A note on the cost of computing odd degree isogenies

Finding an isogenous supersingular elliptic curve of a prescribed odd degree is an important building block for all the isogeny-based protocols proposed to date. In this note we present several strategies for the efficient construction of odd degree isogenies, which outperform previously reported methods when dealing with isogeny degrees in the range $[7, 2^{20}].

Parallel strategies for SIDH: Towards computing SIDH twice as fast

We present novel strategies and concrete algorithms for the parallel computation of the Supersingular Isogeny-based Diffie-Hellman key exchange (SIDH) protocol when executed on multi-core platforms. The most relevant design idea exploited by our approach is that of concurrently computing scalar multiplication operations along with a parallelized version of the strategies required for constructing and evaluating large smooth degree isogenies. We report experimental results showing that a three-core implementation of our parallel approach achieves an acceleration factor of 1.56 compared against a sequential implementation of the SIKE protocol

eSIDH: the revenge of the SIDH

The Supersingular Isogeny-based Diffie-Hellman key exchange protocol (SIDH) was introduced by Jao an De Feo in 2011. SIDH operates on supersingular elliptic curves defined over quadratic extension fields of the form GF($p^2$), where $p$ is a large prime number of the form $p = 4^{e_A} 3^{e_B} - 1,$ where $e_A, e_B$ are positive integers such that $4^{e_A} \approx 3^{e_B}.$ In this paper, a variant of the SIDH protocol that we dubbed extended SIDH (eSIDH) is presented. The eSIDH variant makes use of primes of the form, $p = 4^{e_A} \ell_B^{e_B}\ell_C^{e_C} f - 1.$ Here $\ell_B, \ell_C$ are two small prime numbers; $f$ is a cofactor; and $e_A, e_B$ and $e_C$ are positive integers such that $4^{e_A} \approx \ell_B^{e_B}\ell_C^{e_C}.$ We show that for many relevant instantiations of the SIDH protocol, this new family of primes enjoys a faster field arithmetic than the one associated to traditional SIDH primes. Furthermore, the proposed eSIDH protocol preserves the length and format of SIDH private/public keys, and its richer opportunities for parallelism yields a noticeable speedup factor when implemented on multi-core platforms. Using a single-core SIDH $p_{751}$ implementation as a baseline, a parallel eSIDH $p_{765}$ instantiation yields an acceleration factor of $1.05, 1.30$ and $1.41,$ when implemented on $k = \{1, 2, 3\}$-core processors. In addition, eSIDH $p_{765}$ yields an acceleration factor of $1.050, 1.160$ and $1.162.$ when both protocols are implemented on $k = \{1, 2, 3\}$-core processors. To our knowledge, this work reports the first multi-core implementation of SIDH

Análisis de las competencias didácticas virtuales en la impartición de clases universitarias en línea, durante contingencia del COVID-19

Se llevó a cabo un estudio cuantitativo con diseño transeccional descriptivo con el objetivo de analizar las competencias didácticas virtuales del modelo T-PACK (Shulman, 1986; Koehler y Mishra, 2009), que mayormente fueron desarrolladas por los docentes (N=87, Edad: M=33.91, DE=7.699, Max=51, Min=20) de la Universidad Autónoma de Tamaulipas que cursaron el Diplomado en Ambientes Virtuales de Aprendizaje del 2014 al 2019 e impartieron clases en línea durante contingencia del COVID-19 en el periodo comprendido de marzo a abril del año 2020. Los resultados muestran que los docentes presentaron competencias sobresalientes en su cátedra a distancia durante la contingencia, y además, no se encontraron diferencias significativas (p>0.05) entre el logro de los docentes varones (N=51, Edad: M=35.84, DE=7.298, Max=50, Min=20) y mujeres (N=36, Edad: M=29.33, DE=4.980, Max=49, Min=20) en ninguna de las dimensiones del modelo T-PACK

Koblitz curves over quadratic fields

In this work, we retake an old idea that Koblitz presented in his landmark paper, where he suggested the possibility of defining anomalous elliptic curves over the base field F4. We present a careful implementation of the base and quadratic field arithmetic required for computing the scalar multiplication operation in such curves. We also introduce two ordinary Koblitz-like elliptic curves defined over F4 that are equipped with efficient endomorphisms. To the best of our knowledge these endomorphisms have not been reported before. In order to achieve a fast reduction procedure, we adopted a redundant trinomial strategy that embeds elements of the field F4^m, with m a prime number, into a ring of higher order defined by an almost irreducible trinomial. We also present a number of techniques that allow us to take full advantage of the native vector instructions of high-end microprocessors. Our software library achieves the fastest timings reported for the computation of the timing-protected scalar multiplication on Koblitz curves, and competitive timings with respect to the speed records established recently in the computation of the scalar multiplication over binary and prime fields

Genetic risk score predicting accelerated progression from mild cognitive impairment to Alzheimer's disease

