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→Classical Methods
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===Learning with errors=== | ===Learning with errors=== | ||
== | ===Quantum Capable Homomorphic Encryption=== | ||
===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. | 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. | ||
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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==== | |||
''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.'' | ||
It requires the following two properties. | |||
*''invariance of ciphertext:'' | |||
*''natural XOR operation:'' | |||