Cryptology ePrint Archive: Report 2016/054

Fully Homomorphic Public-Key Encryption with Two Ciphertexts based on Discrete Logarithm Problem

Masahiro Yagisawa

Abstract: In previous paper I proposed the fully homomorphic public-key encryption based on discrete logarithm problem which may be vulnerable to “m and -m attack”. In this paper I propose improved fully homomorphic public-key encryption (FHPKE) with composite number modulus based on the discrete logarithm assumption (DLA) and computational Diffie–Hellman assumption (CDH) of multivariate polynomials on octonion ring which is immune from “m and -m attack”. The scheme has two ciphertexts corresponding to one plaintext.

Category / Keywords: •public-key cryptography/fully homomorphic public-key encryption, discrete logarithm assumption, computational Diffie–Hellman assumption, octonion ring, factorization

Original Publication (with major differences): Masahiro, Y. (2015). Fully Homomorphic Encryption without bootstrapping which was published by LAP LAMBERT Academic Publishing, Saarbrücken/Germany .

Date: received 22 Jan 2016, last revised 30 Nov 2016

Contact author: tfkt8398yagi at outlook jp

Available format(s): PDF | BibTeX Citation

Note: I improved the enciphering scheme by using two ciphertexts corresponding to one plaintext. The scheme is immune from “m and -m attack”.

Version: 20161130:102241 (All versions of this report)

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