October 2015 FHEMMAPs Summer School Paris PRACTICAL FHE
October 2015 FHE+MMAPs Summer School, Paris PRACTICAL (F)HE PART III – BOOTSTRAPPING Shai Halevi 1
October 2015 FHE+MMAPs Summer School, Paris Reminder: Operation Cost • Cost measured in time, added-noise Operation Time Noise Add / Add-Const Mult-by-Const Mult+Key. Switch Automorphism+ Key. Switch Cheap Expensive Cheap Moderate* Expensive Cheap 2
October 2015 FHE+MMAPs Summer School, Paris 3 Recryption for BGV [GHS’ 12 c, AP’ 13, HS’ 15] •
October 2015 FHE+MMAPs Summer School, Paris Simplified Decryption • 4
October 2015 FHE+MMAPs Summer School, Paris Simplified Decryption • 5
October 2015 FHE+MMAPs Summer School, Paris Recryption for BGV • 6
October 2015 FHE+MMAPs Summer School, Paris Homomorphic Bit-Extraction • 7
October 2015 FHE+MMAPs Summer School, Paris 8 Homomorphic “Restricted Division” •
October 2015 FHE+MMAPs Summer School, Paris 9 [GHS 12 c] Homomorphic Bit-Extraction •
October 2015 FHE+MMAPs Summer School, Paris 10 [AP 13] Homomorphic Bit-Extraction •
October 2015 FHE+MMAPs Summer School, Paris • This does not work 11
October 2015 FHE+MMAPs Summer School, Paris 12 [HS 15] •
October 2015 FHE+MMAPs Summer School, Paris 13 [HS 15] • • We use a variant of the Paterson. Stockmeyer procedure for efficient evaluation of plaintext polynomial on a ciphertext
October 2015 FHE+MMAPs Summer School, Paris 14 Recryption of Non-Packed Ciphertext •
October 2015 FHE+MMAPs Summer School, Paris Recryption of Packed Ciphertexts • 15
October 2015 FHE+MMAPs Summer School, Paris 16 Packed Homomorphic Digit-extraction •
October 2015 FHE+MMAPs Summer School, Paris 17 Packed Homomorphic Digit-extraction •
October 2015 FHE+MMAPs Summer School, Paris 18 Packed Homomorphic MSB-extraction •
October 2015 FHE+MMAPs Summer School, Paris 19 Using the “Powerful Basis” [LPR 14] •
October 2015 FHE+MMAPs Summer School, Paris 20 Using the “Powerful Basis” [LPR 14] •
October 2015 FHE+MMAPs Summer School, Paris Recall the Plaintext Slots • 21
October 2015 FHE+MMAPs Summer School, Paris The Lin 2 Transformation • 22
October 2015 FHE+MMAPs Summer School, Paris The Lin 2 Transformation • 23
October 2015 FHE+MMAPs Summer School, Paris Our Linear Transformations • 24
October 2015 FHE+MMAPs Summer School, Paris Our Linear Transformations • 25
October 2015 FHE+MMAPs Summer School, Paris Our Linear Transformations • 26
October 2015 FHE+MMAPs Summer School, Paris Our Linear Transformations • 27
October 2015 • FHE+MMAPs Summer School, Paris 28
October 2015 FHE+MMAPs Summer School, Paris Linearized Polynomials • 29
October 2015 • FHE+MMAPs Summer School, Paris 30
October 2015 FHE+MMAPs Summer School, Paris A Better Implementation • 31
October 2015 FHE+MMAPs Summer School, Paris 35 Packed Homomorphic Digit-extraction •
October 2015 36 FHE+MMAPs Summer School, Paris Performance (Feb 2015) • Tested our implementation in many settings • Targeted 10 remaining levels after recryption Ptxt space Lvls b 4/aftr Init Lin 1, 2 Nonlin Total Mem 21845 76 22/10 177 127 193 320 3. 4 GB 18631 110 20/10 248 131 293 424 3. 5 GB 28679 96 24/11 224 123 342 465 3. 5 GB 35113 159 24/12 694 325 1206 1531 8. 2 GB 45551 106 38/10 1148 735 3135 3870 14. 8 GB 51319 161 32/11 2787 774 1861 2635 39. 9 GB 49981 91 56/10 1533 2834 14616 17448 21. 6 GB
October 2015 37 FHE+MMAPs Summer School, Paris Performance (Feb 2015) • Tested our implementation in many settings • Targeted 10 remaining levels after recryption Ptxt space Lvls b 4/aftr Init Lin 1, 2 Nonlin Total • Rec 193 320 ryptio 76 22/10 177 127 n 110 t - Req 18631 248 131 293 424 s uires ake 20/10 a s li 224 a 96 t t very 24/11 28679 342 465 spars le as 123 1 2 key, i 3250 -11206 35113 159 24/12 e 694 leve 1531 s this ls s a 45551 106 38/10 1148 735 3135 3870 21845 51319 161 32/11 2787 774 49981 91 56/10 1533 2834 Mem 3. 4 GB 3. 5 GB 8. 2 GB fe? 14. 8 GB 1861 2635 39. 9 GB 14616 17448 21. 6 GB
October 2015 FHE+MMAPs Summer School, Paris C'est Tout 38
- Slides: 35