FULLY HOMOMORPHIC ENCRYPTION WITH POLYLOG OVERHEAD

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Homomorphic Encryption • Usual procedures (KeyGen,Enc,Dec) • Say, encrypting bits • Usual semantic-security requirement • (pk, Enc pk(0)) ~ (pk, Enc pk(1)) • Additional Eval procedure • Evaluate arithmetic circuits on ciphertexts • Result decrypted to the evaluation of the same circuit on the underlying plaintext bits • Ciphertext does not grow with circuit complexity • This work: asymptotically efficient Eval
Contemporary HE Schemes • The [Gentry’09] approach • Ciphertext is noisy (to get security) • Noise grow with homomorphic evaluation • Until ciphertext is too noisy to decrypt • Ciphertext is inherently large • Need to leave lots of room for noise to grow • It takes Ω (𝜆)-bit ciphertext to encrypt a single bit • � is the security parameter • Implementing each binary arithmetic gate takes at least Ω (𝜆) time • Ω (𝜆) time just to read the input ciphertexts
Page 1: FULLY HOMOMORPHIC ENCRYPTION WITH P
Page 5 and 6: Our Approach • Use HE over polyno
Page 9 and 10: Homomorphic SIMD [SV’11] SIMD = S
Page 11 and 12: COMPUTING ON DATA ARRAYS Forget abo
Page 13 and 14: + So you want to compute some funct
Page 15 and 16: ℓ-ADD, ℓ-MUL, ℓ-PERMUTE: ℓ-
Page 17: + ℓ-ADD, ℓ-MUL, ℓ-PERMUTE: ×
Page 22 and 23: Realizing Permutation Networks •
Page 24 and 25: Realizing Permutation Networks a 1
Page 26: Realizing Permutation Networks •
Page 29 and 30: QUESTIONS?
Page 31 and 32: Decomposing Permutations 13 18 14 1
Page 37 and 38: Fan-Out and Cloning 2 3 1 1 2 2 1 x
Page 43: Fan-Out and Cloning 4 3 3 2 2 2 2 x

FULLY HOMOMORPHIC ENCRYPTION WITH POLYLOG OVERHEAD

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