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This paper initiates a concrete-security treatment of two-party secure computation. The first step is to propose, as target, a simple, indistinguishability-based definition that we call InI. This could be considered a poor choice if it were weaker than standard simulation-based definitions, but it is not; we show that for functionalities satisfying a condition called invertibility, that we define and show is met by functionalities of practical interest like PSI and its variants, the two definitions are equivalent. Based on this, we move forward to study the concrete security of a canonical OPRF-based construction of PSI, giving a tight proof of InI security of the constructed PSI protocol based on the security of the OPRF. This leads us to the concrete security of OPRFs, where we show how different DH-style assumptions on the underlying group yield proofs of different degrees of tightness, including some that are tight, for the well-known and efficient 2H-DH OPRF, and thus for the corresponding DH PSI protocol. We then give a new PSI protocol, called salted-DH PSI, that is as efficient as DH-PSI, yet enjoys tighter proofs. 

In this study, we examine the performance of a multi-scale model for large-eddy simulation (LES) of tur- bulent combustion. The model referred to as RRLES performs the closure of the filtered reaction-rate term in the species transport equation while performing LES by using the linear eddy mixing (LEM) model. The RRLES model uses a multi-scale strategy to obtain the filtered reaction rate of the species and has been shown to address some of the challenges associated with the well-established LEMLES approach. The orig- inally proposed RRLES strategy used a multilevel adaptive mesh refinement (AMR) framework, which was extended to use a single grid-based strategy to enable the application to complex geometries. Additionally, a local dual-resolution grid strategy has also been developed and can potentially be used with different grid topologies, without the need for the AMR. We assess the accuracy and efficiency of the single and dual-grid RRLES approaches by considering a freely propagating turbulent premixed flame under two different initial conditions corresponding to the thin reaction zone (TRZ) and the broken/distributed reaction zone (B/DRZ) regimes.