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

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

Revision as of 08:28, 11 July 2019

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→‎Stage 1 Client’s Preparation

Shraddha

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 ===Stage 1 Client’s Preparation===
- '''Key Generation (QFHE.KeyGen(1k,1L))'''
+'''Key Generation (QFHE.KeyGen(1k,1L))'''
 *Input: No. of T gates (L), Security Parameter (k),
 *Output: L+1 evaluation keys (encrypted Gadgets, classical HE evaluation key), L+1 public keys, L+1 secret keys
 #	For i = 0 to L
-##Client executes (pki,ski,evki) ← HE.KeyGen(1κ) to obtain L + 1 independent classical homomorphic key sets.
+## Client executes <math>(pk_i, sk_i, evk_i) \leftarrow \text{HE.KeyGen}(1^{\kappa})</math> to obtain <math>L+1</math> independent classical homomorphic key sets.
-#	She sets the public key to be the tuple ( .
+# She sets the public key to be the tuple <math>(pk_i)_{i = 0}^{L}</math>.
-#	She sets the secret key to be the tuple ( .
+# She sets the secret key to be the tuple <math>(sk_i)_{i = 0}^{L}</math>.
-#	For i = 0 to L − 1
+# For i = 0 to L-1
-##Client runs the procedure QFHE.GenGadgetpki+1(ski) to create the gadget Γpki+1(ski).
+## Client runs the procedure <math>\text{QFHE.GenGadget}_{pk_{i+1}}(sk_i)</math> to create the gadget <math>\Gamma_{pk_{i+1}}(sk_i)</math>.
-#	Client sets the evaluation key to be the set of all gadgets created in the previous step (including their encrypted classical information), plus the tuple ( . The resulting evaluation key is the classical-quantum (CQ) state {missing math}
+# Client sets the evaluation key to be the set of all gadgets created in the previous step (including their encrypted classical information), plus the tuple <math>(evk_i)_{i=0}^L</math>. The resulting evaluation key is the classical-quantum  (CQ) state</br><math>\bigotimes_{i = 0}^{L-1}\Big(\Gamma _{pk_{i+1}}(sk_i)\otimes |evk_i\rangle \langle evk_i|)</math>
- '''Encryption(QFHE.Enc())'''
+'''Encryption(QFHE.Enc())'''
-*Input: Quantum Input state density matrix (ρ) (say composed of n single qubit states, σ)
+*Input: Quantum Input state density matrix (<math>\rho</math>) (say composed of n single qubit states, σ)
 *Output: Encrypted pad keys: {a˜[0]...a˜[n], ˜b[i]...˜b[n]}; QOTP state: Xa[1]Zb[1]⊗.....⊗Xa[n]Zb[n]ρZb[1]Xa[1]⊗ ..... ⊗ Xa[n]Zb[n]
 #	For i=1 to n