基于丢番图内核的新型哈希函数

A Hash Function with Diophantine Equation Kernel

传统的哈希函数,如消息摘要算法第5版(MD5)、安全散列算法(SHA-1)等,其抗原象攻击能力依赖于大量杂凑运算的无规律性,安全性无法从理论上得到证明,一些常用的哈希函数已经发现碰撞.提出了一种带有丢番图内核的新型哈希函数(diophantine equation kernel based Hash algorithm,DEKHA).DEKHA以传统哈希架构为主体,在保证计算效率的基础上,添加了一个内核,该内核是由一种数学难题——丢番图问题构建,可保障其安全性.讨论了DEKHA的安全性、性能和效率,并通过仿真实验进行分析比较,结果表明该DEKHA可以满足哈希函数的所有效率和性能需求,与其他哈希函数具有可比性.由于DEKHA很好的单向性及实用性,可以很方便地在密码学应用中使用.

Hash function is the core of information security, especially for the cryptography. Always the traditional Hash functions are based on logical operations, but the security of them can not be proved theoretically. Actually, recent investigations on the collision frequencies have revealed that,in some well-known methods,such as MD5 ,SHA 1 ,there exist flaws that were not discovered before. To overcome the said drawbacks,a new Hash function with diophantlne equation kernel based Hash algorithm（DEKHA） is pro- posed. Different from the traditional Hash functions, DEKHA has a kernel of diophantine equation constructed from the product of polynomial integers. In that way,the security of DEKHA relies on the well-known diophantine equation problem which is computa tionally hard. （）ur theoretical analysis and computer simulations indicate that the proposed Hash algorithm can satisfy all the perform ance requirements of Hash function in an efficient and flexible manner. DEKHA seems to be a good candidate as a secure Hash func tion for use in cryptographic applications.