主要探讨了基于MD方式构造hash函数时平衡度的保持问题，说明了压缩函数满足何种条件时hash函数能够取得最好的平衡度，提出了局部平衡度的概念，并利用此概念解决了压缩函数局部平衡度与Hash函数平衡度的关系的问题。这对于未来的hash函数的设计有非常重要的意义。

The balance of hash functions is a newly conception introduced by Bellare .It is a measure of the "amount of regularity" of a hash function. The complexity of birthday attack on hash functions is greatly affected by the balance of it, which will decrease quickly with the reduction of the balance. Therefore the balance of hash functions can be used as a new measure of hash functions security .In this paper we study the relation between the balance of compression functions and the balance of hash functions in MD construction. A new conception, partial balance of function, is introduced and used to analyse the relation above. It can be shown that the hash function will have a good balance on the condition that the compression function has a good partial balance.