The Generalized Montgomery Coordinate:A New Computational Tool for Isogeny-based Cryptography

Recently, some studies have constructed one-coordinate arithmetics on elliptic curves. For example, formulas of the 𝑥-coordinate of Montgomery curves, 𝑥-coordinate of Montgomery− curves, 𝑤-coordinate of Edwards curves, 𝑤-coordinate of Huff’s curves, 𝜔-coordinates of twisted Jacobi intersections have been proposed. These formulas are useful for isogeny-based cryptography because of their compactness and efficiency. In this paper, we define a novel function on elliptic curves called the generalized Montgomery coordinate that has the five coordinates described above as special cases. For a generalized Montgomery coordinate, we construct an explicit formula of scalar multiplication that includes the division polynomial, and both a formula of an image point under an isogeny and that of a coefficient of the codomain curve. Finally, we present two applications of the theory of a generalized Montgomery coordinate. The first one is the construction of a new efficient formula to compute isogenies on Montgomery curves. This formula is more efficient than the previous one for high degree isogenies as the√élu’s formula in our implementation. The second one is the construction of a new generalized Montgomery coordinate for Montgomery−curves used for CSURF

Spin Dynamics in Iron-based Layered Superconductor (La_{0.87}Ca_{0.13})FePO Revealed by ^{31}P and ^{139}La NMR Studies

We report ^{31}P and ^{139}La NMR studies of (La_{0.87}Ca_{0.13})FePO, which is a family member of the recently discovered superconductor LaFeAs(O_{1-x}F_x). In the normal state, Knight shift and $1/T_1T$ show that a Fermi-liquid state with moderate ferromagnetic fluctuations emerges below 30K. From 1/T_1T of ^{31}P and ^{139}La, quasi-two dimensional electronic structure is suggested, in which the FeP layer is more conductive than the LaO layer. In the superconducting (SC) state, although a clear Meissner signal was observed, 1/T_1T increases below T_c, in contrast to a decrease of 1/T_1T due to the opening of a SC gap, suggesting that novel low-energy spin dynamics develop in the SC state.Comment: Phys. Rev. Lett. 101, 077006 (2008

Lower bound of costs of formulas to compute image curves of 33-isogenies in the framework of generalized Montgomery coordinates

In 2022, Moriya, Onuki, Aikawa, and Takagi proposed a new framework named generalized Montgomery coordinates to treat one-coordinate type formulas to compute isogenies. This framework generalizes some already known one-coordinate type formulas of elliptic curves. Their result shows that a formula to compute image points under isogenies is unique in the framework of generalized Montogmery coordinates; however, a formula to compute image curves is not unique. Therefore, we have a question: What formula is the most efficient to compute image curves in the framework of generalized Montogmery coordinates? In this paper, we analyze the costs of formulas to compute image curves of $3$-isogenies in the framework of generalized Montgomery coordinates. From our result, the lower bound of the costs is $1\mathbf{M}+1\mathbf{S}$ as a formula whose output and input are in affine coordinates, $2\mathbf{S}$ as an affine formula whose output is projective, and $2\mathbf{M}+3\mathbf{S}$ as a projective formula

The Generalized Montgomery Coordinate: A New Computational Tool for Isogeny-based Cryptography

Recently, some studies have constructed one-coordinate arithmetics on elliptic curves. For example, formulas of the $x$-coordinate of Montgomery curves, $x$-coordinate of Montgomery$^-$ curves, $w$-coordinate of Edwards curves, $w$-coordinate of Huff\u27s curves, $\omega$-coordinates of twisted Jacobi intersections have been proposed. These formulas are useful for isogeny-based cryptography because of their compactness and efficiency. In this paper, we define a novel function on elliptic curves called the generalized Montgomery coordinate that has the five coordinates described above as special cases. For a generalized Montgomery coordinate, we construct an explicit formula of scalar multiplication that includes the division polynomial, and both a formula of an image point under an isogeny and that of a coefficient of the codomain curve. Finally, we present two applications of the theory of a generalized Montgomery coordinate. The first one is the construction of a new efficient formula to compute isogenies on Montgomery curves. This formula is more efficient than the previous one for high degree isogenies as the $\sqrt{\vphantom{2}}$\\u27{e}lu\u27s formula in our implementation. The second one is the construction of a new generalized Montgomery coordinate for Montgomery$^-$ curves used for CSURF

US Research Interest in Asian and Oceanian Education Systems: Thomas Misco’s Research History and Methodology

This paper recapitulates a lecture given on June 26, 2018 at the Educational Vision Research Institute, Hiroshima University by Thomas Misco, a professor from Miami University. The title of Prof. Misco’s lecture was “Education in Asia and Oceania: Why are these contexts so intriguing for a US researcher?” The lecture described how Prof. Misco became interested in education systems throughout Asia and Oceania, and also outlined the development of his career. The lecture also showed how Prof. Misco’s studies focusing on specific examples of education systems in various countries were significant in generating hypotheses for other current or future contexts. Prof. Misco’s research career was shown to be suitable for exploring the context of US social studies education in recent years and is also applicable for future studies of Japanese social studies education

ECOMICS: A Web-Based Toolkit for Investigating the Biomolecular Web in Ecosystems Using a Trans-omics Approach

Ecosystems can be conceptually thought of as interconnected environmental and metabolic systems, in which small molecules to macro-molecules interact through diverse networks. State-of-the-art technologies in post-genomic science offer ways to inspect and analyze this biomolecular web using omics-based approaches. Exploring useful genes and enzymes, as well as biomass resources responsible for anabolism and catabolism within ecosystems will contribute to a better understanding of environmental functions and their application to biotechnology. Here we present ECOMICS, a suite of web-based tools for ECosystem trans-OMICS investigation that target metagenomic, metatranscriptomic, and meta-metabolomic systems, including biomacromolecular mixtures derived from biomass. ECOMICS is made of four integrated webtools. E-class allows for the sequence-based taxonomic classification of eukaryotic and prokaryotic ribosomal data and the functional classification of selected enzymes. FT2B allows for the digital processing of NMR spectra for downstream metabolic or chemical phenotyping. Bm-Char allows for statistical assignment of specific compounds found in lignocellulose-based biomass, and HetMap is a data matrix generator and correlation calculator that can be applied to trans-omics datasets as analyzed by these and other web tools. This web suite is unique in that it allows for the monitoring of biomass metabolism in a particular environment, i.e., from macromolecular complexes (FT2DB and Bm-Char) to microbial composition and degradation (E-class), and makes possible the understanding of relationships between molecular and microbial elements (HetMap). This website is available to the public domain at: https://database.riken.jp/ecomics/

Cubic Rashba spin-orbit interaction of two-dimensional hole gas in strained-Ge/SiGe quantum well

The spin-orbit interaction (SOI) of the two-dimensional hole gas in the inversion symmetric semiconductor Ge is studied in a strained-Ge/SiGe quantum well structure. We observed weak anti-localization (WAL) in the magnetoconductivity measurement, revealing that the WAL feature can be fully described by the k-cubic Rashba SOI theory. Furthermore, we demonstrated electric field control of the Rashba SOI. Our findings reveal that the heavy hole (HH) in strained-Ge is a purely cubic-Rashba-system, which is consistent with the spin angular momentum mj = +-3/2 nature of the HH wave function.Comment: To be published in Phys. Rev. Let

Knee extension muscle strength in elderly women who underwent total knee arthroplasty, and regional differences in the Japanese Orthopedic Association knee disease treatment criteria

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