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On the impossibility of efficiently combining collision resistant hash functions
 In Proc. Crypto ’06
, 2006
"... Abstract. Let H1, H2 be two hash functions. We wish to construct a new hash function H that is collision resistant if at least one of H1 or H2 is collision resistant. Concatenating the output of H1 and H2 clearly works, but at the cost of doubling the hash output size. We ask whether a better constr ..."
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Abstract. Let H1, H2 be two hash functions. We wish to construct a new hash function H that is collision resistant if at least one of H1 or H2 is collision resistant. Concatenating the output of H1 and H2 clearly works, but at the cost of doubling the hash output size. We ask whether a better construction exists, namely, can we hedge our bets without doubling the size of the output? We take a step towards answering this question in the negative — we show that any secure construction that evaluates each hash function once cannot output fewer bits than simply concatenating the given functions. 1
The MD6 hash function A proposal to NIST for SHA3
, 2008
"... This report describes and analyzes the MD6 hash function and is part of our submission package for MD6 as an entry in the NIST SHA3 hash function competition 1. Significant features of MD6 include: • Accepts input messages of any length up to 2 64 − 1 bits, and produces message digests of any desir ..."
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This report describes and analyzes the MD6 hash function and is part of our submission package for MD6 as an entry in the NIST SHA3 hash function competition 1. Significant features of MD6 include: • Accepts input messages of any length up to 2 64 − 1 bits, and produces message digests of any desired size from 1 to 512 bits, inclusive, including
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"... Abstract. An rcollision for a function is a set of r distinct inputs with identical outputs. Actually finding rcollisions for a random map over a finite set of cardinality N requires at least about N (r−1)/r units of time on a sequential machine. For r=2, memoryless and wellparallelisable algorit ..."
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Abstract. An rcollision for a function is a set of r distinct inputs with identical outputs. Actually finding rcollisions for a random map over a finite set of cardinality N requires at least about N (r−1)/r units of time on a sequential machine. For r=2, memoryless and wellparallelisable algorithms are known. The current paper describes memoryefficient and parallelisable algorithms for r ≥ 3. The main results are: (1) A sequential algorithm for 3collisions, roughly using memory N α and time N 1−α for α ≤ 1/3. I.e., given N 1/3 units of storage, on can find 3collisions in time N 2/3. Note that there is a timememory tradeoff which allows to reduce the memory consumption. (2) A parallelisation of this algorithm using N 1/3 processors running in time N 1/3. Each single processor only needs a constant amount of memory. (3) An generalisation of this second approach to rcollisions for r ≥ 3: given N s parallel processors, on can generate rcollisions roughly in time N ((r−1)/r)−s, using memory N ((r−2)/r)−s on every processor.