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Classical Fully Homomorphic Encryption for Quantum Circuits: Difference between revisions
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Classical Fully Homomorphic Encryption for Quantum Circuits (edit)
Revision as of 00:31, 26 November 2018
, 26 November 2018→Stage 2 Server’s Computation
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::::#The server uses <math>pk_{i+1}</math> to compute HE.Enc<math>_{pk_{i+1}}(c_{x,z,pk_i})</math> and <math>\mathrm{HE.Enc}_{pk_{i+1}}(\hat{c},y,d)</math>. | ::::#The server uses <math>pk_{i+1}</math> to compute HE.Enc<math>_{pk_{i+1}}(c_{x,z,pk_i})</math> and <math>\mathrm{HE.Enc}_{pk_{i+1}}(\hat{c},y,d)</math>. | ||
::::#The server computes the encryption of <math>x,z</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 <math>\mathrm{HE.Enc}_{pk_{i+1}}(c_{x,z,pk_i})</math>. | ::::#The server computes the encryption of <math>x,z</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 <math>\mathrm{HE.Enc}_{pk_{i+1}}(c_{x,z,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 <math>pk_{i+1}</math>). The server then uses this result, along with the secret texts encrypting <math>x,z,d</math>, to homomorphically compute <math>\tilde{z} = z + (d\cdot ((\mu_0,r_0)\oplus (\mu_1,r_1)),0)</math> and <math>\tilde{x} = x + (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 <math>pk_{i+1}</math>). The server then uses this result, along with the secret texts encrypting <math>x,z,d</math>, to homomorphically compute <math>\tilde{z} = z + (d\cdot ((\mu_0,r_0)\oplus (\mu_1,r_1)),0)</math> and <math>\tilde{x} = x + (0,\mu_0)</math>.</br> | ||
3. Server sends updated encryptions of Pauli corrections <math>\tilde{x},\tilde{z}</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 === | ||