Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time

We present families of (hyper)elliptic curve which admit an efficient deterministic encoding function

Chosen-ciphertext security from subset sum

We construct a public-key encryption (PKE) scheme whose security is polynomial-time equivalent to the hardness of the Subset Sum problem. Our scheme achieves the standard notion of indistinguishability against chosen-ciphertext attacks (IND-CCA) and can be used to encrypt messages of arbitrary polynomial length, improving upon a previous construction by Lyubashevsky, Palacio, and Segev (TCC 2010) which achieved only the weaker notion of semantic security (IND-CPA) and whose concrete security decreases with the length of the message being encrypted. At the core of our construction is a trapdoor technique which originates in the work of Micciancio and Peikert (Eurocrypt 2012

Characterization of K2-167 b and CALM, a new stellar activity mitigation method

We report precise radial velocity (RV) observations of HD 212657 (= K2-167), a star shown by K2 to host a transiting sub-Neptune-sized planet in a 10 day orbit. Using Transiting Exoplanet Survey Satellite (TESS) photometry, we refined the planet parameters, especially the orbital period. We collected 74 precise RVs with the HARPS-N spectrograph between August 2015 and October 2016. Although this planet was first found to transit in 2015 and validated in 2018, excess RV scatter originally limited mass measurements. Here, we measure a mass by taking advantage of reductions in scatter from updates to the HARPS-N Data Reduction System (2.3.5) and our new activity mitigation method called CCF Activity Linear Model (CALM), which uses activity-induced line shape changes in the spectra without requiring timing information. Using the CALM framework, we performed a joint fit with RVs and transits using EXOFASTv2 and find $M_p = 6.3_{-1.4}^{+1.4}$ $M_{\oplus}$ and $R_p = 2.33^{+0.17}_{-0.15}$ $R_{\oplus}$, which places K2-167 b at the upper edge of the radius valley. We also find hints of a secondary companion at a $\sim$ 22 day period, but confirmation requires additional RVs. Although characterizing lower-mass planets like K2-167 b is often impeded by stellar variability, these systems especially help probe the formation physics (i.e. photoevaporation, core-powered mass loss) of the radius valley. In the future, CALM or similar techniques could be widely applied to FGK-type stars, help characterize a population of exoplanets surrounding the radius valley, and further our understanding of their formation

Deterministic Encoding and Hashing to Odd Hyperelliptic Curves

The original publication is available at www.springerlink.comInternational audienceIn this paper we propose a very simple and efficient encoding function from Fq to points of a hyperelliptic curve over Fq of the form H : y2 = f(x) where f is an odd polynomial. Hyperelliptic curves of this type have been frequently considered in the literature to obtain Jacobians of good order and pairing-friendly curves. Our new encoding is nearly a bijection to the set of Fq -rational points on H . This makes it easy to construct well-behaved hash functions to the Jacobian J of H , as well as injective maps to J (Fq ) which can be used to encode scalars for such applications as ElGamal encryption. The new encoding is already interesting in the genus 1 case, where it provides a well-behaved encoding to Joux?s supersingular elliptic curves

Identifying exoplanets with deep learning. IV. Removing stellar activity signals from radial velocity measurements using neural networks

Funding: This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (SCORE grant agreement No. 851555). A.C.C. acknowledges support from the Science and Technology Facilities Council (STFC) consolidated grant No. ST/R000824/1 and UKSA grant ST/R003203/1. R.D.H. is funded by the UK Science and Technology Facilities Council (STFC)’s Ernest Rutherford Fellowship (grant number ST/V004735/1). M.P. acknowledges financial support from the ASI-INAF agreement No. 2018-16-HH.0. A.M. acknowledges support from the senior Kavli Institute Fellowships.Exoplanet detection with precise radial velocity (RV) observations is currently limited by spurious RV signals introduced by stellar activity. We show that machine-learning techniques such as linear regression and neural networks can effectively remove the activity signals (due to starspots/faculae) from RV observations. Previous efforts focused on carefully filtering out activity signals in time using modeling techniques like Gaussian process regression. Instead, we systematically remove activity signals using only changes to the average shape of spectral lines, and use no timing information. We trained our machine-learning models on both simulated data (generated with the SOAP 2.0 software) and observations of the Sun from the HARPS-N Solar Telescope. We find that these techniques can predict and remove stellar activity both from simulated data (improving RV scatter from 82 to 3 cm s−1) and from more than 600 real observations taken nearly daily over 3 yr with the HARPS-N Solar Telescope (improving the RV scatter from 1.753 to 1.039 m s−1, a factor of ∼1.7 improvement). In the future, these or similar techniques could remove activity signals from observations of stars outside our solar system and eventually help detect habitable-zone Earth-mass exoplanets around Sun-like stars.Publisher PDFPeer reviewe

