Key Exchange (KE) from RLWE (Ring-Learning with Errors) is a potential alternative to Diffie-Hellman (DH) in a post quantum setting. Key leakage with RLWE key exchange protocols in the context of key reuse has already been pointed out in previous work. The initial attack described by Fluhrer is designed in such a way that it only works on Peikert’s KE protocol and its variants that derives the shared secret from the most significant bits of the approximately equal keys computed by both parties. It does not work on Ding’s key exchange that uses the least significant bits to derive a shared key. The Signal leakage attack relies on changes in the signal sent by the responder reusing his key, in a sequence of key exchange sessions initiated by an attacker with a malformed key. A possible defense against this attack would be to require the initiator of a key exchange to send the signal, which is the one pass case of the KE protocol. In this work, we describe a new attack on Ding’s one pass case without relying on the signal function output but using only the information of whether the final key of both parties agree. We also use LLL reduction to create the adversary’s keys in such a way that the party being compromised cannot identify the attack in trivial ways. This completes the series of attacks on RLWE key exchange with key reuse for all variants in both cases of the initiator and responder sending the signal. Moreover, we show that the previous Signal leakage attack can be made more efficient with fewer queries and how it can be extended to Peikert’s key exchange, which was used in the BCNS implementation and integrated with TLS and a variant used in the New Hope implementation.

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Image retargeting techniques adjust images into different sizes and have attracted much attention recently. Objective quality assessment (OQA) of image retargeting results is often desired to automatically select the best results. Existing OQA methods train a model using some benchmarks (e.g., RetargetMe), in which subjective scores evaluated by users are provided. Observing that it is challenging even for human subjects to give consistent scores for retargeting results of different source images (diff-source-results), in this paper we propose a learning-based OQA method that trains a General Regression Neural Network (GRNN) model based on relative scores --- which preserve the ranking --- of retargeting results of the same source image (same-source-results). In particular, we develop a novel training scheme with provable convergence that learns a common base scalar for same-source-results. With this source specific offset, our computed scores not only preserve the ranking of subjective scores for same-source-results, but also provide a reference to compare the diff-source-results. We train and evaluate our GRNN model using human preference data collected in RetargetMe. We further introduce a subjective benchmark to evaluate the generalizability of different OQA methods. Experimental results demonstrate that our method outperforms ten representative OQA methods in ranking prediction and has better generalizability to different datasets.

We prove an approximation result showing how operators of the type (x ) in L^ 2 ({\bb R}^ 2), where is a graph, can be modelled in the strong resolvent sense by point-interaction Hamiltonians with an appropriate arrangement of the potentials. The result is illustrated on finding the spectral properties in cases when is a ring or a star. Furthermore, we use this method to indicate that scattering on an infinite curve which is locally close to a loop shape or has multiple bends may exhibit resonances due to quantum tunnelling or repeated reflections.