Paper 2016/837

Fully Homomorphic Encryption over the Integers Revisited

Jung Hee Cheon and Damien Stehle


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 softO(lambda), where lambda refers to the security parameter.

Note: Updated the Eurocrypt 2015 version, to fix a few minor errors.

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Publication info
A minor revision of an IACR publication in EUROCRYPT 2015
Contact author(s)
damien stehle @ gmail com
2016-09-04: revised
2016-09-03: received
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      author = {Jung Hee Cheon and Damien Stehle},
      title = {Fully Homomorphic Encryption over the Integers Revisited},
      howpublished = {Cryptology ePrint Archive, Paper 2016/837},
      year = {2016},
      note = {\url{}},
      url = {}
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