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Classical Fully Homomorphic Encryption for Quantum Circuits: Difference between revisions
Classical Fully Homomorphic Encryption for Quantum Circuits (edit)
Revision as of 13:35, 20 November 2018
, 20 November 2018→Stage 2 Server’s Computation
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####The server computes the encryption of <math>a,b</math> under <math>pk_{i+1}</math> by homomorphically running the decryption circuit on inputs <math>\mathrm{HE.Enc}_{pk_{i+1}}(sk_i)</math> and HE.Enc<math>_{pk_{i+1}}(c_{a,b,pk_i})</math>. | ####The server computes the encryption of <math>a,b</math> under <math>pk_{i+1}</math> by homomorphically running the decryption circuit on inputs <math>\mathrm{HE.Enc}_{pk_{i+1}}(sk_i)</math> and HE.Enc<math>_{pk_{i+1}}(c_{a,b,pk_i})</math>. | ||
####The server homomorphically computes <math>(\mu_0,r_0)</math> and <math>(\mu_1,r_1)</math>, using the secret texts encrypting <math>t_{sk_i},sk_i,\hat{c},y,d</math> (all encrypted with HE under public key $pk_{i+1}$). The server then uses this result, along with the secret texts encrypting <math>a,b,d</math>, to homomorphically compute <math>\tilde{b} = b + (d\cdot ((\mu_0,r_0)\oplus (\mu_1,r_1)),0)</math> and <math>\tilde{a} = a + (0,\mu_0)</math>. | ####The server homomorphically computes <math>(\mu_0,r_0)</math> and <math>(\mu_1,r_1)</math>, using the secret texts encrypting <math>t_{sk_i},sk_i,\hat{c},y,d</math> (all encrypted with HE under public key $pk_{i+1}$). The server then uses this result, along with the secret texts encrypting <math>a,b,d</math>, to homomorphically compute <math>\tilde{b} = b + (d\cdot ((\mu_0,r_0)\oplus (\mu_1,r_1)),0)</math> and <math>\tilde{a} = a + (0,\mu_0)</math>. | ||
# Server sends updated encryptions of Pauli corrections | #Server sends updated encryptions of Pauli corrections <math>\tilde{a},\tilde{b}</math> and the classical outcome after measurement of the output state (or Quantum one time padded state in case of quantum output) to Client. | ||
=== '''Stage 3''' Client’s Output Correction === | === '''Stage 3''' Client’s Output Correction === | ||