An efficient key generation of ZHFE public key cryptosystem

Yasuhiko Ikematsu, Dung Hoang Duong, Albrecht Petzoldt, Tsuyoshi Takagi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


ZHFE, proposed by Porras et al. at PQCrypto'14, is one of the very few existing multivariate encryption schemes and a very promising candidate for post-quantum cryptosystems. The only one drawback is its slow key generation. At PQCrypto'16, Baena et al. proposed an algorithm to construct the private ZHFE keys, which is much faster than the original algorithm, but still inefficient for practical parameters. Recently, Zhang and Tan proposed another private key generation algorithm, which is very fast but not necessarily able to generate all the private ZHFE keys. In this paper we propose a new efficient algorithm for the private key generation and estimate the number of possible keys generated by all existing private key generation algorithms for the ZHFE scheme. Our algorithm generates as many private ZHFE keys as the original and Baena et al.'s ones and reduces the complexity from O(n2ω+1) by Baena et al. to O(nω+3), where n is the number of variables and ω is a linear algebra constant. Moreover, we also analyze when the decryption of the ZHFE scheme does not work.

Original languageEnglish
Pages (from-to)29-38
Number of pages10
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - Jan 2018

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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