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Fully Homomophic Encryption over the Integers Revisited


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 O˜(λ), where λ refers to the security parameter.

Dates and versions

hal-01240437 , version 1 (09-12-2015)



Jung Hee Cheon, Damien Stehlé. Fully Homomophic Encryption over the Integers Revisited. EUROCRYPT 2015 - 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Apr 2015, Sofia, Bulgaria. pp.513-536, ⟨10.1007/978-3-662-46800-5_20⟩. ⟨hal-01240437⟩
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