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JMI2011B-2 An improvement of key generation algorithm for Gentry's homomorphic encryption scheme from ideal lattices (pp.99-106)

Author(s): Naoki Ogura, Go Yamamoto, Tetsutaro Kobayashi and Shigenori Uchiyama

J. Math-for-Ind. 3B (2011) 99-106.

One way of improving efficiency of Gentry's fully homomorphic encryption from ideal lattices is controlling the number of operations, but our recollection is that any scheme which controls the bound has not proposed. In this paper, we propose a key generation algorithm for Gentry's scheme that controls the bound of the circuit depth by using the relation between the circuit depth and the eigenvalues of a basis of a lattice. We present experimental results that show that the proposed algorithm is practical. We discuss security of the basis of the lattices generated by the algorithm for practical use.

Keyword(s).  homomorphic encryption, ideal lattice, circulant matrix