Prepare-and-Send Verifiable Quantum Fully Homomorphic Encryption: Difference between revisions

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keys using the FHE scheme. This again requires the ability to perform Paulis, execute an error-correcting encoding, and the generation of basic single-qubit states.
keys using the FHE scheme. This again requires the ability to perform Paulis, execute an error-correcting encoding, and the generation of basic single-qubit states.


** Majority of the single-qubit and two-qubit quantum states are encrypted using the global permutation. A [[CSS]] concatenated Steane code is selected with specific requirements. The quantum state is first encoded using this CSS code which results in a state with $m$ qubits. Then, $m$ computational and $m$ Hadamard traps (<math>|0\rangle</math> and <math>|+\rangle</math> states) are added to that state and the resulting state is permutated using the global permutation. Next, if $n$ is the number of qubits that will be encrypted, two bits strings are picked of length $n$ to encrypt the state with [[Quantum one time pad]]. After this, we obtain our magic state for that particular quantum state. Here it is important to note that the keys for [[Quantum one time pad]] are selected during Encryption rather than Key Generation.
** Majority of the single-qubit and two-qubit quantum states are encrypted using the global permutation. A [[CSS]] concatenated Steane code is selected with specific requirements. The quantum state is first encoded using this CSS code which results in a state with <math>m</math> qubits. Then, <math>m</math> computational and <math>m</math> Hadamard traps (<math>|0\rangle</math> and <math>|+\rangle</math> states) are added to that state and the resulting state is permutated using the global permutation. Next, if <math>n</math> is the number of qubits that will be encrypted, two bits strings are picked of length <math>n</math> to encrypt the state with [[Quantum one time pad]]. After this, we obtain our magic state for that particular quantum state. Here it is important to note that the keys for [[Quantum one time pad]] are selected during Encryption rather than Key Generation.
** For the <math>T</math> gate, error correcting gadgets are prepared from [[garden-hose gadgets]].
** For the <math>T</math> gate, error correcting gadgets are prepared from [[garden-hose gadgets]].
** Then the evaluation key is formed by MAC which uses the auxiliary states, including the magic states.
** Then the evaluation key is formed by MAC which uses the auxiliary states, including the magic states.
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