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