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School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
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2023/6/16
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Riemann-Hilbert problem of confluent hypergeometric systems and Seiberg-Witten curves
超几何系统 塞伯格-维滕曲线 黎曼-希尔伯特问题
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2023/4/21
This talk first solves explicitly a Riemann-Hilbert problem of confluent hypergeometric systems. It then conjectures and proves a special case that the WKB approximation of the monodromy data of confl...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational points and homogeneous spaces over function fields of curves
曲线函数场 有理点 齐次空间
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2023/4/17
In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Pseudorandomness of Sato-Tate Distributions for Elliptic Curves
椭圆曲线 佐藤-泰特分布 伪随机性
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2023/4/13
Equidistribution is an important theme in number theory. The Sato-Tate conjecture, which was established by Richard Taylor et.al. in 2008, asserts that given an elliptic curve over Q without complex m...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Vanishing of some algebraic cycles on powers of Shimura curves
志村曲线 幂 代数 循环消失
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2023/4/27
For a smooth projective variety over a number field, the Beilinson—Bloch conjecture predicts that Chow groups of algebraic cycles modulo rational equivalence can be determined using cohomological data...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Strong approximation and integral quadratic forms over affine curves
仿射曲线 强近似 积分二次形式
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2023/5/9
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Birkhoff genericity for points on curves in expanding horospheres and Diophantine applications
星座图 曲线 Birkhoff泛型 丢番图应用
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2023/5/16
Let $\{a(t):t \in \mathbb{R}\}$ be a diagonalizable subgroup of $SL(d,\mathbb{R})$ for which the expanded horosphere $U$ is abelian. By the Birkhoff ergodic theorem, for any point $x \in SL(d,\mathbb{...
A New Public Key Cryptosystem Based on Edwards Curves
Elliptic curves Twisted Edwards curves RSA cryptosystem
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2019/9/19
The elliptic curve cryptography plays a central role in various cryptographic schemes and protocols. For efficiency reasons, Edwards curves and twisted Edwards curves have been introduced. In this pap...
How to Construct CSIDH on Edwards Curves
Isogeny-based cryptography Montgomery curves Edwards curves
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2019/7/22
CSIDH is an isogeny-based key exchange protocol proposed by Castryck, Lange, Martindale, Panny, and Renes in 2018. CSIDH is based on the ideal class group action on FpFp-isomorphic classes of Montgome...
Optimal TNFS-secure pairings on elliptic curves with composite embedding degree
Optimal ate pairing twists of elliptic curves jacobian coordinates
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2019/5/27
In this paper we present a comprehensive comparison between pairing-friendly elliptic curves, considering different curve forms and twists where possible. We define a measure of the efficiency of a pa...
Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation
NFS optimal ate pairing computation
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2019/4/28
Recent algorithmic improvements of discrete logarithm computation in special extension fields threaten the security of pairing-friendly curves used in practice. A possible answer to this delicate situ...
Miller Inversion is Easy for the Reduced Tate Pairing on Trace Zero Supersingular Curves
elliptic curve cryptosystem pairing inversion Tate pairing
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2019/4/16
We present a simple algorithm for Miller inversion for the reduced Tate pairing on supersingular elliptic curve of trace zero defined over the finite fields with q elements. Our algorithm runs with O(...
Horizontal Collision Correlation Attack on Elliptic Curves
side-channel analysis elliptic curves implementations ECDSA
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2019/4/1
Elliptic curves based algorithms are nowadays widely spread among embedded systems. They indeed have the double advantage of providing efficient implementations with short certi cates and of being rel...
A SAT-based approach for index calculus on binary elliptic curves
discrete logarithm index calculus elliptic curves
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2019/3/22
Logical cryptanalysis, first introduced by Massacci in 2000, is a viable alternative to common algebraic cryptanalysis techniques over boolean fields. With XOR operations being at the core of many cry...
Hash functions from superspecial genus-2 curves using Richelot isogenies
isogeny-based cryptography genus 2 hyperelliptic curve CGL hash function
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2019/3/21
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...