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Fully Homomophic Encryption over the Integers Revisited

  • Jung Hee CheonEmail author
  • Damien Stehlé
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9056)

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.

Keywords

Fully homomorphic encryption Approximate GCD   DGHV LWE 

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Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.SNUSeoulRepublic of Korea
  2. 2.ENS de LyonLyonFrance

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