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Homomorphic Encryption is an encryption scheme that allows one to compute something like something like a Turing complete framework. Homomorphic encryption (HE) is limited because each ciphertext is noisy, and such noise grows as one keeps performing additions and multiplications in the ciphertext space. The presence of noise is essential to guarantee a certain degree of security and protecting the secret operands and results of intermediate computations. The role of the secret key is to decipher and reconstruct and reconstruct securely the encrypted data.
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