The EXPRES Stellar Signals Project II. State of the Field in Disentangling Photospheric Velocities

Measured spectral shifts due to intrinsic stellar variability (e.g., pulsations, granulation) and activity (e.g., spots, plages) are the largest source of error for extreme-precision radial-velocity (EPRV) exoplanet detection. Several methods are designed to disentangle stellar signals from true center-of-mass shifts due to planets. The Extreme-precision Spectrograph (EXPRES) Stellar Signals Project (ESSP) presents a self-consistent comparison of 22 different methods tested on the same extreme-precision spectroscopic data from EXPRES. Methods derived new activity indicators, constructed models for mapping an indicator to the needed radial-velocity (RV) correction, or separated out shape- and shift-driven RV components. Since no ground truth is known when using real data, relative method performance is assessed using the total and nightly scatter of returned RVs and agreement between the results of different methods. Nearly all submitted methods return a lower RV rms than classic linear decorrelation, but no method is yet consistently reducing the RV rms to sub-meter-per-second levels. There is a concerning lack of agreement between the RVs returned by different methods. These results suggest that continued progress in this field necessitates increased interpretability of methods, high-cadence data to capture stellar signals at all timescales, and continued tests like the ESSP using consistent data sets with more advanced metrics for method performance. Future comparisons should make use of various well-characterized data sets—such as solar data or data with known injected planetary and/or stellar signals—to better understand method performance and whether planetary signals are preserved

Public-Key Cryptographic Primitives Provably as Secure as Subset Sum

We propose a semantically-secure public-key encryption scheme whose security is polynomial-time equivalent to the hardness of solving random instances of the subset sum problem. The subset sum assumption required for the security of our scheme is weaker than that of existing subset-sum based encryption schemes, namely the lattice-based schemes of Ajtai and Dwork (STOC ’97), Regev (STOC ’03, STOC ’05), and Peikert (STOC ’09). Additionally, our proof of security is simple and direct. We also present a natural variant of our scheme that is secure against key-leakage attacks, as well as an oblivious transfer protocol that is secure against semi-honest adversaries

Seasonal Migration and Home Ranges of Female Elk in the Black Hills of South Dakota and Wyoming

Understanding the movement and dispersion patterns of elk (Cervus elaphus) on public lands and the underlying factors that affect each will facilitate elk management and help resolve conflicts between management that benefit elk and other uses of land resources. Consequently, there is a need to identify and examine the movement and dispersion patterns of elk in the Black Hills of South Dakota and Wyoming. Our study quantified seasonal movements, determined home ranges of female elk in two areas of the Black Hills, and examined underlying factors associated with each. Elk in the northern area did not demonstrate seasonal migration patterns. Rather, winter ranges in the northern area were contained mostly within the boundaries of the summer range. Elk in the southern area exhibited a north-south migration pattern that coincided with seasonal patterns of snowfall. These elk migrated to winter range in late November and returned to summer range in late April. Home ranges of elk in the southern area were larger (P \u3c 0.01) than home ranges in the northern area. Landscape characteristics with marginally-significant correlations to elk home range area included road density (P = 0.10), and forage:cover ratio (P = 0.08); density of primary and secondary roads and average slope were significantly correlated with elk home range area (P \u3c 0.01). Managers can use this information to develop strategies that meet population goals and reduce conflicts between management for elk and with other resources

How to Hash into Elliptic Curves

We describe a new explicit function that given an elliptic curve $E$ defined over \FF_{p^n}, maps elements of \FF_{p^n} into $E$ in \emph{deterministic} polynomial time and in a constant number of operations over \FF_{p^n}. The function requires to compute a cube root. As an application we show how to hash \emph{deterministically} into an elliptic curve