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→Topological Error Correction
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===Stabilizer Codes=== | ===Stabilizer Codes=== | ||
===Topological Error Correction=== | ===Topological Error Correction=== | ||
===Quantum Capable Homomorphic Encryption=== | |||
====Homomorphic Encryption==== | |||
A homomorphic encryption scheme HE is a scheme to carry out classical computation from the Server while hiding the inputs, outputs and computation. It can be divided into following four stages. | |||
* ''Key Generation.'' The algorithm (pk,evk,sk) ← HE.Keygen(1λ) takes a λ, a security parameter as input and outputs a public key encryption key pk, a public evaluation key evk and a secret decryption key sk. | |||
* ''Encryption.'' The algorithm c ← HE.Encpk(µ) takes the public key pk and a single bit message µ ∈ {0,1} and outputs a ciphertext c. The notation HE.Encpk(µ;r) is be used to represent the encryption of a bit µ using randomness r. | |||
* ''Decryption''. The algorithm µ∗ ← HE.Decsk(c) takes the secret key sk and a ciphertext c and outputs a message µ∗ ∈ {0,1}. | |||
* ''Homomorphic Evaluation'' The algorithm cf ← HE.Evalevk(f,c1,...,cl) takes the evaluation key evk, a function f : {0,1}l → {0,1} and a set of l ciphertexts c1,...,cl, and outputs a ciphertext cf. It must be the case that: | |||
HE.Decsk(cf) = f(HE.Decsk(c1),...,HE.Decsk(cl)) (1) | |||
with all but negligible probability in λ. This means classical HE decrypts ciphertext bit by bit. | |||
HE scheme is compact if HE.Eval is independent of any inputs or computation. It is fully homomorphic if it can compute any boolean computation. | |||
====Quantum Capable==== | |||
''A classical HE is quantum capable if it can be used to evaluate quantum circuits.'' | |||
Any HE scheme to be quantum capable requires the following two properties. | |||
*''invariance of ciphertext:'' | |||
*''natural XOR operation:'' | |||
===Encrypted CNOT operation=== | ===Encrypted CNOT operation=== | ||
====Trapdoor Claw-free function(TCF)==== | ====Trapdoor Claw-free function(TCF)==== | ||