An algebraic surface cryptosystem

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 cryp- tosystem is one of the shortest among those of post-quantum public-key cryptosystems known at present.© Inernational Association for Cryptologic Research 2009.