FULLY HOMOMORPHIC ENCRYPTION WITH POLYLOG OVERHEAD

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ℓ-ADD, ℓ-MUL, ℓ-PERMUTE: ℓ-ADD + a complete set of SIMD ops + x1 x2 x3 x4 x5 0 + x1 x3 x5 0 0 0 0 + + x1 x3 x5 0 0 0 0 x2 x4 0 0 0 0 0 x 2 x 4
+ ℓ-ADD, ℓ-MUL, ℓ-PERMUTE: × + 1 + + + + + x1 x2 x3 x4 x5 0 x7 x8 x9 x10 x11 x12 1 x14 x15 x16 x17 x18 x19 1 x21 x22 x23 x24 x25 x26 Use ℓ-PERMUTE for routing between circuit levels • Not quite obvious × + × + × + × + a complete set of SIMD ops × + × + + × + + × + + × + + 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 and 12: COMPUTING ON DATA ARRAYS Forget abo
Page 13 and 14: + So you want to compute some funct
Page 15: ℓ-ADD, ℓ-MUL, ℓ-PERMUTE: ℓ-
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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