Koichiro Akiyama

An Algebraic Surface Cryptosystem

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.

A Public-Key Encryption Scheme Based on Non-linear Indeterminate Equations

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.