l is getting larger, then the parallelizability of the construction is also getting near to that of complete tree based constructions. We also give a sufficient condition for valid domain extension in sequential domain extension." />


Construction of UOWHF: Two New Parallel Methods

Wonil LEE  Donghoon CHANG  Sangjin LEE  Soohak SUNG  Mridul NANDI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.1   pp.49-58
Publication Date: 2005/01/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.1.49
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Symmetric Key Cryptography
Keyword: 
UOWHF,  hash function,  masking assignment,  sequential construciton,  parallel construction,  tree based construction,  

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Summary: 
We present two new parallel algorithms for extending the domain of a UOWHF. The first algorithm is complete binary tree based construction and has less key length expansion than Sarkar's construction which is the previously best known complete binary tree based construction. But only disadvantage is that here we need more key length expansion than that of Shoup's sequential algorithm. But it is not too large as in all practical situations we need just two more masks than Shoup's. Our second algorithm is based on non-complete l-ary tree and has the same optimal key length expansion as Shoup's which has the most efficient key length expansion known so far. Using the recent result, we can also prove that the key length expansion of this algorithm and Shoup's sequential algorithm are the minimum possible for any algorithms in a large class of "natural" domain extending algorithms. But its parallelizability performance is less efficient than complete tree based constructions. However if l is getting larger, then the parallelizability of the construction is also getting near to that of complete tree based constructions. We also give a sufficient condition for valid domain extension in sequential domain extension.