International Workshop on Public Key Cryptography

PKC 2009: Public Key Cryptography – PKC 2009 pp 425-442

An Algebraic Surface Cryptosystem

  • Koichiro Akiyama
  • Yasuhiro Goto
  • Hideyuki Miyake
Conference paper

DOI: 10.1007/978-3-642-00468-1_24

Volume 5443 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Akiyama K., Goto Y., Miyake H. (2009) An Algebraic Surface Cryptosystem. In: Jarecki S., Tsudik G. (eds) Public Key Cryptography – PKC 2009. PKC 2009. Lecture Notes in Computer Science, vol 5443. Springer, Berlin, Heidelberg


We construct a public-key cryptosystem based on an NP-complete problem in algebraic geometry. It is a problem of finding sections on fibered algebraic surfaces; in other words, we use a solution to a system of multivariate equations of high degrees. Our cryptosystem is a revised version of the algebraic surface cryptosystem (ASC) we constructed earlier (cf. [AG04, AG06]). We revise its encryption algorithm to avoid known attacks. Further, we show that the key size of our cryptosystem is one of the shortest among those of post-quantum public-key cryptosystems known at present.


Public-key CryptosystemAlgebraic SurfaceSection
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Koichiro Akiyama
    • 1
  • Yasuhiro Goto
    • 2
  • Hideyuki Miyake
    • 1
  1. 1.Computer & Network Systems Laboratory, Corporate Research & Development CenterToshiba Corp.KawasakiJapan
  2. 2.Department of MathematicsHokkaido University of Education at HakodateHakodateJapan