FULLY HOMOMORPHIC ENCRYPTION WITH POLYLOG OVERHEAD

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From Shifts to Arbitrary Permutations Use Beneš/Walksman Permutation Networks: • Two back-to-back butterflies • Every exchange is controlled by a bit • Values sent on either straight edges or cross edges • Every permutation can be realized by appropriate setting of the control bits
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 23 and 24: Realizing Permutation Networks a 1
Page 25 and 26: Realizing Permutation Networks Clai
Page 28 and 29: Low Overhead Homomorphic Encryption
Page 30 and 31: Handling Large Permutations • Can
Page 32 and 33: Decomposing Permutations 13 18 14 1
Page 38 and 39: Fan-Out and Cloning 2 3 1 1 2 2 1 x

FULLY HOMOMORPHIC ENCRYPTION WITH POLYLOG OVERHEAD

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