Cryptology ePrint Archive: Report 2012/240

Field Switching in BGV-Style Homomorphic Encryption

Craig Gentry and Shai Halevi and Chris Peikert and Nigel P. Smart

Abstract: The security of contemporary homomorphic encryption schemes over cyclotomic number field relies on fields of very large dimension. This large dimension is needed because of the large modulus-to-noise ratio in the key-switching matrices that are used for the top few levels of the evaluated circuit. However, a smaller modulus-to-noise ratio is used in lower levels of the circuit, so from a security standpoint it is permissible to switch to lower-dimension fields, thus speeding up the homomorphic operations for the lower levels of the circuit. However, implementing such field-switching is nontrivial, since these schemes rely on the field algebraic structure for their homomorphic properties.

A basic ring-switching operation was used by Brakerski, Gentry and Vaikuntanathan, over rings of the form $\Z[X]/(X^{2^n}+1)$, in the context of bootstrapping. In this work we generalize and extend this technique to work over any cyclotomic number field, and show how it can be used not only for bootstrapping but also during the computation itself (in conjunction with the ``packed ciphertext'' techniques of Gentry, Halevi and Smart).

Category / Keywords: public-key cryptography / Homomorphic Encryption, Ring-LWE

Original Publication (with major differences): SCN 2012, Springer LNCS vol. 7485

Date: received 29 Apr 2012, last revised 13 Sep 2013

Contact author: shaih at alum mit edu

Available format(s): PDF | BibTeX Citation

Note: Jan-2013, major revision: transformation generalized and simplified

Version: 20130913:220414 (All versions of this report)

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