Active Domain Expansion for Normal Narrow-pipe Hash Functions

Abstract

Recently several reports of Cryptology ePrint Archive showed the discovering that for a normal iterative hash function the entropy and codomain would reduce greatly,then some conclusions were given: Narrow-pipe hash functions couldn’t resist this reducing (But wide-pipe hash functions could.),and generic collision attacks on narrow-pipe hash functions would be faster than birthday paradox.The discovering and conclusions rely on the cases of active domain reducing which causes the empty set of a approximative probability e −1 in a iteration.However,we can thwart the conclusions by the way of Active Domain Expansion to keep or recover the entropy, by some amending for any a normal narrow-pipe hash function to realize it.And some hash mode such as LAB Mode[1]can more simply do it.In this paper,we’d introduce Active Domain Expansion which includes Surjection Round and the sum block ΣMi.The most important is to define a sum block ΣMi to replace the input of a normal message block Mi in compression function.ΣMi is a sum of the foregoing i “Encoded Blocks”.since the surjection round has the same purport and the form is a part of Active Domain Expansion,Surjections Round will be non-critical section in this paper.Besides,we can redefine the last block of additional bits.By these,a normal narrow-pipe hash function can resist the reducing completely.. keywords: narrow-pipe hash, Active Domain Expansion,Encoded Block,entropy, recove