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 code was updated on February 27, 2026.The Foundation - Constructing the High-Dimensional Element Space1. Introduction: Translating Chemistry into GeometryThe primary challenge
The code was updated on February 27, 2026.Advances in Machine Learning and Their Application to Materials ScienceMachine learning is rapidly transforming materials science, shiftin