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→Quantum Capable Homomorphic Encryption
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===Topological Error Correction=== | ===Topological Error Correction=== | ||
==Quantum Capable Homomorphic Encryption== | ==Quantum Capable Homomorphic Encryption== | ||
*'''Homomorphic Encryption'''<br/>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. | |||
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. | * ''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. | * ''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. | ||
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with all but negligible probability in λ. This means classical HE decrypts ciphertext bit by bit. | 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. | 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'''<br/> | |||
''A classical HE is quantum capable if it can be used to evaluate quantum circuits.'' | ''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. | Any HE scheme to be quantum capable requires the following two properties. | ||