Bootstrapping BGV Ciphertexts with a Wider Choice of $$p$$ and $$q$$
| Autor: | Nigel P. Smart, Joop van de Pol, Emmanuela Orsini |
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| Rok vydání: | 2015 |
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| Zdroj: | Lecture Notes in Computer Science ISBN: 9783662464465 Public Key Cryptography |
| DOI: | 10.1007/978-3-662-46447-2_30 |
| Popis: | We describe a method to bootstrap a packed BGV ciphertext which does not depend (as much) on any special properties of the plaintext and ciphertext moduli. Prior “efficient” methods such as that of Gentry et al. (PKC 2012) required a ciphertext modulus \(q\) which was close to a power of the plaintext modulus \(p\). This enables our method to be applied in a larger number of situations. Also unlike previous methods our depth grows only as \(O(\log p + \log \log q)\) as opposed to the \(\log q\) of previous methods. Our basic bootstrapping technique makes use of a representation of the group \({\mathbb {Z}}_q^+\) over the finite field \({\mathbb {F}}_p\) (either based on polynomials or elliptic curves), followed by polynomial interpolation of the reduction mod \(p\) map over the coefficients of the algebraic group. |
| Databáze: | OpenAIRE |
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