Learning with Errors in the Exponent

We initiate the study of a novel class of group-theoretic intractability problems. Inspired by the theory of learning in presence of errors [Regev, STOC\u2705] we ask if noise in the exponent amplifies intractability. We put forth the notion of Learning with Errors in the Exponent (LWEE) and rather surprisingly show that various attractive properties known to exclusively hold for lattices carry over. Most notably are worst-case hardness and post-quantum resistance. In fact, LWEE\u27s duality is due to the reducibility to two seemingly unrelated assumptions: learning with errors and the representation problem [Brands, Crypto\u2793] in finite groups. For suitable parameter choices LWEE superposes properties from each individual intractability problem. The argument holds in the classical and quantum model of computation. We give the very first construction of a semantically secure public-key encryption system in the standard model. The heart of our construction is an ``error recovery\u27\u27 technique inspired by [Joye-Libert, Eurocrypt\u2713] to handle critical propagations of noise terms in the exponent

Comparison Of Early Total Thyroidectomy With Antithyroid Treatment In Patients With Moderate-Severe Graves' Orbitopathy: A Randomized Prospective Trial

Background: The optimal therapeutic choice for Graves' hyperthyroidism in the presence of moderate-severe Graves' orbitopathy (GO) remains controversial. Objectives: We aimed to compare GO course in patients with moderate-severe GO treated with early total thyroidectomy (TTx) versus antithyroid drug (ATD) regimens, in a prospective, randomized manner. Methods: Forty-two patients with moderate-severe GO were enrolled. A total of 4.5 g of pulse corticosteroids were given intravenously to all patients before randomization. Patients in the first group were given TTx, whereas patients in the second group were treated with ATDs. TSH was kept between 0.4 and 1 mIU/l. The clinical course of GO was evaluated with proptosis, lid aperture, clinical activity score (CAS), and diplopia. Results: Eighteen and 24 patients were randomized to the TTx and ATD groups, respectively. Thyroid autoantibodies decreased significantly, and there were significant improvements in proptosis, lid aperture, and CAS in the TTx group. While in the ATD group the decrement in thyroid autoantibodies was not significant, there were significant improvements in proptosis and CAS. When the TTx group was compared with the ATD group, anti-TPO, anti-Tg, and TSH-receptor antibodies were significantly decreased in the TTx group (p < 0.01), but there was no significant difference with respect to proptosis, lid aperture, CAS, and diplopia between the two groups during a median (min.-max.) follow-up period of 60 months (36-72). Conclusion: Although no definitive conclusions could be drawn from the study, mainly due to limited power, early TTx and the ATD treatment regimens, followed by intravenous pulse corticosteroid therapy, seemed to be equally effective on the course of GO in this relatively small group of patients with moderate-severe GO during a median (min.-max.) follow-up period of 60 months (36-72). (C) 2016 European Thyroid Association Published by S. Karger AG, BaselWo