The 2018 International Symposium on Information Theory and Its Applications (ISITA2018)
An Improvement on the Linear Algebraic Attack for the Indeterminate Equation Encryption Scheme
Yasuhiko Ikematsu, Koichiro Akiyama, Tsuyoshi Takagi,
At SAC2017, Akiyama et al. proposed the indeterminate equation encryption scheme whose security is based on a solution problem of indeterminate equation. It is an extension of algebraic surface encryption scheme. A public key X for this scheme is a polynomial in two variables over a finite ring. Akiyama et al. also proposed two attacks, the linear algebraic attack (LAA) and the key recovery attack (KRA), by using the lattice structure associated with this scheme. In this paper, we give an improvement on LAA. Also we explain the relation between our improvement and the improvement on LAA proposed by Xagawa and examine parameters that those attacks fail by experiments. As a result, we conclude that if the total degree of the public key X is one, then KRA is more efficient than LAA and if that of X is two, then LAA is more efficient than KRA.