Paper 2011/121

More Practical Fully Homomorphic Encryption

Gu Chunsheng


In this paper, we first modify the Smart-Vercauteren’s fully homomorphic encryption scheme [SV10] by applying self-loop bootstrappable technique. The security of the modified scheme only depends on the hardness of the polynomial coset problem, removing the assumption of the sparse subset sum problem in the original paper in [SV10]. Moreover, we construct a non-self-loop in FHE by using cycle keys. Then, we further improve our scheme to make it be practical. The securities of our improving FHE’s are respectively based on the hardness of factoring integer problem, solving Diophantine equation problem, and finding approximate greatest common divisor problem.

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Published elsewhere. Unknown where it was published
Fully Homomorphic EncryptionPolynomial Coset ProblemFactoring IntegerDiophantine Equation ProblemApproximate GCDSSSP
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guchunsheng @ gmail com
2011-08-17: last of 4 revisions
2011-03-10: received
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      author = {Gu Chunsheng},
      title = {More Practical Fully Homomorphic Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2011/121},
      year = {2011},
      note = {\url{}},
      url = {}
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