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Special Cases of Lattices
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Classroom Contents
Quantum Algorithms and Post-Quantum Cryptography
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- 1 Intro
- 2 Exponential Speedups for Oracle Problems
- 3 NIST Post-Quantum Cryptography Standardization
- 4 Developing New Systems
- 5 Looking for Hard Problems for Crypto
- 6 Back to Lattices and Quantum Algorithms
- 7 What Makes Good Crypto?
- 8 Lattices, Cryptography, and Quantum Algorithms
- 9 Quantum Algorithm for the Unit Group
- 10 Special Cases of Lattices
- 11 The Unit Group and Finding Short Generators
- 12 Computing the Short Generator
- 13 Quantum Algorithm for Lattices?
- 14 What Else Can be used for Post-Quantum Crypto?
- 15 Crypto and Algorithms
- 16 Hard Isogeny Problem
- 17 The isogeny problem
- 18 The supersingular -isogeny graph
- 19 Two types of isogeny graphs
- 20 More Assumptions for Efficiency
- 21 How Secure is Isogeny-Based Crypto?
- 22 Computational Challenges
- 23 Three hardness assumptions
- 24 Finding Cycles in the Isogeny Graph using Structure
- 25 Summary
