### Fully homomorphic public-key encryption with small ciphertext size

Masahiro Yagisawa

##### Abstract

In previous work I proposed a fully homomorphic encryption without bootstrapping which has the large size of ciphertext. This tme I propose the fully homomorphic public-key encryption scheme on non-associative octonion ring over finite field with the small size of ciphertext. In this scheme the size of ciphertext is one-third of the size in the scheme proposed before. Because proposed scheme adopts the medium text with zero norm, it is immune from the “p and -p attack”. As the proposed scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree, it is immune from the Gröbner basis attack, the differential attack, rank attack and so on.

Note: In previous report 2017/763 in Cryptology ePrint Archive, I proposed “Improved Fully Homomorphic Public-key Encryption without Bootstrapping” which has three ciphertexts corresponding to one plaintext. This time I propose the scheme which has only one ciphertext corresponding to one plaintext. Then in this scheme the size of ciphertext is one-third of the size in the scheme proposed before(2017/763).

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. MAJOR revision.Masahiro, Y. (2015). Fully Homomorphic Encryption without bootstrapping which was published by LAP LAMBERT Academic Publishing, Saarbrücken/Germany .
Keywords
fully homomorphic public-key encryptionmultivariate algebraic equationGröbner basisnon-associative ring
Contact author(s)
tfkt8398yagi @ outlook jp
History
Short URL
https://ia.cr/2018/088

CC BY

BibTeX

@misc{cryptoeprint:2018/088,
author = {Masahiro Yagisawa},
title = {Fully homomorphic public-key encryption with small ciphertext size},
howpublished = {Cryptology ePrint Archive, Paper 2018/088},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/088}},
url = {https://eprint.iacr.org/2018/088}
}

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