A public-key encryption scheme based on non-linear indeterminate equations

Koichiro Akiyama, Yasuhiro Goto, Shinya Okumura, Tsuyoshi Takagi, Koji Nuida, Goichiro Hanaoka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)


In this paper, we propose a post-quantum public-key encryption scheme whose security depends on a problem arising from a multivariate non-linear indeterminate equation. The security of lattice cryptosystems, which are considered to be the most promising candidate for a post-quantum cryptosystem, is based on the shortest vector problem or the closest vector problem in the discrete linear solution spaces of simultaneous equations. However, several improved attacks for the underlying problems have recently been developed by using approximation methods, which result in requiring longer key sizes. As a scheme to avoid such attacks, we propose a public-key encryption scheme based on the “smallest” solution problem in the non-linear solution spaces of multivariate indeterminate equations that was developed from the algebraic surface cryptosystem. Since no efficient algorithm to find such a smallest solution is currently known, we introduce a new computational assumption under which proposed scheme is proven to be secure in the sense of IND-CPA. Then, we perform computational experiments based on known attack methods and evaluate that the key size of our scheme is able to be much shorter than those of previous lattice cryptosystems.

Original languageEnglish
Title of host publicationSelected Areas in Cryptography – SAC 2017 - 24th International Conference, Revised Selected Papers
EditorsCarlisle Adams, Jan Camenisch
PublisherSpringer Verlag
Number of pages20
ISBN (Print)9783319725642
Publication statusPublished - 2018
Event24th International Conference on Selected Areas in Cryptography, SAC 2017 - Ottawa, Canada
Duration: Aug 16 2017Aug 18 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10719 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other24th International Conference on Selected Areas in Cryptography, SAC 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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