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 encryptionmultivariate algebraic equationGröbner basisoctonion
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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2015/474}},
      url = {https://eprint.iacr.org/2015/474}
}
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