FULLY HOMOMORPHIC ENCRYPTION WITH POLYLOG OVERHEAD

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Routing Values Between Levels + • We need to map this x 1 x 2 x 3 x 4 x 5 0 x 7 x 15 x 16 x 17 x 18 x 19 1 x 21 • Into that + + + x 1 x 3 x 5 x 7 x 9 x 11 1 x 2 x 4 0 x 8 x 10 x 12 x 14 x 8 x 9 x 10 x 11 x 12 1 x 14 x 22 x 15 x 23 x 24 x 25 x 26 … so we can use ℓ-add + + + + + + x 17 x 19 x 21 x 23 x 25 x 16 x 18 1 x 22 x 24 x 26 + + +
ℓ-ADD, ℓ-MUL, ℓ-PERMUTE: ℓ-PERMUTE(π) ℓ-MULT + a complete set of SIMD ops + x 1 x 2 x 3 x 4 x 5 x 1 x 2 x 3 x 4 x 5 x 7 x 1 x 2 x 3 x 4 x 5 x 7 x 1 x 3 x 5 * * * * + 0 1 1 1 0 0 0 0 x 2 x 4 * * * * * 1 1 0 0 0 0 0 x 1 x 3 x 5 0 0 0 0 x 2 x 4 0 0 0 0 0
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: + So you want to compute some funct
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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