Discrete exponential operation, such as modular exponentiation and scalar multiplication on elliptic curves, is a basic operation of many public-key cryptosystems. However, the exponential operations are considered prohibitively expensive for resource-constrained mobile devices. In this paper, we address the problem of secure outsourcing of exponentiation operations to one single untrusted server. Our proposed scheme (ExpSOS) only requires very limited number of modular multiplications at local mobile environment thus it can achieve impressive computational gain. ExpSOS also provides a secure verification scheme with probability approximately 1 to ensure that the mobile end-users can always receive valid results. The comprehensive analysis as well as the simulation results in real mobile device demonstrates that our proposed ExpSOS can significantly improve the existing schemes in efficiency, security and result verifiability. We apply ExpSOS to securely outsource several cryptographic protocols to show that ExpSOS is widely applicable to many cryptographic computations.

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Introduction: Helicobacter pylori -induced chronic infection is associated with peptic ulcer, chronic gastritis, gastric cancer, and increasing antibiotic resistance. We aimed to evaluate the efficacy of clarithromycin-based triple therapy and non-bismuth based quadruple therapy for eradicating H. pylori in patients with chronic gastritis in Kuwait. Methods: We enrolled a total of 603 treatment-naive dyspeptic patients with gastric biopsy-proven chronic gastritis secondary to H. pylori in a prospective, open-label, randomized study. Patients were randomized into two groups: a group received the standard triple therapy (omeprazole, amoxicillin, and clarithromycin) for 14 days and a group received quadruple therapy (omeprazole, amoxicillin, clarithromycin, and metronidazole) for 14 days. All patients were tested for the eradication of H. pylori by carbon-13 urea breath test 1 month after eradication therapy. Results: The overall eradication rate was 63.2%. The eradication rates in intention-to-treat (ITT) and per protocol (PP) population were 58.4% and 64.6%, respectively, in triple therapy group. In the quadruple therapy group, the eradication rates in ITT and PP population were 68.0% and 78.5%, respectively, with a statistically significant higher eradication rate in patients treated by quadruple therapy than the triple therapy ( P < 0.01). Multivariate logistic regression analysis revealed that treatment regimen was the only significant predictor for successful H. pylori eradication. The most common adverse events were abnormal taste, headache, dizziness, and abdominal pain. Conclusion: Non-bismuth based quadruple therapy is more effective than standard clarithromycin-based triple therapy for eradicating H. pylori in patients with chronic gastritis. ClinicalTrials.gov Identifier: NCT04617613