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Error reconciliation is an important technique for learning with error (LWE) and ring-LWE (RLWE)-based constructions. In this paper, we present a comparison analysis on two error reconciliation-based RLWE key exchange protocols: Ding et al. in 2012 (DING12) and Bos et al. in 2015 (BCNS15). We take them as examples to explain the core idea of error reconciliation, building key exchange over RLWE problem, implementation and real-world performance, and compare them comprehensively. We also analyse a LWE key exchange 'Frodo' that uses an improved error reconciliation mechanism in BCNS15. To the best of our knowledge, our work is the first to present at least 128-bit classic (80-bit quantum) and 256-bit classic (> 200-bit quantum) secure parameter choices for DING12 with efficient portable C/C++ implementations. Benchmark shows that our efficient implementation is 11× faster than BCNS15 and one key exchange execution only costs 0.07 ms on a four-year-old middle range CPU. Error reconciliation is 1.57× faster than BCNS15.

It is well acknowledged in image processing domain that the information can be decomposed into different frequency parts and each part has its own merits. However, existing neural networks always ignore the distinctions and straightforwardly feed all the information into neural networks together, treating them equally. In this paper, we propose a novel neural networks framework named J-Net that decomposes images into different frequency bands and then processes them sequentially. Concretely, the images have been decomposed by wavelet transformation and then the wavelet coefficients are fed into neural networks gradually in different depth according to their decomposition levels. An attention module is utilized to facilitate the fusion of neural network features and injected information, yielding significant performance gain. Furthermore, we show how does the information with different frequency impact the accuracy of neural networks. Experiments show that 5.91%, 5.32% and 2.00% accuracy improvements on Caltech 101, Caltech256 and ImageNet, respectively.

We extend recent results by Pisier on$K$-subcouples, i.e. subcouples of an interpolation couple that preserve the$K$-functional (up to constants) and corresponding notions for quotient couples. Examples include interpolation (in the pointwise sense) and a reinterpretation of the Adamyan-Arov-Krein theorem for Hankel operators.

No abstract uploaded!