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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...
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Chapter2 Discrete-time Signal and Systems。
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...
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...
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. ...
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...
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...
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 ...
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...
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...
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...
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...

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