The probability prototype in Hash function collision tests and standardization of the test

Abstract

Having pointed out in the literatures the existent problems in familiar two kinds of collision tests for Hash functions, we established two probabilistic models for the collision tests, corresponding to the random mapping and the random self-mapping, respectively. One kind of collision test aims to examine if a Hash function seems an uniformly ergodic random mapping, the other kind of collision test aims to examine if a Hash function seems an uniformly ergodic self-mapping. Through analyzing the theoretical distribution of the probabilistic models and their statistical characteristics, we found the theoretical criterions of collision tests to appraise the results of the tests, and then provided two testing models for standardizing the collision tests. Using the testing models, we analyzed many chaos Hash functions as well as many traditional Hash functions. It turns out that the test's results had reflected the statistical rule of the tests, and had the comparability and authenticity.