Lattices, Post-Quantum Security and Homomorphic Encryption

Lattices, Post-Quantum Security and Homomorphic Encryption

Simons Institute via YouTube Direct link

Public Key Encryption

15 of 26

15 of 26

Public Key Encryption

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Classroom Contents

Lattices, Post-Quantum Security and Homomorphic Encryption

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

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