Search for: All records

Homomorphic encryption allows computations to be performed directly on ciphertexts, serving as a key enabler for privacy-preserving cloud computing. The computations over ciphertexts involve large integer modular multiplications. Besides, the overall complexity of ciphertext multiplication can be further reduced by utilizing quotients of integer divisions. An efficient quotient computation architecture was developed in our previous work for the case that the divisor has three nonzero bits. This paper first generalizes our prior design to accommodate divisors with more nonzero bits. To further reduce the latency, a new non-iterative quotient computation method is developed by simplifying the Barrett reduction. Rigorous mathematical proofs are provided for both proposed schemes, and they are also adopted for modular reduction. Besides, this paper developed efficient hardware implementation architectures for our proposed algorithms, and optimizations are carried out to reduce the complexity further. Compared to the best prior integer division (modular reduction) schemes, our proposed designs can achieve around 60% (57%) smaller area and 70% (71%) shorter latency when the modulus has 64 bits. 

Abstract Dust transported from rangelands of the Southwestern United States (US) to mountain snowpack in the Upper Colorado River Basin during spring (March‐May) forces earlier and faster snowmelt, which creates problems for water resources and agriculture. To better understand the drivers of dust events, we investigated large‐scale meteorology responsible for organizing two Southwest US dust events from two different dominant geographic locations: (a) the Colorado Plateau and (b) the northern Chihuahuan Desert. High‐resolution Weather Research and Forecasting coupled with Chemistry model (WRF‐Chem) simulations with the Air Force Weather Agency dust emission scheme incorporating a MODIS albedo‐based drag‐partition was used to explore land surface‐atmosphere interactions driving two dust events. We identified commonalities in their meteorological setups. The meteorological analyses revealed that Polar and Sub‐tropical jet stream interaction was a common upper‐level meteorological feature before each of the two dust events. When the two jet streams merged, a strong northeast‐directed pressure gradient upstream and over the source areas resulted in strong near‐surface winds, which lifted available dust into the atmosphere. Concurrently, a strong mid‐tropospheric flow developed over the dust source areas, which transported dust to the San Juan Mountains and southern Colorado snowpack. The WRF‐Chem simulations reproduced both dust events, indicating that the simulations represented the dust sources that contributed to dust‐on‐snow events reasonably well. The representativeness of the simulated dust emission and transport in different geographic and meteorological conditions with our use of albedo‐based drag partition provides a basis for additional dust‐on‐snow simulations to assess the hydrologic impact in the Southwest US.