FULLY HOMOMORPHIC ENCRYPTION WITH POLYLOG OVERHEAD

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Realizing Permutation Networks a 1 a 2 a 3 a 4 a 5 0 1 2 3 4 5 6 7 2 3 4 5 6 7 0 1 6 7 0 1 2 3 4 5 2 1 4 3 6 7 0 1 2 1 0 3 6 7 4 5 2 1 0 3 6 7 4 5 input shift(-2) shift(2) SELECT(a 1,a 2) SELECT(a 3,a 4) output
Realizing Permutation Networks Claim: every level of the Benes network can be realized by two shifts and two SELECTs Proof : In every level, all the exchanges are between nodes at the same distance • Distance 2 i for some i Can implement all these exchanges using shift(2 i ), shift(-2 i ), and two SELECTs
Page 1 and 2: FULLY HOMOMORPHIC ENCRYPTION WITH P
Page 3 and 4: Contemporary HE Schemes • The [Ge
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 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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