The existence of one-way functions seems to depend, intuitively, on certain irregular properties of polynomial-time computable functions. Therefore, for functions with continuity properties, it suggests that all such functions are not one-way. It is shown here that in the formal complexity theory of real functions, this nonexistence of continuous one-way functions can be proved for one-to-one one-dimensional real functions, but fails for one-to-one two-dimensional real functions, if certain strong discrete one-way functions exist. Furthermore, for k-to-one functions, we can prove the existence of four-to-one one-dimensional one-way functions under the same assumption of the existence of strong discrete one-way functions. (A function f is k-to-one if for any y there exist at most k distinct values x such that $f(x)=y$.)

单向函数的存在似乎直观地取决于多项式时间可计算函数的某些不规则性质。因此，对于具有连续性的函数，建议所有这些函数都不是单向的。此处表明，在实函数的形式复杂性理论中，可以针对一对一的一维实函数证明连续的单向函数的不存在，而对于一对一的二维实函数则证明失败。 ，如果存在某些强大的离散单向函数。此外，对于k对1函数，我们可以在存在强离散单向函数的相同假设下证明4对1一维单向函数的存在。（函数f是k对一的，如果有的话y最多存在k个不同的值x，使得$F（X）=ÿ$）