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Homomorphic Encryption

Homomorphic Encryption. Alexander Maximov. Overview. History Partially Homomorphic Encryption Schemes HE Usage Scenarios Somewhat HE and Fully HE over the Integers Bootstrapping Technique Ciphertext Squashing Technique Ciphertext Reduction Technique Converting Somewhat HE to Fully HE

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Homomorphic Encryption

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  1. Homomorphic Encryption Alexander Maximov

  2. Overview • History • Partially Homomorphic Encryption Schemes • HE Usage Scenarios • Somewhat HE and Fully HE over the Integers • Bootstrapping Technique • Ciphertext Squashing Technique • Ciphertext Reduction Technique • Converting Somewhat HE to Fully HE • Approximate GCD Problem • Recent Research Results • BGV FHE Scheme • Leveled FHE with(out) Bootstrapping • Performance, Implementations, Patents

  3. Introduction

  4. PartialLY HE

  5. HE Usage Scenarios

  6. Real-Life Usage

  7. Does Fully Homomorphic Encryption Ever Exists?

  8. “Holy Grail” for 30 years

  9. Types of HE Schemes

  10. SHE over the Integers

  11. SHE over the Integers

  12. SHE over the Integers

  13. Noise Count

  14. SHE over the Integers

  15. Ciphertext Reduction

  16. Bootstrapping

  17. SHEFHE over the Integers

  18. Squashing Technique

  19. Security. Approximate GCD

  20. Security. Approximate GCD

  21. Security. Approximate GCD

  22. Security. Approximate GCD

  23. Security. Approximate GCD

  24. New Recent Research

  25. BGV: Leveled FHE Scheme

  26. BGV: Leveled FHE Scheme

  27. Performance

  28. Evaluation of AES

  29. HElib

  30. Patents Activity

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