1. 椭圆曲线上的 Abel 群结构设 $\mathbb{F}_q$ 为有限域， $q = p$ 为奇素数（密码学中最常见情形）。一条椭圆曲线 $E$ 的短 Weierstrass 形式为$$
E : \; y^2 = x^3 + A x + B, \quad A, B \in \mathbb{F}_p,
$$其中判别式$$
\Delta = -16(4A^
2025年9月
SM4 分组密码算法推导SM4是一种分组密码算法，其分组长度和密钥长度均为128位。它采用32轮迭代的非平衡Feistel结构。1. 初始设定明文分组长度为128位，密钥长度为128位。首先，将128位的输入明文 $P$ 分为4个32位的字 $(X_0, X_1, X_2, X_3)$。$$
P = (X_0, X_1, X_2, X_3) \quad \t
The Foundation - Constructing the High-Dimensional Element Space1. Introduction: Translating Chemistry into GeometryThe primary challenge in applying machine learning to materials
Advances in Machine Learning and Their Application to Materials ScienceMachine learning is rapidly transforming materials science, shifting the field from a traditional trial-and-e