FULLY HOMOMORPHIC ENCRYPTION WITH POLYLOG OVERHEAD

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+ So you want to compute some function… × + 1 × + + × + + × + + × + + × + + 0 1 1 x1 x2 x3 x4 x5 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x21 x22 x23 x24 x25 x26 ADD and MUL are a complete set of operations. × + + × + + × + + × + + 1 × + + Input bits
+ So you want to compute some function using SIMD… × + 1 × + + × + + × + + × + + × + + 0 1 1 x1 x2 x3 x4 x5 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x21 x22 x23 x24 x25 x26 x1 x2 x3 x4 x5 x7 x8 x9 x10 x11 x12 x14 x15 x16 x17 x18 x19 x21 x22 x23 x24 x25 x26 ℓ-ADD and ℓ-MUL are not a complete set of operations!!! … unless, of course, we use ℓ=1… � × + + × + + × + + × + + 1 × + + Input 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: COMPUTING ON DATA ARRAYS Forget abo
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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