The Learning with Errors (LWE) problem is a versatile basis for building various purpose post-quantum schemes. Goldwasser et al. [ISC 2010] initialized the study of a variant of this problem called the Entropic LWE problem, where the LWE secret is generated from a distribution with a certain min-entropy. Brakerski and Döttling recently further extended the study in this field, and first proved the hardness of the Entropic LWE problem with unbounded secret [Eurocrypt 2020], then gave a similar result for the Entropic Ring-LWE problem [TCC 2020]. In this work, we systematically study the hardness of the Entropic Module-LWE problem. Adapting the “lossiness approach” to the module setting, we give lower entropy bounds for the secret distributions that guarantee the hardness of the Entropic Module-LWE problem in both search and decision cases, where results are divided into two settings: bounded and unbounded norm. We also present that our search entropy lower bound in the unbounded case is essentially tight. An application of our bounded result is to deduce the hardness for the Binary Module-LWE problem. One of our central techniques is a new generalized leftover hash lemma over rings, which might be of independent interest.@en

Silicon heterojunction (SHJ) solar cells have reached high power conversion efficiency owing to their effective passivating contact structures. Improvements in the optoelectronic properties of these contacts can enable higher device efficiency, thus further consolidating the commercial potential of SHJ technology. Here we increase the efficiency of back junction SHJ solar cells with improved back contacts consisting of p-type doped nanocrystalline silicon and a transparent conductive oxide with a low sheet resistance. The electrical properties of the hole-selective contact are analysed and compared with a p-type doped amorphous silicon contact. We demonstrate improvement in the charge carrier transport and a low contact resistivity (<5 mΩ cm2). Eventually, we report a series of certified power conversion efficiencies of up to 26.81% and fill factors up to 86.59% on industry-grade silicon wafers (274 cm2, M6 size).@en