A Variant Of MDx Hash Function-GIN

Hash function in Cryptography is a function which can compressed arbitrary length input into a fixed length message digest.Hash functions can be used in data compression,data integrity testing,random number generator,designing the zero-knowledge proof scheme,and they are also the necessary and sufficient conditions of the safety and the effectivity of digital signature schemes.Hash functions h process es a message M with arbitrary length,returns the Hash value with fixed length h=h(M).According to level of security,Hash functions can be divided into two categories:■collision-free Hash Function■weak collision-free Hash FunctionIf a function h meets the following conditions,h is a collision-free Hash function:1)The input of h is messages with arbitrary length;2)The output of h is Hash value with fixed length(for resistance the birthday attacks,according to the current computing power,the length of the output is at least 128 bit);3)If you get h and M,it is easy to be calculated h(M);4)If you get h,it is calculated unviable to find different M₁ and M₂,such that h(M₁)=h(M₂).Weak collision-free Hash fun ction has the same conditions 1),2),3),and the fourth condition is if you get h and a random message M₁,finding another message M₂(M₁≠M₂),such that h(M₁)=h(M₂)is calculated unviable.Obviously collision-free Hash Function is more secure than weak collision-free Hash function,because for a weak collision-free Hash Function we can not guarantee that we can not find one pair of different messages M₁,M₂,such that h(M₁)≠h(M₂).Hash functions not only play an important role in secure communications,and they are the prerequisites of many cryptography algorithms and cryptography protocols.There are Hash functions that are widely used,for example MD5, RIPEMD,HAVAL,and SHA-1.Since it is very effective to apply the Modular Differential and Message Modification Method to MD4,MD5,RIPEMD,HAVAL,SHA-0,even SHA-1,designing hash functions to which it is more difficult to apply those methods is a meaningful research.We do some work on this topic,and designed a new hash function—GIN,which is a variant of MDx Hash functions.GIN algorithm has 5 link variables,and outputs a 160bit message digest of any messages.The message-expending function of GIN algorithm is more complicated than SHA-1's.In the round functions,GIN employs modulo-2³² addition and bit operations,and combines linearity and non-linearity.When processing the link variables,GIN has more complicated processing functions than MD5's.We also gave the Statistical Test result and the speed of GIN.Because of the slow speed of the message-expending algorithm,we also put forward a variant of GIN,that is GIN2,which has a high speed.We compared the efficiency of MD4,MD5,SHA-1,GIN,and GIN2.Then,we analyzed the GIN algorithm briefly,and indicated the innovations of GIN according to the influences of applying Modular Differential Method and Message Modification Method.At last,we raised some concepts to improve GIN,and pointed the work in the future.