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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach: Part II discrete case
KP-户田约简法 NLS类型 方程孤子解 统一方法 离散情况
2023/4/27
In the second part, I will mainly focus on two semi-discrete models: Ablowitz-Ladik equation and fully discrete NLS equation. First, I will clarify the connection of these two discrete models with dis...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A diffusion scheme based on the foliation graph stripe for optimizing discrete harmonic foliation energy
叶子图条带 优化 离散谐波 叶能量 扩散方案
2023/4/28
Consumer expenditures in the United Kingdom account for over 50% of Gross Domestic Product on the expenditure side, yet their impact on economic activity is often Global geometric structures live on m...
西安电子科技大学数字信号处理英文课件Chapter5 The Discrete Fourier Transform
西安电子科技大学 数字信号处理 英文课件 Chapter5 Discrete Fourier Transform
2020/6/22
西安电子科技大学数字信号处理英文课件Chapter5 The Discrete Fourier Transform。
西安电子科技大学数字信号处理英文课件Chapter3 The Discrete-time Fourier Analysis
西安电子科技大学 数字信号处理 英文课件 Chapter3 The Discrete-time Fourier Analysis
2020/6/22
西安电子科技大学数字信号处理英文课件Chapter3 The Discrete-time Fourier Analysis。
西安电子科技大学数字信号处理英文课件Chapter2 Discrete-time Signal and Systems
西安电子科技大学 数字信号处理 英文课件 Chapter2 Discrete-time Signal Systems
2020/6/22
西安电子科技大学数字信号处理英文课件Chapter2 Discrete-time Signal and Systems。
A New Method for Geometric Interpretation of Elliptic Curve Discrete Logarithm Problem
Intersection of Curves Grobner Basis Vanishing Ideals
2019/9/19
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DL...
Compact and Scalable Arbitrary-centered Discrete Gaussian Sampling over Integers
Lattice-based crypto discrete Gaussian sampling implementation
2019/9/16
The arbitrary-centered discrete Gaussian sampler is a fundamental subroutine in implementing lattice trapdoor sampling algorithms. However, existing approaches typically rely on either a fast implemen...
Efficient zero-knowledge arguments in the discrete log setting, revisited
zero-knowledge argument quadratic equations arithmetic circuit satisfiability
2019/8/20
This work revisits zero-knowledge proofs in the discrete logarithm setting. First, we identify and carve out basic techniques (partly being used implicitly before) to optimize proofs in this setting. ...
Low Weight Discrete Logarithms and Subset Sum in 20.65n with Polynomial Memory
Low weight dlog subset sum representations Nested Rho
2019/8/19
We propose two polynomial memory collision finding algorithms for the low Hamming weight discrete logarithm problem in any abelian group GG. The first one is a direct adaptation of the Becker-Coron-Jo...
Algorithmic aspects of elliptic bases in finite field discrete logarithm algorithms
discrete logarithm problem finite fields elliptic representation
2019/7/10
Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant way of representing finite field extensions. A natural question which seems to have been considered independently by sever...
Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic
discrete logarithm problem finite field
2019/6/26
We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can ...
Polar Sampler: Discrete Gaussian Sampling over the Integers Using Polar Codes
Discrete Gaussian sampling Polar codes Integer lattice
2019/6/10
Cryptographic constructions based on hard lattice problems have emerged as a front runner for the standardization of post quantum public key cryptography. As the standardization process takes place, o...
Pushing the speed limit of constant-time discrete Gaussian sampling. A case study on Falcon
Post-quantum signature Falcon constant-time
2019/3/6
Sampling from discrete Gaussian distribution has applications in lattice-based post-quantum cryptography. Several efficient solutions have been proposed in recent years. However, making a Gaussian sam...
Short Discrete Log Proofs for FHE and Ring-LWE Ciphertexts
Zero-Knowledge Proofs Bulletproofs FHE
2019/1/26
In applications of fully-homomorphic encryption (FHE) that involve computation on encryptions produced by several users, it is important that each user proves that her input is indeed well-formed. Thi...
FACCT: FAst, Compact, and Constant-Time Discrete Gaussian Sampler over Integers
Lattice-based crypto Discrete Gaussian sampling Constant-time
2019/1/2
The discrete Gaussian sampler is one of the fundamental tools in implementing lattice-based cryptosystems. However, a naive discrete Gaussian sampling implementation suffers from side-channel vulnerab...