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New Parallel Domain Extenders for UOWHF
 Lecture Notes in Computer Science
"... Abstract. 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 disad ..."
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Abstract. 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 noncomplete lary 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 [9], 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.
Masking Based Domain Extenders for UOWHFs: Bounds and Constructions
 CRYPTOLOGY EPRINT ARCHIVE
, 2003
"... We study the class of masking based domain extenders for UOWHFs. Our first contribution is to show that any correct masking based domain extender for UOWHF which invokes the compression UOWHF s times must use at least ⌈log 2 s⌉ masks. As a consequence, we obtain the key expansion optimality of sev ..."
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We study the class of masking based domain extenders for UOWHFs. Our first contribution is to show that any correct masking based domain extender for UOWHF which invokes the compression UOWHF s times must use at least ⌈log 2 s⌉ masks. As a consequence, we obtain the key expansion optimality of several known algorithms among the class of all masking based domain extending algorithms. Our second contribution is to present a new parallel domain extender for UOWHF. The new algorithm achieves asymptotically optimal speedup over the sequential algorithm and the key expansion is almost everywhere optimal, i.e., it is optimal for almost all possible number of invocations of the compression UOWHF. Our algorithm compares favourably with all previously known masking based domain extending algorithms.
Higher Order Universal OneWay Hash Functions
 Asiacrypt'04, LNCS 3329
, 2004
"... Abstract. Universal OneWay Hash Functions (UOWHFs) are families of cryptographic hash functions for which first a target input is chosen and subsequently a key which selects a member from the family. Their main security property is that it should be hard to find a second input that collides with th ..."
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Abstract. Universal OneWay Hash Functions (UOWHFs) are families of cryptographic hash functions for which first a target input is chosen and subsequently a key which selects a member from the family. Their main security property is that it should be hard to find a second input that collides with the target input. This paper generalizes the concept of UOWHFs to UOWHFs of order r. We demonstrate that it is possible to build UOWHFs with much shorter keys than existing constructions from fixedsize UOWHFs of order r. UOWHFs of order r can be used both in the linear (r + 1)round MerkleDamg˚ard construction and in a tree construction.
A New Tree Based Domain Extension of UOWHF
, 2003
"... We present a new binary tree based parallel algorithm for extending the domain of a UOWHF. The key length expansion is m(t + O(log (t))) bits. In particular, the key length expansion is 2m bits for t = 2; m(t + 1) bits for 3 t 6 and m(t + 2) bits for 7 t 134, where m is the length of the m ..."
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We present a new binary tree based parallel algorithm for extending the domain of a UOWHF. The key length expansion is m(t + O(log (t))) bits. In particular, the key length expansion is 2m bits for t = 2; m(t + 1) bits for 3 t 6 and m(t + 2) bits for 7 t 134, where m is the length of the message digest and t 2 is the height of the binary tree. The previously best known binary tree algorithm required a key length expansion of m(t+blog 2 (t 1)c) bits. We also give a sucient condition for valid domain extension in sequental domain extension.
A Sufficient Condition and an Optimal Domain Extension of UOWHF
, 2004
"... In this paper we will provide a nontrivial sufficient condition for UOWHFpreserving domain extension which will be very easy to verify. Using this result we can prove very easily that all known domain extension algorithms are valid. This will be a nice technique to prove a domain extension is vali ..."
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In this paper we will provide a nontrivial sufficient condition for UOWHFpreserving domain extension which will be very easy to verify. Using this result we can prove very easily that all known domain extension algorithms are valid. This will be a nice technique to prove a domain extension is valid. We also propose an optimal (w.r.t. both time complexity and key size) domain extension algorithm based on an incomplete binary tree. In Asiacrypt'03 [6] (also in [5]) author proposed a binary tree based domain extension of UOWHF. We will show that the binary tree based construction [5] is optimal in a subclass of full binary tree based domain extension. A full binary tree based...
PAPER Special Section on Cryptography and Information Security PGVStyle BlockCipherBased Hash Families and BlackBox Analysis
, 2005
"... SUMMARY In [1] it was proved that 20 of 64 PGV hash functions [2] based on block cipher are collisionresistant and oneway in the blackbox model of the underlying block cipher. Here, we generalize the definition of PGVhash function into a hash family and we will prove that, aside from the previou ..."
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SUMMARY In [1] it was proved that 20 of 64 PGV hash functions [2] based on block cipher are collisionresistant and oneway in the blackbox model of the underlying block cipher. Here, we generalize the definition of PGVhash function into a hash family and we will prove that, aside from the previously reported 20 hash functions, we have 22 more collisionresistant and oneway hash families. As all these 42 families are keyed hash family, these are also targetcollisionresistant. All these 42 hash families have tight upper and lower bounds on (target) collisionresistant and onewayness. key words: hash function, block cipher, blackbox model, provable security 1.