Two main computational problems serve as security foundations of current fully homomorphic encryption schemes: Regev’s Learning With Errors problem (LWE) and Howgrave-Graham’s Approximate Greatest Common Divisor problem (AGCD). Our first contribution is a reduction from LWE to AGCD. As a second contribution, we describe a new AGCD-based fully homomorphic encryption scheme, which outperforms all prior 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 Õ(λ), where λ refers to the security parameter.
CITATION STYLE
Cheon, J. H., & Stehlé, D. (2015). Fully homomophic encryption over the integers revisited. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9056, pp. 513–536). Springer Verlag. https://doi.org/10.1007/978-3-662-46800-5_20
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