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→Encrypted CNOT operation
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===Garden Hose Complexity Model=== | ===Garden Hose Complexity Model=== | ||
*Gadget Construction for QFHE | *Gadget Construction for QFHE | ||
===Encrypted CNOT operation=== | ===Encrypted CNOT operation (FHE)=== | ||
<math>\sum_{a,b\in\{0,1\}}\alpha_{ab}CNOT^s|a\rangle|b\rangle</math> | |||
<math>=\alpha_{ab}|a\rangle|b\oplus a.s\rangle</math>, | |||
<math>=\alpha_{ab}|a\rangle|b\oplus a.(\mu_0+\mu_1)\rangle</math>, | |||
<math>=\alpha_{ab}|0\rangle|b\oplus 0\rangle+\alpha_{ab}|1\rangle|b\oplus \mu_0+\mu_1\rangle</math> | |||
<math>=\alpha_{ab}|0\rangle|b\oplus \mu_0+\mu_1\rangle+\alpha_{ab}|1\rangle|b\oplus \mu_0+\mu_1\rangle</math>, <math>\because q\oplus q=0</math> | |||
<math>=\alpha_{0b}|0\rangleX^{\mu_0}|b\oplus \mu_0\rangle+\alpha_{1b}|1\rangleX^{\mu_0}|b\oplus \mu_1\rangle</math>, <math>\because |w\oplus y\rangle=X^y|b\rangle</math> | |||
<math>=\alpha_{ab}|a\rangleX^{\mu_0}|b\oplus \mu_a\rangle | |||
===Trapdoor Claw-Free Function (TCF)=== | ===Trapdoor Claw-Free Function (TCF)=== | ||