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

Prepare-and-Send Quantum Fully Homomorphic Encryption (edit)

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 == Notations ==
+*	<math>\mathrm{k}</math>, security parameter
-*	{pki,ski,evki}, ith homomorphic key set generated from HE.KeyGen(). Public key for encryption, secret key for decryption, evaluation function key, respectively for given k, the security parameter.
+*	<math>\mathrm{L}</math>, number of T gates in the evaluation circuit
-*	Γpki+1(ski), Gadget using ith secret key (ski) and encrypted by (i + 1)th public key (pki+1)
+*	<math>\mathrm{n}</math>, dimension of input qubit
-*	σ, single qubit state
+*	<math>\mathrm{{pk_i,sk_i,evk_i}}</math>, <math>\mathrm{i_{th}}</math> homomorphic key set generated from HE.KeyGen(). Public key for encryption, secret key for decryption, evaluation function key, respectively for given k, the security parameter.
-*	ρ = |ψihψ|, here ρ is the density matrix of quantum state |ψi
+*	<math>\Gamma_{pk_{i+1}}(\mathrm{sk_i})</math>, Gadget using <math>\mathrm{i_th}</math> secret key (<math>sk_i</math>) and encrypted by <math>\mathrm{(i + 1)_{th}}</math> public key (<math>\mathrm{pk_{i+1}}</math>)
+*	<math>\sigma</math>, single qubit state
+*	<math>\rho=\ket{\psi}\bra{\psi}</math>, here <math>\rho</math> is the density matrix of quantum state |ψi
 *	ρ, n-qubit input state, where n is determined by the Client
 *	ρ(HE.Encpk(a)), a is encrypted with public key pk and is represented by density matrix ρ