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In this talk, we report several very recent asymptotic results on certain classical geometric quantities viewed as random variables on the moduli space of Riemann surfaces for large genus (and many cu...
2021年1月27日,中国地质大学赖旭龙教授领导的古DNA研究团队与德国波兹坦大学、丹麦哥本哈根大学等单位合作研究的成果“Ancient mitochondrial genomes from Chinese cave hyenas provide insights into the evolutionary history of the genus Crocuta(中国洞鬣狗古线粒体基因组为斑鬣狗...
Last year Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed ov...
Genus 2 curves with given split Jacobian     given split Jacobian  elliptic Kummer surfaces       font style='font-size:12px;'> 2018/11/29
We construct a genus 2 curve inside the product of 2 elliptic curves. The formula for this construction has appeared in a previous paper. The current paper discusses how this formula arises naturally ...
We present the first hardware implementations of Diffie-Hellman key exchange based on the Kummer surface of Gaudry and Schost's genus-22 curve targeting a 128128-bit security level. We describe a sing...
The aim of this work was to suggest a reliable method for distinguishing between diploid and tetraploid taxa of the genus Betula Linnaeus, based on leaf measurements. In total, 97 individuals from 6 ...
We explore the function field of the jacobian JH of a hyperelliptic curve H of genus 2 in order to find reduced coordinates to represent points of JH and do arithmetic. We show how this relates to the...
We give one- and two-dimensional scalar multiplication algorithms for Jacobians of genus~2 curves that operate by projecting to Kummer surfaces, where we can exploit faster and more uniform pseudomult...
Kummer for Genus One over Prime Order Fields     Kummer Line  Field Arithmetic  SIMD       font style='font-size:12px;'> 2016/12/8
This work considers the problem of fast and secure scalar multiplication using curves of genus one defined over a field of prime order. Previous work by Gaudry and Lubicz had suggested the use of the ...
Researchers analyzing the genomes of microorganisms living in shale oil and gas wells have found evidence of sustainable ecosystems taking hold there—populated in part by a never-before-seen genus of ...
The similarity of and differences between the fungi Pestalotiopsis funerea (Desmazières) Steyaert and Truncatella hartigii (Tubeuf) Steyaert that damage the needles of the host plants Pinus ponderosa ...
Constructing genus 3 hyperelliptic Jacobians with CM     CM  explicit method       font style='font-size:12px;'> 2016/3/28
Given a CM sextic field K, we give an explicit method for finding and constructing all genus 3 hyperelliptic curves whose Jacobians have complex multiplication by the maximal order of this field. Our ...
We outline an algorithm to compute θ(z, τ ) in genus 2 in quasi-optimal time, borrowing ideas from the algorithm for theta constants and the one for θ(z, τ ) in genus 1. Our implementation shows a l...
In this paper, we present a variant of Diem’s Oe(q) index calculus algorithm to attack the discrete logarithm problem (DLP) in Jacobians of genus 3 non-hyperelliptic curves over a finite field Fq. W...
We present an efficient endomorphism for the Jacobian of a curve C of genus 2 for divisors having a Non disjoint support. This extends the work of Costello in [12] who calculated explicit formul?for ...

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