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In 2004, Akiyama and Goto proposed an algebraic surface public-key cryptosystem (ASC04) which is based on the hardness of finding sections on fibered algebraic surfaces. In 2007, Uchiyama and Tokunaga gave an efficient attack, which is called the reduction attack, against ASC04 under some condition of a public-key of the scheme. In 2008, Iwami proposed its improved attack. In this paper, we point out a flaw in Iwami’s attack and propose a generalized reduction attack. The attack is based on Iwami’s attack, and the flaw is fixed. We also discuss our experiments of the attack.

On the reduction attack against the algebraic surface public-key cryptosystem(ASC04)