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