Pushing the Limits of Valiant\u27s Universal Circuits: Simpler, Tighter and More Compact

A universal circuit (UC) is a general-purpose circuit that can simulate arbitrary circuits (up to a certain size $n$). Valiant provides a $k$-way recursive construction of universal circuits (STOC 1976), where $k$ tunes the complexity of the recursion. More concretely, Valiant gives theoretical constructions of 2-way and 4-way UCs of asymptotic (multiplicative) sizes $5n\log n$ and $4.75 n\log n$ respectively, which matches the asymptotic lower bound $\Omega(n\log n)$ up to some constant factor. Motivated by various privacy-preserving cryptographic applications, Kiss et al. (Eurocrypt 2016) validated the practicality of 2-way universal circuits by giving example implementations for private function evaluation. G{ü}nther et al. (Asiacrypt 2017) and Alhassan et al. (J. Cryptology 2020) implemented the 2-way/4-way hybrid UCs with various optimizations in place towards making universal circuits more practical. Zhao et al. (Asiacrypt 2019) optimized Valiant\u27s 4-way UC to asymptotic size $4.5 n\log n$ and proved a lower bound $3.64 n\log n$ for UCs under Valiant framework. As the scale of computation goes beyond 10-million-gate ($n=10^7$) or even billion-gate level ($n=10^9$), the constant factor in circuit size plays an increasingly important role in application performance. In this work, we investigate Valiant\u27s universal circuits and present an improved framework for constructing universal circuits with the following advantages. [*Simplicity*] Parameterization is no longer needed. In contrast to that previous implementations resort to a hybrid construction combining $k=2$ and $k=4$ for a tradeoff between fine granularity and asymptotic size-efficiency, our construction gets the best of both worlds when configured at the lowest complexity (i.e., $k=2$). [*Compactness*] Our universal circuits have asymptotic size $3n\log n$, improving upon the best previously known $4.5n\log n$ by 33\% and beating the $3.64n\log n$ lower bound for UCs constructed under Valiant\u27s framework (Zhao et al., Asiacrypt 2019). [*Tightness*] We show that under our new framework the universal circuit size is lower bounded by $2.95 n\log n$, which almost matches the $3n\log n$ circuit size of our 2-way construction. We implement the 2-way universal circuits and evaluate its performance with other implementations, which confirms our theoretical analysis

Sulfidation of CoCuO_<i>x</i> Supported on Nickel Foam to Form a Heterostructure and Oxygen Vacancies for a High-Performance Anion-Exchange Membrane Water Electrolyzer

Anion-exchange membrane water electrolyzer (AEMWE) is attracting attention for hydrogen production owing to its ability to employ nonprecious metal catalysts and high energy conversion efficiency. Spinel-structured transition metal oxides exhibit excellent potential in oxygen evolution reaction (OERs). Nevertheless, the research on highly active and durable spinel-structured electrodes for the anodic OER of AEMWE is deficient. Herein, a self-supported S-CoCu oxide/nickel foam (S-CoCuOx/NF) anode was synthesized through a two-step method (electrodeposition and sulfidation). The formation of abundant oxygen vacancies and heterostructure collaboratively enhances the electron and mass transfer, resulting in an overpotential of 313 mV at 100 mA cm–2 for OER. For the lab-scale AEMWE system with the S-CoCuOx/NF anode, a current density of 1 A cm–2 was obtained at 1.87 V (cell voltage) with high durability for 110 h (1 A cm–2) at 60 °C. The results will provide insights into developing the spinel structure-derived anode for high-performance AEMWE

Sulfidation of CoCuO_<i>x</i> Supported on Nickel Foam to Form a Heterostructure and Oxygen Vacancies for a High-Performance Anion-Exchange Membrane Water Electrolyzer

Anion-exchange membrane water electrolyzer (AEMWE) is attracting attention for hydrogen production owing to its ability to employ nonprecious metal catalysts and high energy conversion efficiency. Spinel-structured transition metal oxides exhibit excellent potential in oxygen evolution reaction (OERs). Nevertheless, the research on highly active and durable spinel-structured electrodes for the anodic OER of AEMWE is deficient. Herein, a self-supported S-CoCu oxide/nickel foam (S-CoCuOx/NF) anode was synthesized through a two-step method (electrodeposition and sulfidation). The formation of abundant oxygen vacancies and heterostructure collaboratively enhances the electron and mass transfer, resulting in an overpotential of 313 mV at 100 mA cm–2 for OER. For the lab-scale AEMWE system with the S-CoCuOx/NF anode, a current density of 1 A cm–2 was obtained at 1.87 V (cell voltage) with high durability for 110 h (1 A cm–2) at 60 °C. The results will provide insights into developing the spinel structure-derived anode for high-performance AEMWE