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A Brief Story of Computing on Private Data

A Brief Story of Computing on Private Data. Ten H Lai Ohio State University. Agenda. Computing on private data Fully homomorphic encryption (FHE) Gentry’s bootstrapping theorem Our result. FHE: The Holy Grail of Cryptography. Cloud Computing. Networks. Applications. Storages.

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A Brief Story of Computing on Private Data

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  1. A Brief Story of Computing on Private Data Ten H Lai Ohio State University

  2. Agenda • Computing on private data • Fully homomorphic encryption (FHE) • Gentry’s bootstrapping theorem • Our result

  3. FHE: The Holy Grail of Cryptography

  4. Cloud Computing Networks Applications Storages Servers

  5. 天上有多少星星 城裡有多少姑娘 但人間只有一個妳 天上只有一顆月亮

  6. Cloud Computing Encrypt Cloud server Internet

  7. Computing on private data Encrypt Cloud server Internet

  8. Computing on private data Cloud • A question proposed by Rivest, Aldeman, Dertouzos in 1978 (one year after RSA was invented).

  9. C-Homomorphism

  10. C-homomorphic

  11. RSA is multiplicatively homomorphic

  12. Fully Homomorphic Encryption (FHE)

  13. Bootstrapping

  14. Evaluate Decrypt skA Decrypt m m m m encrypted under a pink key pkA

  15. Evaluate Decrypt skA Decrypt m m skA Encrypt under a blue key pkB Evaluate Decrypt m m

  16. NAND-augmented Decrypt circuit: skA skA Decrypt NAND m1 m1NANDm2 Decrypt m2

  17. Evaluate skA c1 skA c2 Decrypt NAND m1 m1NANDm2 Decrypt fresh m2

  18. Under a pink key PKA Under a blue key PKB m1 m1NANDm2 m2 fresh skA 23

  19. m1 m1NANDm2 m2 Increased noise 24

  20. skA m1 m2 m1NANDm2 Evaluate Decrypt-NAND m1NANDm2 (m1NAND m2) NAND (m3NAND m4) Evaluate Decrypt-NAND skB skA m3 m4 m3NANDm4 Evaluate Decrypt-NAND m3NANDm4

  21. skA m1 m2 m1NANDm2 Evaluate Decrypt-NAND m1NANDm2 (m1NAND m2) NAND (m3NAND m4) Evaluate Decrypt-NAND skB skA m3 m4 m3NANDm4 Evaluate Decrypt-NAND m3NANDm4

  22. NAND Decrypt Decrypt

  23. Encryption key • Evaluation key • Decryption key

  24. Decrypt Decrypt

  25. Encryption key • Evaluation key • Decryption key

  26. level d level 1 …

  27. level d level 1 … Decrypt circuits

  28. … Decrypt circuits

  29. Encryption key • Evaluation key • Decryption key

  30. NAND Decrypt Decrypt

  31. Decryption algorithm Secret-key independent , Computationally intensive, Done with encryption Secret-keydependent

  32. FHE is still in its infantry

  33. Multi-Key/Multi-Scheme FHE

  34. Single-key FHE

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