Homomorphic Encryption based on Hidden Subspace Membership
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In this paper, we propose a leveled fully homomorphic encryption scheme based on multivariate polynomial evaluation. We first identify a decision problem called the Hidden Subspace Membership (HSM) problem and show that it is related to the well-known Learning with Errors (LWE) problem. We show that an adversary against the LWE problem can be translated into an adversary against the HSM problem and on the contrary, solving the HSM problem is equivalent to solving the LWE problem with multiple secrets. We then show that the security of the proposed scheme rely on the hardness of the Hidden Subspace Membership problem. Further, we propose a batch variant of the scheme where multiple plaintext bits can be packed into a single ciphertext.
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