A course in computational algebraic number theory
A course in computational algebraic number theory
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
A fully homomorphic encryption scheme
A fully homomorphic encryption scheme
An improvement of key generation algorithm for Gentry's homomorphic encryption scheme
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
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
Fully homomorphic encryption from ring-LWE and security for key dependent messages
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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
Fully homomorphic SIMD operations
Designs, Codes and Cryptography
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A key problem with the original implementation of the Gentry Fully Homomorphic Encryption scheme was the slow key generation process. Gentry and Halevi provided a fast technique for 2-power cyclotomic fields. We present an extension of the Gentry---Halevi key generation technique for arbitrary cyclotomic fields. Our new method is roughly twice as efficient as the previous best methods. Our estimates are backed up with experimental data.