Abstract
Two main computational problems serve as security foundations of current fully homomorphic encryption schemes: Regev’s Learning With Errors problem (\(\mathrm {LWE}\)) and Howgrave-Graham’s Approximate Greatest Common Divisor problem (\(\mathrm {AGCD}\)). Our first contribution is a reduction from \(\mathrm {LWE}\) to \(\mathrm {AGCD}\). As a second contribution, we describe a new \(\mathrm {AGCD}\)-based fully homomorphic encryption scheme, which outperforms all prior \(\mathrm {AGCD}\)-based proposals: its security does not rely on the presumed hardness of the so-called Sparse Subset Sum problem, and the bit-length of a ciphertext is only \(\widetilde{O}(\lambda )\), where \(\lambda \) refers to the security parameter.
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Cheon, J.H., Stehlé, D. (2015). Fully Homomophic Encryption over the Integers Revisited. In: Oswald, E., Fischlin, M. (eds) Advances in Cryptology -- EUROCRYPT 2015. EUROCRYPT 2015. Lecture Notes in Computer Science(), vol 9056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46800-5_20
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