Fully Homomorphic Encryption without bootstrapping

Masahiro Yagisawa

Paper 2015/474

Fully Homomorphic Encryption without bootstrapping

Masahiro Yagisawa

Abstract

Gentry’s bootstrapping technique is the most famous method of obtaining fully homomorphic encryption. In this paper I propose a new fully homomorphic encryption scheme on non-associative octonion ring over finite field without bootstrapping technique. The security of the proposed fully homomorphic encryption scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. Because proposed fully homomorphic encryption scheme is based on multivariate algebraic equations with high degree or too many variables, it is against the Gröbner basis attack, the differential attack, rank attack and so on. The key size of this system and complexity for enciphering/deciphering become to be small enough to handle.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Minor revision. Masahiro, Y. (2015). Fully Homomorphic Encryption without bootstrapping which was published by LAP LAMBERT Academic Publishing, Saarbrücken/Germany .
Keywords: fully homomorphic encryption multivariate algebraic equation Gröbner basis octonion
Contact author(s): tfkt8398yagi @ hb tp1 jp
History: 2015-06-21: last of 5 revisions; 2015-05-19: received; See all versions
Short URL: https://ia.cr/2015/474
License: CC BY

BibTeX

@misc{cryptoeprint:2015/474,
      author = {Masahiro Yagisawa},
      title = {Fully Homomorphic Encryption without bootstrapping},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/474},
      year = {2015},
      url = {https://eprint.iacr.org/2015/474}
}