International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Fractal Hash Sequence Representation and Traversal

Markus Jakobsson
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Abstract: We introduce a novel amortization technique for computation of consecutive preimages of hash chains, given knowledge of the seed. While all previously known techniques have a memory-times-computational complexity of $O(n)$ per chain element, the complexity of our technique can be upper bounded at $O(log^2 n)$, making it a useful primitive for low-cost applications such as authentication, signatures and micro-payments. Our technique uses a logarithmic number of {\em pebbles} associated with points on the hash chain. The locations of these pebbles are modified over time. Like fractals, where images can be found within images, the pebbles move within intervals and sub-intervals according to a highly symmetric pattern.
  title={Fractal Hash Sequence Representation and Traversal},
  booktitle={IACR Eprint archive},
  keywords={foundations / amortization, authentication, hash chain, smart dust},
  note={ 11762 received 2 Jan 2002, last revised 16 Mar 2002},
  author={Markus Jakobsson},