Aside from APOE, the genetic factors that influence in the progression from mild cognitive impairment (MCI) to Alzheimer´s disease (AD) remain largely unknown. We assessed whether a genetic risk score (GRS), based on 8 non-APOE genetic variants previously associated with AD risk in genome-wide association studies, is associated with either risk of conversion or with rapid progression from MCI to AD. Among 288 subjects with MCI, follow-up (mean 26.3 months) identified 118 MCI-converters to AD and 170 MCI-nonconverters. We genotyped ABCA7 rs3764650, BIN1 rs744373, CD2AP rs9296559, CLU rs1113600, CR1 rs1408077, MS4A4E rs670139, MS4A6A rs610932, and PICALM rs3851179. For each subject we calculated a cumulative GRS, defined as the number of risk alleles (range 0-16) with each allele weighted by the AD risk odds ratio. GRS was not associated with risk of conversion from MCI to AD. However, MCI-converters to AD harboring 6 or more risk alleles (second and third GRS tertiles) progressed 2-fold more rapidly to AD when compared with those with less than 6 risk alleles (first GRS tertile). Our GRS is a first step toward development of prediction models for conversion from MCI to AD that incorporate aggregate genetic factors

The Fifteenth Data Release of the Sloan Digital Sky Surveys: First Release of MaNGA-derived Quantities, Data Visualization Tools, and Stellar Library

Twenty years have passed since first light for the Sloan Digital Sky Survey (SDSS). Here, we release data taken by the fourth phase of SDSS (SDSS-IV) across its first three years of operation (2014 July–2017 July). This is the third data release for SDSS-IV, and the 15th from SDSS (Data Release Fifteen; DR15). New data come from MaNGA—we release 4824 data cubes, as well as the first stellar spectra in the MaNGA Stellar Library (MaStar), the first set of survey-supported analysis products (e.g., stellar and gas kinematics, emission-line and other maps) from the MaNGA Data Analysis Pipeline, and a new data visualization and access tool we call "Marvin." The next data release, DR16, will include new data from both APOGEE-2 and eBOSS; those surveys release no new data here, but we document updates and corrections to their data processing pipelines. The release is cumulative; it also includes the most recent reductions and calibrations of all data taken by SDSS since first light. In this paper, we describe the location and format of the data and tools and cite technical references describing how it was obtained and processed. The SDSS website (www.sdss.org) has also been updated, providing links to data downloads, tutorials, and examples of data use. Although SDSS-IV will continue to collect astronomical data until 2020, and will be followed by SDSS-V (2020–2025), we end this paper by describing plans to ensure the sustainability of the SDSS data archive for many years beyond the collection of data

The 16th Data Release of the Sloan Digital Sky Surveys: First Release from the APOGEE-2 Southern Survey and Full Release of eBOSS Spectra

This paper documents the 16th data release (DR16) from the Sloan Digital Sky Surveys (SDSS), the fourth and penultimate from the fourth phase (SDSS-IV). This is the first release of data from the Southern Hemisphere survey of the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2); new data from APOGEE-2 North are also included. DR16 is also notable as the final data release for the main cosmological program of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), and all raw and reduced spectra from that project are released here. DR16 also includes all the data from the Time Domain Spectroscopic Survey and new data from the SPectroscopic IDentification of ERosita Survey programs, both of which were co-observed on eBOSS plates. DR16 has no new data from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey (or the MaNGA Stellar Library "MaStar"). We also preview future SDSS-V operations (due to start in 2020), and summarize plans for the final SDSS-IV data release (DR17)

The 16th Data Release of the Sloan Digital Sky Surveys: First Release from the APOGEE-2 Southern Survey and Full Release of eBOSS Spectra

This paper documents the 16th data release (DR16) from the Sloan Digital Sky Surveys (SDSS), the fourth and penultimate from the fourth phase (SDSS-IV). This is the first release of data from the Southern Hemisphere survey of the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2); new data from APOGEE-2 North are also included. DR16 is also notable as the final data release for the main cosmological program of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), and all raw and reduced spectra from that project are released here. DR16 also includes all the data from the Time Domain Spectroscopic Survey and new data from the SPectroscopic IDentification of ERosita Survey programs, both of which were co-observed on eBOSS plates. DR16 has no new data from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey (or the MaNGA Stellar Library "MaStar"). We also preview future SDSS-V operations (due to start in 2020), and summarize plans for the final SDSS-IV data release (DR17)

A Roadmap for HEP Software and Computing R&D for the 2020s

Particle physics has an ambitious and broad experimental programme for the coming decades. This programme requires large investments in detector hardware, either to build new facilities and experiments, or to upgrade existing ones. Similarly, it requires commensurate investment in the R&D of software to acquire, manage, process, and analyse the shear amounts of data to be recorded. In planning for the HL-LHC in particular, it is critical that all of the collaborating stakeholders agree on the software goals and priorities, and that the efforts complement each other. In this spirit, this white paper describes the R&D activities required to prepare for this software upgrade.Peer reviewe