Classical Fully Homomorphic Encryption for Quantum Circuits: Difference between revisions

::::#The server computes the encryption of <math>x,z</math> (stored in <math>\tilde{z},\tilde{x}</math>) under <math>pk_{i+1}</math> by performing decryption circuit on <math>\mathrm{HE.Enc}_{pk_{i+1}}(c)</math> using <math>\mathrm{HE.Enc}_{pk_{i+1}}(sk_i)</math> (provided by the evaluation key). Here, c, as stated before was the concatenation of encryptions of x, z under <math>pk_{i}</math>.

::::#The server (homomorphically) computes <math>(\mu_0,r_0)</math> and <math>(\mu_1,r_1)</math>, using <math>t_{sk_i},sk_i</math>, provided by the evaluation key <math>\mathrm{evk}_i</math> encrypted under <math>pk_{i+1}</math>, and <math>\mathrm{HE.Enc}_{pk_{i+1}}(\hat{c},y,d)</math>, from the previous step.  

::::#The server then uses this results of the last three steps, to (homomorphically) update Pauli encryptions for encrypted <math>CNOT^s_{l,n}</math>: </br>(<math>\tilde {x}^{[l]},\tilde{z}^{[l]};\tilde {x}^{[n]},\tilde{z}^{[n]})\rightarrow (<math>\tilde {x}^{[l]},\tilde{z}^{[l]}+d\cdot ((\mu_0,r_0)\oplus (\mu_1,r_1);\tilde {x}^{[n]}+\mu_0,\tilde{z}^{[n]})</math></br>