2003年Akavia基于列表译码提出研究硬核谓词的一般框架,并将该方法成功地应用于许多硬核谓词的研究.但是,对于ax+b mod p的任意比特是任意单向函数的硬核谓词,这个关于单向函数的一般性结论能否适用,仍是一个公开问题.文章利用这种新方法研究积性码可接近的单向陷门函数的比特安全性,并且证明ax+b mod p的任意比特是p阶循环群上该类单向函数的硬核谓词. Akavia proposed a general framework for hard-core predicate based on list decoding in 2003, and successfully applied this method to many hard-core predicates. However, any bit for ax + b mod p is a hard core of any one-way function Predicate, the general conclusion of the one-way function is still an open problem.This paper uses this new method to study the bit security of the one-way trapdoor function with approximation of the product of positive codes, and proves that ax + b mod Any bit of p is a hard-core predicate for such a one-way function on p-order circular groups.