FULLY HOMOMORPHIC ENCRYPTION WITH POLYLOG OVERHEAD

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Our Result • Homomorphic evaluation of T-gate binary arithmetic circuits of average width Ω (𝜆) in time T∙polylog(𝛌) • More Generally, a T-gate, W-average-width circuit can be evaluated homomorphically in time 𝑶 ( 𝑾 𝝀 ⋅ 𝛌 ⋅ 𝑻 𝑾 ) time per level # of levels
Our Approach • Use HE over polynomial rings • Pack an array of bits in each ciphertext • Use ring-automorphisms to move bits around in the arrays • Efficient data-movement schemes • Using Beneš/Waksman networks and extensions
Page 1 and 2: FULLY HOMOMORPHIC ENCRYPTION WITH P
Page 3: Contemporary HE Schemes • The [Ge
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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