Paper 2010/642

More Insights on Blockcipher-Based Hash Functions

Yiyuan Luo and Xuejia Lai

Abstract

In this paper we give more insights on the security of blockcipher-based hash functions. We give a very simple criterion to build a secure large class of Single-Block-Length (SBL) or double call Double-Block-Length (DBL) compression functions based on $(kn, n)$ blockciphers, where $kn$ is the key length and $n$ is the block length and $k$ is an integer. This criterion is simpler than previous works in the literature. Based on the criterion, we can get many results from this criterion, and we can get a conclusion on such class of blockcipher-based hash functions. We solved the open problem left by Hirose. Our results show that to build a secure double call DBL compression function, it is required $k >= m+1$ where $m$ is the number of message blocks. Thus, we can only build rate 1/2 secure double DBL blockcipher-based compression functions if $k==2$. At last, we pointed out flaws in Stam's theorem about supercharged functions and gave a revision of this theorem and added another condition for the security of supercharged compression functions.