Abstract
We show that if there exists a computationally collision free function f from m bits to t bits where m > t, then there exists a computationally collision free function h mapping messages of arbitrary polynomial lengths to t-bit strings.
Let n be the length of the message. h can be constructed either such that it can be evaluated in time linear in n using 1 processor, or such that it takes time O(log(n)) using O(n) processors, counting evaluations of f as one step. Finally, for any constant k and large n, a speedup by a factor of k over the first construction is available using k processors.
Apart from suggesting a generally sound design principle for hash functions, our results give a unified view of several apparently unrelated constructions of hash functions proposed earlier. It also suggests changes to other proposed constructions to make a proof of security potentially easier.
We give three concrete examples of constructions, based on modular squaring, on Wolfram’s pseudoranddom bit generator [Wo], and on the knapsack problem.
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These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The author is with Mathematical Institute, Aarhus University, Ny Munkegade, DK 8000 Aarhus C, Denmark.
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References
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© 1990 Springer-Verlag Berlin Heidelberg
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Damgård, I.B. (1990). A Design Principle for Hash Functions. In: Brassard, G. (eds) Advances in Cryptology — CRYPTO’ 89 Proceedings. CRYPTO 1989. Lecture Notes in Computer Science, vol 435. Springer, New York, NY. https://doi.org/10.1007/0-387-34805-0_39
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DOI: https://doi.org/10.1007/0-387-34805-0_39
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