The Application Of Probability And Statistics In The Computer Of Cryptography

In the cryptology ,the Hash function can be used in the data integrity and the news authentication as well as the digital signature, the latest collision attack for MD5, SHA-1 and so on showed that the random statistical properties in the internal iterative affect the security of a Hash function.So it's important to study the random output sequence in the Hash function iterative process for the security of the Hash function.Using of the probability and statistics to study the nature of the Hash function will not only provide some new methods and ideas for Password analysts, but also be a new study hot.The decipher of the Hash functions such as MD5 also means that it's urgent and important to study the SHA-224, SHA-256, SHA-384 and SHA-512.SHA-256 is one kind of Hash functions which is used widespreadly. This article aims at SHA-256, We carry on the random test as well as the avalanche effect test to it with x~2 text in the statistical examination method (including frequency tests, following tests, run-length test), two representative inputs were used for each test: regular input and random input. Finally, the test results were analyzed and discussed, concluded:1. In iterative process for SHA-256, with the increase in the number of iterative, on the whole, the output of random sequence is more good.2. In the process of gradually good randomness,it's a very bad compared to randomness with the first round or after for the round of 27,30,43 and 59.There are certain deficiencies for SHA-256 algorithm from the above conclusions. These findings will also provide useful new methods and new ideas for the password analysts.