We show that one-way functions exist if and only there exists an efficient distribution relative to which almost-optimal compression is hard on average. The result is obtained by combining a theorem of Ilango, Ren, and Santhanam and one by Bauwens and Zimand.

翻译：我们证明，单向函数存在的充要条件是：存在一种高效分布，使得相对于该分布，几乎最优压缩在平均意义下是困难的。该结果通过结合Ilango、Ren和Santhanam的定理与Bauwens和Zimand的定理而得到。