并用群及群运算规范状态集合及状态转移函数。

Then use group and a group of operation to standardize state set and state shift function.

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群：二元结合运算为闭合的数学集合，具有单位元素。集合中每一元素都有逆元素。

Mathematics a set with an associative binary operation under which the set is closed, which contains an identity element and an inverse for every element in the set.

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本文利用来自不同群的运算，构造一种能证明其安全性的杂凑算法，并应用已证明的结果构造安全的消息认证码。

The construction of a provable hash algorithm is developed based on the operations from various groups, also, a safety message authentication code is presented by the result.

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