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Lattices, Post-Quantum Security, and Fully Homomorphic Encryption
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Lattices, Post-Quantum Security and Homomorphic Encryption
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- 1 Lattices, Post-Quantum Security, and Fully Homomorphic Encryption
- 2 Modern Cryptography
- 3 Factoring and Quantum (In)Security
- 4 Subset-Sum Problem
- 5 Subset-Sum / Knapsack • Also known as the "Knapsack" problem - Fill a knapsack of capacity b - using a selection of items of size ai.....an
- 6 Lattice/Knapsack Cryptgraphy: abridged (pre-)history . Knapsack public key cryptosystem
- 7 Subset-Sum vs Lattice Problems
- 8 Geometry of Lattices
- 9 Linear functions
- 10 Learning With Errors (LWE)
- 11 Encrypting with LWE
- 12 FHE Timeline
- 13 Homomorphic Addition
- 14 Multiplication by any constant
- 15 Public Key Encryption
- 16 How to multiply two ciphertexts
- 17 Multiplication by Encryption Nesting
- 18 Multiplication by Tensoring
- 19 Decryption is linear
- 20 Multiplication via Homomorphic Decryption
- 21 Homomorphic "decrypt and multiply"
- 22 Relation to GSW encryption
- 23 Bootstrapping and FHE
- 24 FHEW: gate bootstrapping
- 25 Summary
- 26 Additional References
