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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Isometric embedding and fluid mechanics
等距嵌入 流体力学 理论流体力学
2023/5/10
In this talk, I first discuss isometric embedding from differential geometry and its relation with fluid mechanic equations. Then I will present recent progress and my works on isometric embeddings of...
Optimal TNFS-secure pairings on elliptic curves with composite embedding degree
Optimal ate pairing twists of elliptic curves jacobian coordinates
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
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...
Optimal TNFS-secure pairings on elliptic curves with even embedding degree
TNFS-secure optimal pairing twisted Ate pairing
2018/11/6
In this paper we give a comprehensive comparison between pairing-friendly elliptic curves in Jacobi Quartic and Edwards form with quadratic, quartic, and sextic twists. Our comparison looks at the bes...
Embedding Multiplications at a Linear Rate and its Applications
algebraic function fields Embedding Multiplications
2018/5/2
Although the study of this embedding problem is of independent theoretical interest, we present a few representative applications to secure computation. We construct a linear number of oblivious trans...
In Praise of Twisted Canonical Embedding
Lattice techniques number theory canonical embedding
2018/4/19
In ideal-lattice cryptography, lattices are generated by defining a bijective map between an ideal of a ring of integers and a subset of Cn. This map can be taken to be the coefficient embedding and, ...
Contract signing protocols have been proposed and analyzed for more than three decades now. One of the main problems that appeared while studying such schemes is the impossibility of achieving both fa...
Optimal Ate Pairing on Elliptic Curves with Embedding Degree 9,15 and 27
Elliptic Curves Optimal Pairings Miller's algorithm
2017/1/3
Since the advent of pairing based cryptography, much attention has been given to efficient computation of pairings on elliptic curves with even embedding degrees. The few works that exist in the case ...
On Implementing Pairing-Based Protocols with Elliptic Curves of Embedding Degree One
public-key cryptography implement pairing-based protocols
2016/4/26
We observe that the conventional classification of pairings into Types 1, 2, 3 and 4 is not applicable to pairings from elliptic curves with embedding degree one. We define three kinds of pairings fro...
Time Reversal and Charge Conjugation in an Embedding Quantum Simulator
Charge Conjugation Embedding Quantum Simulator
2016/1/22
A quantum simulator is an important device that may soon outperform current classical computations. A basic arithmetic operation, the complex conjugate, however, is considered to be impossible to be i...
On near prime-order elliptic curves with small embedding degrees
Pairing Friendly Elliptic Curve MNT curves Complex Multiplication
2015/12/23
In this paper, we extend the method of Scott and Barreto and present an explicit and simple algorithm to
generate families of generalized MNT elliptic curves. Our algorithm allows us to obtain all fa...
An embedding theorem for automorphism groups of Cartan geometries
Cartan geometries embedding theorem
2015/10/14
The main motivation of this paper arises from classical questions about
actions of Lie groups preserving a geometric structure: which Lie groups can
act on a manifold preserving a given structure, a...
Embedding Web-Based Statistical Translation Models in Cross-Language Information Retrieval
Statistical Translation Models Cross-Language Information
2015/8/28
Although more and more language pairs are covered by machine translation (MT) services, there
are still many pairs that lack translation resources. Cross-language information retrieval (CLIR)
is an ...
Hessian Eigenmaps: new locally linear embedding techniques for high-dimensional data
Manifold Learning Locally Linear Embedding
2015/8/21
We describe a method to recover the underlying parametrization of scattered data
(mi) lying on a manifold M embedded in high-dimensional Euclidean space. The method,
Hessian-based Locally Linear Emb...
Operator splitting for conic optimization via homogeneous self-dual embedding
Segmentation method multiplier nonzero subspace double lonely computational subspace
2015/8/7
We introduce a first order method for solving very large cone programs to modest accuracy. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the ...