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1.3 对称群 交错群 二面体群
1.4 阿贝尔群
1.5 群作用
1.6 Sylow 定理 有限群分类
1.7 幂零群和可解群 正规列和次正规列
ChapterII
ChapterII
2.1 环基本定义
2.2 理想
2.3 交换环上的因子分解
2.4 分式环 局部化
2.5 多项式环 形式幂级数
2.6 多项式环上的分解
ChapterIII
ChapterIII
3.1 模 模同态 正合列
3.2 自由模和向量空间
3.3 投射摸和内射模
3.4 Hom 和 Tensor
3.5 主理想整环上的有限生成模
ChapterIV
ChapterIV
4.1 域扩张
4.2 Galois 理论基本定理
4.3 分裂域 代数闭包 正规性
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Final Exam
NumberTheory
NumberTheory
1 Euclidean Algorithm and Factorization
2 Modular Arithmetic
3 Some Diophantine Equations
4 Order of units & Application in cryptography
5 Sum of Two Squares
6 Quadratic Reciprocity Law
7 Sum of Four Squares
8 Quadratic Gauss Sum
9 Pell's Equation
10 Factorization in Quadratic Fields
11 Primes of Arithmetic Progression
12 Sum of Three Squares
13 Congruent Number
Homework archive
Final Exam
RepresentationTheory
RepresentationTheory
Linear Representations of Finite Groups
Linear Representations of Finite Groups
Generalities on linear representations
Character theory
Subgroups, products, induced representations
AlgebraicNumberTheory
AlgebraicNumberTheory
1 Integrality
2 Norm, Trace, Discriminant
3 Dedekind Domains
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FunctionalAnalysis
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Modern Cryptography Basic
Modern Cryptography Basic
1 Defining Security
A Graduate Course in Applied Cryptography
A Graduate Course in Applied Cryptography
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Lattice
1 基本概念
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4 低加密指数 RSA 的攻击
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Homomorphic Encryption
1 定义
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Quantum Computation and Quantum Information
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Introduction to quantum mechanics
Introduction to computer science
Quantum circuits
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Quantum noise and quantum operations
Distance measures for quantum information
Appendix
Lecture Notes on Quantum Algorithms
Lecture Notes on Quantum Algorithms
1 Preliminaries
4 The abelian quantum Fourier transform and phase estimation
5 Discrete log and the hidden subgroup problem
6 The abelian $\op{HSP}$ and decomposing abelian groups
7 Quantum attacks on elliptic curve cryptography
8 Quantum algorithms for number fields
9 Period finding from $\mathbb{Z}$ to $\mathbb{R}$
10 Quantum query complexity of the $\op{HSP}$
11 Fourier analysis in nonabelian groups
12 Fourier sampling
13 Kuperberg's algorithm for the dihedral $\op{HSP}$
14 The $\op{HSP}$ in the Heisenberg group
15 Schur-Weyl duality
17 Continuous-time quantum walk
21 Query complexity and the polynomial method
22 The collision problem
23 The quantum adversary method
24 Span programs and formula evaluation
26 The compressed oracle method
Papers
Papers
Notions of Reducibility between Cryptographic Primitives
Random Oracles in a Quantum World
How to Construct Quantum Random Functions
Secure Identity-Based Encryption in the Quantum Random Oracle Model
Quantum-Secure Message Authentication Codes
How to Use a Short Basis: Trapdoors for Hard Lattices and New Cryptographic Constructions
Quantum Proof of Knowledge
On the Compressed-Oracle Technique, and Post-Quantum Security of Proofs of Sequential Work
Attention is still what you need: Another Round of Exploring Shoup's GGM
Separating $\mathsf{QMA}$ from $\mathsf{QCMA}$ with a classical oracle
低加密指数 RSA 的攻击
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