A Survey on Homomorphic Encryption Schemes: Theory and Implementation

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the survey that is being submitted to ACM CSUR and has been uploaded to arXiv for feedback from stakeholder

Molecular Gas Properties of the Giant Molecular Cloud Complexes in the Arms and Inter-arms of the Spiral Galaxy NGC 6946

Combining observations of multiple CO lines with radiative transfer modeling is a very powerful tool to investigate the physical properties of the molecular gas in galaxies. Using new observations as well as literature data, we provide the most complete CO ladders ever generated for eight star-forming regions in the spiral arms and inter-arms of the spiral galaxy NGC 6946, with observations of the CO(1-0), CO(2-1), CO(3-2), CO(4-3), CO(6-5), 13CO(1-0) and 13CO(2-1) transitions. For each region, we use the large velocity gradient assumption to derive beam-averaged molecular gas physical properties, namely the gas kinetic temperature (T_K), H2 number volume density n(H2) and CO number column density N(CO). Two complementary approaches are used to compare the observations with the model predictions: chi-square minimisation and likelihood. The physical conditions derived vary greatly from one region to the next: T_K=10-250 K, n(H2)=10^2.3-10^7.0 cm^-3 and N(CO)=10^15.0-10^19.3 cm^-2. The spectral line energy distribution (SLED) of some of these extranuclear regions indicates a star-formation activity that is more intense than that at the centre of our own Milky Way. The molecular gas in regions with a large SLED turnover transition (J_max>4) is hot but tenuous with a high CO column density, while that in regions with a low SLED turnover transition (J_max<=4) is cold but dense with a low CO column density. We finally discuss and find some correlations between the physical properties of the molecular gas in each region and the presence of young stellar population indicators (supernova remnants, HII regions, HI holes, etc.)Comment: 23 pages, 11 figures, MNRAS, Accepte

Threshold cryptography based on Asmuth–Bloom secret sharing

Cataloged from PDF version of article.In this paper, we investigate how threshold cryptography can be conducted with the Asmuth-Bloom secret sharing scheme and present three novel function sharing schemes for RSA, ElGamal and Paillier cryptosysterns. To the best of our knowledge, these are the first provably secure threshold cryptosystems realized using the Asmuth-Bloom secret sharing. Proposed schemes are comparable in performance to earlier proposals in threshold cryptography. (c) 2007 Elsevier Inc. All rights reserved

ISM chemistry in metal rich environments: molecular tracers of metallicity

In this paper we use observations of molecular tracers in metal rich and alpha-enhanced galaxies to study the effect of abundance changes on molecular chemistry. We selected a sample of metal rich spiral and star bursting objects from the literature, and present here new data for a sample of early-type galaxies (ETGs). We conducted the first survey of CS and methanol emission in ETGs, detecting 7 objects in CS, and 5 in methanol emission. We find evidence to support the hypothesis that CS is a better tracer of dense star-forming gas than HCN. We suggest that the methanol emission in these sources is driven by dust mantle destruction due to ionisation from high mass star formation, but cannot rule out shocks dominating in some sources. The derived source averaged CS/methanol column densities and rotation temperatures are similar to those found in normal spiral and starburst galaxies, suggesting dense clouds are little affected by the differences between galaxy types. Finally we used the total column density ratios for our galaxy samples to show for the first time that some molecular tracers do seem to show systematic variations that appear to correlate with metallicity, and that these variations roughly match those predicted by chemical models. Using this fact, the chemical models of Bayet et al. (2012b), and assumptions about the optical depth we are able to roughly predict the metallicity of our spiral and ETG sample, with a scatter of ~0.3 dex. We provide the community with linear approximations to the relationship between the HCN and CS column density ratio and metallicity. Further study will clearly be required to determine if this, or any, molecular tracer can be used to robustly determine gas-phase metallically, but that a relationship exists at all suggests that in the future it may be possible to calibrate a metallicity indicator for the molecular interstellar medium (abridged).Comment: 14 pages, 9 figures. MNRAS, accepte