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Recent new constructions of rate-1 OT [Döttling, Garg, Ishai, Malavolta, Mour, and Ostrovsky, CRYPTO 2019] have brought this primitive under the spotlight and the techniques have led to new feasibility results for private-information retrieval, and homomorphic encryption for branching programs. The receiver communication of this construction consists of a quadratic (in the sender's input size) number of group elements for a single instance of rate-1 OT. Recently [Garg, Hajiabadi, Ostrovsky, TCC 2020] improved the receiver communication to a linear number of group elements for a single string-OT. However, most applications of rate-1 OT require executing it multiple times, resulting in large communication costs for the receiver. In this work, we introduce a new technique for amortizing the cost of multiple rate-1 OTs. Specifically, based on standard pairing assumptions, we obtain a two-message rate-1 OT protocol for which the amortized cost per string-OT is asymptotically reduced to only four group elements. Our results lead to significant communication improvements in PSI and PIR, special cases of SFE for branching programs. - PIR: We obtain a rate-1 PIR scheme with client communication cost of $$O(\lambda\cdot\log N)$$ group elements for security parameter $$\lambda$$ and database size $$N$$. Notably, after a one-time setup (or one PIR instance), any following PIR instance only requires communication cost $$O(\log N)$$ number of group elements. - PSI with unbalanced inputs: We apply our techniques to private set intersection with unbalanced set sizes (where the receiver has a smaller set) and achieve receiver communication of $$O((m+\lambda) \log N)$$ group elements where $m, N$ are the sizes of the receiver and sender sets, respectively. Similarly, after a one-time setup (or one PSI instance), any following PSI instance only requires communication cost $$O(m \cdot \log N)$$ number of group elements. All previous sublinear-communication non-FHE based PSI protocols for the above unbalanced setting were also based on rate-1 OT, but incurred at least $$O(\lambda^2 m \log N)$$ group elements. 

Abstract The ATLAS detector is installed in its experimental cavern at Point 1 of the CERN Large Hadron Collider. During Run 2 of the LHC, a luminosity of  ℒ = 2 × 10³⁴cm^-2s^-1was routinely achieved at the start of fills, twice the design luminosity. For Run 3, accelerator improvements, notably luminosity levelling, allow sustained running at an instantaneous luminosity of  ℒ = 2 × 10³⁴cm^-2s^-1, with an average of up to 60 interactions per bunch crossing. The ATLAS detector has been upgraded to recover Run 1 single-lepton trigger thresholds while operating comfortably under Run 3 sustained pileup conditions. A fourth pixel layer 3.3 cm from the beam axis was added before Run 2 to improve vertex reconstruction and b-tagging performance. New Liquid Argon Calorimeter digital trigger electronics, with corresponding upgrades to the Trigger and Data Acquisition system, take advantage of a factor of 10 finer granularity to improve triggering on electrons, photons, taus, and hadronic signatures through increased pileup rejection. The inner muon endcap wheels were replaced by New Small Wheels with Micromegas and small-strip Thin Gap Chamber detectors, providing both precision tracking and Level-1 Muon trigger functionality. Trigger coverage of the inner barrel muon layer near one endcap region was augmented with modules integrating new thin-gap resistive plate chambers and smaller-diameter drift-tube chambers. Tile Calorimeter scintillation counters were added to improve electron energy resolution and background rejection. Upgrades to Minimum Bias Trigger Scintillators and Forward Detectors improve luminosity monitoring and enable total proton-proton cross section, diffractive physics, and heavy ion measurements. These upgrades are all compatible with operation in the much harsher environment anticipated after the High-Luminosity upgrade of the LHC and are the first steps towards preparing ATLAS for the High-Luminosity upgrade of the LHC. This paper describes the Run 3 configuration of the ATLAS detector.