, the RC with a predetermined rhythm does not require intensive computational efforts to dynamically control vehicles, which may possibly lead to frequent accelerations or decelerations. Assuming stationary vehicle arrivals, we conduct a theoretical investigation to show that RC can considerably increase intersection capacity and reduce vehicle delay. Finally, the performance of RC is tested in the simulations with both stationary and nonstationary vehicle arrivals at both symmetric and asymmetric intersections. 

Connected and automated vehicle (CAV) technology is providing urban transportation managers tremendous opportunities for better operation of urban mobility systems. However, there are significant challenges in real-time implementation as the computational time of the corresponding operations optimization model increases exponentially with increasing vehicle numbers. Following the companion paper (Chen et al. 2021), which proposes a novel automated traffic control scheme for isolated intersections, this study proposes a network-level, real-time traffic control framework for CAVs on grid networks. The proposed framework integrates a rhythmic control method with an online routing algorithm to realize collision-free control of all CAVs on a network and achieve superior performance in average vehicle delay, network traffic throughput, and computational scalability. Specifically, we construct a preset network rhythm that all CAVs can follow to move on the network and avoid collisions at all intersections. Based on the network rhythm, we then formulate online routing for the CAVs as a mixed integer linear program, which optimizes the entry times of CAVs at all entrances of the network and their time–space routings in real time. We provide a sufficient condition that the linear programming relaxation of the online routing model yields an optimal integer solution. Extensive numerical tests are conducted to show the performance of the proposed operations management framework under various scenarios. It is illustrated that the framework is capable of achieving negligible delays and increased network throughput. Furthermore, the computational time results are also promising. The CPU time for solving a collision-free control optimization problem with 2,000 vehicles is only 0.3 second on an ordinary personal computer. 

A series of Ag( i ) and Cu( i ) complexes [Ag 3 (L 1 ) 2 ][PF 6 ] 3 ( 8 ), [Ag 3 (L 2 ) 2 ][PF 6 ] 3 ( 9 ), [Cu(L 1 )][PF 6 ] ( 10 ) and [Cu(L 2 )][PF 6 ] ( 11 ) have been synthesized by reactions of the tridentate amine-bis(N-heterocyclic carbene) ligand precursors [H 2 L 1 ][PF 6 ] 2 ( 6 ) and [H 2 L 2 ][PF 6 ] 2 ( 7 ) with Ag 2 O and Cu 2 O, respectively. Complexes 10 and 11 can also be obtained by transmetalation of 8 and 9 , respectively, with 3.0 equiv. of CuCl. A heterometallic Cu/Ag–NHC complex [Cu 2 Ag(L 1 ) 2 (CH 3 CN) 2 ][PF 6 ] 3 ( 12 ) is formed by the reaction of 8 with 2.0 equiv. of CuCl. All complexes have been characterized by NMR, electrospray ionization mass spectrometry (ESI-MS), and single-crystal X-ray diffraction studies. The luminescence properties of 10–12 in solution and the solid state have been studied. At room temperature, 10–12 exhibit evident luminescence in solution and the solid state. The emission wavelengths are found to be identical at 483 nm in CH 3 CN, but they are 484, 480 and 592 nm in the solid state for 10–12 , respectively. These results suggest that 12 dissociates into two molecules of 10 and Ag( i ) ions in solution. Complex 12 is the first luminescent heterometallic Cu/Ag–NHC complex.