2. Quantum Homomorphic Encryption
Stacey Jeffery
(including joint work with Anne Broadbent)

3. Homomorphic Encryption

4. Quantum Homomorphic Encryption

5. Outline

6. Quantum Information

7. Classical Information

8. Classical Information

9. Quantum Bits: “Qubits”

10. Classical vs. Quantum Circuits

11. Classical Circuits

12. Quantum Circuits

13. Quantum vs. Classical Circuits

14. Encrypting Quantum Information: The Quantum One-time Pad

15. The Pauli Group and Quantum One-Time Pad

16. The Pauli Group and Quantum One-Time Pad

17. The Pauli Group and Quantum One-Time Pad

18. Homomorphic Encryption

19. (Classical) Homomorphic Encryption

20. The Trivial Scheme

21. (Classical) Homomorphic Encryption

22. Quantum Homomorphic Encryption

23. Computational Security of QHE

24. Our Results

25. Prior Results

26. Summary of Results

27. Clifford Scheme

28. The Clifford Group

29. Scheme 1: QHE for Cliffords (CL)

30. Features of the Clifford Scheme

31. Summary of Results

32. Summary of Results

33. Summary of Results

34. Summary of Results

35. Adding Reversible Multiplication?

36. Reversible Multiplication: Toffoli Gate

37. Aside: No-Cloning/Uncertainty

38. Aside: No-Cloning/Uncertainty

39. Homomorphic Reversible Multiplication?

40. Homomorphic Reversible Multiplication?

41. Homomorphic Reversible Multiplication?

42. Summary

43. Further Reading