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The construction method of one kind of one-way hash function based on 1-D Logistic map is analyzed. The design problem and some collision problems are pointed out. By using the dictionary attack, the collision probability of the arithmetic realized with signal floating point numbers is 2-23, and the collision probability of the arithmetic realized with double floating point numbers is 2-55. The reasons for these design problems are discussed, and some key problems are pointed out which should be taken care of while constructing one-way hash function based on a digital chaotic map.