FULLY HOMOMORPHIC ENCRYPTION: CURRENT STATE OF THE ...

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Bootstrapping: What’s the Motivation? � So far, the overhead grows polynomially with L. � For example, ciphertext size grows with L 2 . � Want overhead to be independent on L. � To only depend on the security parameter k. � Achievable! � We can make the overhead polylog(k) asymptotically. � But the overhead is still very large in practice.
Bootstrapping: What Is It? � So far, we can evaluate bounded depth funcs F: F x1 x2 … x t c F(x 1, x 2 ,…, x t) � We have a noisy evaluated ciphertext c. � We want to get a less noisy c’ that encrypts the same value, but with less noise. � Bootstrapping refreshes ciphertexts, using the encrypted secret key.
Page 1 and 2: FULLY HOMOMORPHIC ENCRYPTION: CURRE
Page 3 and 4: Homomorphic Encryption “Somewhat
Page 5 and 6: Fully Homomorphic Encryption: Curre
Page 7 and 8: Somewhat Homomorphic Encryption wit
Page 9 and 10: How To Construct a SWHE Scheme? Mos
Page 11 and 12: Polly Cracker Cryptanalysis [see AF
Page 13 and 14: Noisy Polly Cracker: A Framework fo
Page 15 and 16: SWHE with Integers [vDGHV10] Main I
Page 17 and 18: Encrypting More than Bits � So fa
Page 19 and 20: SWHE with Integers (Mod-15) Divisib
Page 21 and 22: Cyclotomic Ring R = Z[x]/Ф N(x)
Page 23 and 24: Security of SWHE over Cyclotomic Ri
Page 25 and 26: Managing Ciphertext Noise
Page 27 and 28: Better Noise Management? � Crazy
Page 29 and 30: How Does Modulus Switching Help? [B
Page 31 and 32: Where Are We? (The Good News) � W
Page 33 and 34: Packing Plaintexts into Ciphertexts
Page 35 and 36: Our Weird Cyclotomic Plaintext Spac
Page 37 and 38: SIMD (Single Instruction Multiple D
Page 39 and 40: SIMD (Single Instruction Multiple D
Page 41 and 42: A Taste of Cyclotomic Rings � Cho
Page 43 and 44: What Is Our Overhead Now? � A cip
Page 45 and 46: AES (Advanced Encryption Standard)
Page 47 and 48: The Inversion Step of AES � For m
Page 49 and 50: Parameter Sizes L (levels) N n = φ
Page 51: Bootstrapping
Page 55 and 56: Bootstrapping in [BGV12] � Set L
Page 57 and 58: Summary
Page 59 and 60: Next Steps
Page 61 and 62: Open Problem: A Fast Refresh Proced
Page 63 and 64: Homomorphic Encryption “Fully”
Page 65 and 66: SWHE with Integers [vDGHV10] Divisi
Page 67 and 68: Relinearizing and “Key Switching
Page 69 and 70: Basic PERMUTEs (Rotations) Array of
Page 71 and 72: n-PERMUTE(π) from n-ADD, n-MULT, a

FULLY HOMOMORPHIC ENCRYPTION: CURRENT STATE OF THE ...

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