Editing Classical Fully Homomorphic Encryption for Quantum Circuits
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*''Circular Security'' This protocol has a stronger notion of circular security where not only the secret key but also the trapdoor functions are encrypted when provided to the Server. | *''Circular Security'' This protocol has a stronger notion of circular security where not only the secret key but also the trapdoor functions are encrypted when provided to the Server. | ||
== Notation == | == Notation == | ||
*<math>m</math>: | *<math>m</math>: Message | ||
*<math>\lambda</math>: security parameter | *<math>\lambda</math>: security parameter | ||
* <math>k</math>: security parameter | * <math>k</math>: security parameter | ||
* <math>\tilde{x}</math>: encrypted pad key | * <math>\tilde{x}</math>: encrypted pad key | ||
* <math>\tilde{x}^{[l]}</math>: <math>l^{th}</math> bit of encrypted pad key | * <math>\tilde{x}^{[l]}</math>: <math>l^{th}</math> bit of encrypted pad key | ||
* <math>L_c</math>: depth of a layer of circuit where each layer contains Clifford gates and Toffoli gates | * <math>L_c</math>: depth of a layer of circuit where each layer contains Clifford gates and Toffoli gates | ||
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*The functions <math>f_0, f_1</math> used must be trapdoor claw-free(TCF) such that one it is not possible to find a triple <math>(\mu_0,\mu_1,y)</math> such that <math>f_0(\mu_0)=f_1(\mu_1)=y</math> | *The functions <math>f_0, f_1</math> used must be trapdoor claw-free(TCF) such that one it is not possible to find a triple <math>(\mu_0,\mu_1,y)</math> such that <math>f_0(\mu_0)=f_1(\mu_1)=y</math> | ||
== | == Pseudocode== | ||
*Boxed texts are not part of the code but contain proofs used in various steps, illustrated for a better understanding of the protocol. | *Boxed texts are not part of the code but contain proofs used in various steps, illustrated for a better understanding of the protocol. | ||
==='''Stage 1''' Client’s Preparation=== | ==='''Stage 1''' Client’s Preparation=== |