An Algebraic Surface Cryptosystem

Authors:
Koichiro Akiyama;Yasuhiro Goto;Hideyuki Miyake
Affiliations:
Computer & Network Systems Laboratory, Corporate Research & Development Center, Toshiba Corp., Kawasaki, Japan 212-8582;Department of Mathematics, Hokkaido University of Education at Hakodate, Hakodate, Japan 040-8567;Computer & Network Systems Laboratory, Corporate Research & Development Center, Toshiba Corp., Kawasaki, Japan 212-8582
Venue:
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
Year:
2009

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Abstract

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.