A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
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STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
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Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
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EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
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A fully homomorphic encryption scheme
A fully homomorphic encryption scheme
A Course in Computational Algebraic Number Theory
A Course in Computational Algebraic Number Theory
Fully homomorphic encryption with relatively small key and ciphertext sizes
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Implementing Gentry's fully-homomorphic encryption scheme
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
The geometry of lattice cryptography
Foundations of security analysis and design VI
Improved key generation for gentry's fully homomorphic encryption scheme
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
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One way of improving efficiency of Gentry's fully homomorphic encryption 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 homomorphic encryption 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.