TY - GEN
T1 - Analysis of lattice reduction attack against the somewhat homomorphic encryption based on ideal lattices
AU - Yasuda, Masaya
AU - Yajima, Jun
AU - Shimoyama, Takeshi
AU - Kogure, Jun
PY - 2013/12/1
Y1 - 2013/12/1
N2 - In 2009, Gentry first proposed a concrete method for constructing a fully homomorphic encryption (FHE) scheme, which supports arbitrary operations on encrypted data. The construction of the FHE scheme starts from a somewhat homomorphic encryption (SHE) scheme, which only supports limited operations but can be much faster than the FHE scheme. The Gentry's scheme is based on ideal lattices, and Chen and Nguyen estimated that it needs at least 10,000 lattice dimension to make the FHE scheme secure. In contrast, the security of the SHE scheme can be guaranteed for lower lattice dimensions, depending on the possible operations which are determined by key parameters. The aim of this paper is to classify which key parameters are feasible to be solved. We attack the lattice problem of lower dimensions by practical lattice reduction algorithms, and estimate the key parameters which can be solved in practice.
AB - In 2009, Gentry first proposed a concrete method for constructing a fully homomorphic encryption (FHE) scheme, which supports arbitrary operations on encrypted data. The construction of the FHE scheme starts from a somewhat homomorphic encryption (SHE) scheme, which only supports limited operations but can be much faster than the FHE scheme. The Gentry's scheme is based on ideal lattices, and Chen and Nguyen estimated that it needs at least 10,000 lattice dimension to make the FHE scheme secure. In contrast, the security of the SHE scheme can be guaranteed for lower lattice dimensions, depending on the possible operations which are determined by key parameters. The aim of this paper is to classify which key parameters are feasible to be solved. We attack the lattice problem of lower dimensions by practical lattice reduction algorithms, and estimate the key parameters which can be solved in practice.
UR - http://www.scopus.com/inward/record.url?scp=84894179724&partnerID=8YFLogxK
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U2 - 10.1007/978-3-642-40012-4_1
DO - 10.1007/978-3-642-40012-4_1
M3 - Conference contribution
AN - SCOPUS:84894179724
SN - 9783642400117
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 1
EP - 16
BT - Public Key Infrastructures, Services and Applications - 9th European Workshop, EuroPKI 2012, Revised Selected Papers
T2 - 9th European Workshop on Public Key Infrastructures, Services and Applications, EuroPKI 2012
Y2 - 13 September 2012 through 14 September 2012
ER -