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Lattice-Based Public Key Cryptosystems Invoking Linear Mapping Mask

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Provable and Practical Security (ProvSec 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13600))

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Abstract

In ProvSec 2018, Yasuda proposed a multivariate public key cryptosystem using the pq-method, whose security is based on the constrained MQ problem. Afterward, in SCIS 2020, he improved the cryptosystem by adding noise elements and simultaneously considered the cryptanalysis using the NTRU method. This improved cryptosystem is the first one combining lattice and multivariate public-key cryptosystem. In this paper, we propose three variants of Yasuda’s cryptosystem. The main improvement is that we invite the linear structures instead of the multivariate quadratic polynomials. In particular, we simplify the procedure in key generation mechanism by using a linear mapping mask which produces resistance against the key-recovery attack. Furthermore, we propose a ring version that is quite efficient compared to the standard versions. Finally, we adopt the ring-LWE method instead of the original NTRU method to give a more promising cryptanalysis.

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Acknowledgement

We thank Dr. Atsushi Takayasu for his helpful comments on this work. This work was supported by JSPS KAKENHI Grant Number JP20K23322, JP21K11751, JP19K20266, JP20K03741, Japan. This work is based on the discussions at FY2019 IMI Joint Usage Research Program Short-term Joint Research “New Development of Constructing Next-Generation Cryptography via Unified Approaches of Mathematics Theory, Computation and Cryptology”.

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Authors and Affiliations

  1. Graduate School of Engineering, Osaka University, Suita, Japan

    Yuntao Wang

  2. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Yasuhiko Ikematsu

  3. Institute for the Advancement of Higher Education, Okayama University of Science, Okayama, Japan

    Takanori Yasuda

Authors
  1. Yuntao Wang
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  2. Yasuhiko Ikematsu
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  3. Takanori Yasuda
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Corresponding author

Correspondence to Yuntao Wang .

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Editors and Affiliations

  1. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Chunpeng Ge

  2. University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

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Wang, Y., Ikematsu, Y., Yasuda, T. (2022). Lattice-Based Public Key Cryptosystems Invoking Linear Mapping Mask. In: Ge, C., Guo, F. (eds) Provable and Practical Security. ProvSec 2022. Lecture Notes in Computer Science, vol 13600. Springer, Cham. https://doi.org/10.1007/978-3-031-20917-8_7

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  • DOI: https://doi.org/10.1007/978-3-031-20917-8_7

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