Title
Single-Layer Fractal Hash Chain Traversal with Almost Optimal Complexity
Abstract
We study the problem of traversing a hash chain with dynamic helper points (called pebbles). Basically, two kinds of algorithms for this problem are known to date. Jakobsson algorithm is a single-layer fractal algorithm with the computational cost of ⌈logn ⌉ (hash evaluations per chain link) and ⌈logn ⌉ pebbles. Coppersmith-Jakobsson algorithm is a complicated double-layer fractal algorithm that improves efficiency at the expense of simplicity; with a complex movement pattern and some extra pebbles, it reduces the computational cost by half. Specifically, Coppersmith-Jakobsson algorithm requires $\lfloor \frac{1}{2}\log n \rfloor$ hash evaluations per chain link and ⌈logn ⌉ + ⌈log(logn  + 1) ⌉ pebbles, which attains an almost optimal complexity. We introduce a new hash chain traversal algorithm that achieves both simplicity and efficiency. While our algorithm is based on the simple single-layer fractal structure of the Jakobsson algorithm, it reduces the computational cost by half without using extra pebbles; specifically, $\lceil \frac{1}{2}\log n \rceil$ hash evaluations per chain link and ⌈logn ⌉ pebbles are needed.
Year
DOI
Venue
2009
10.1007/978-3-642-00862-7_22
CT-RSA
Keywords
Field
DocType
single-layer fractal algorithm,extra pebble,jakobsson algorithm,hash chain,complicated double-layer fractal algorithm,coppersmith-jakobsson algorithm,almost optimal complexity,single-layer fractal hash chain,computational cost,chain link,log n,hash evaluation,double layer
Discrete mathematics,Binary logarithm,Combinatorics,Tree traversal,Fractal,Canonical form,Hash function,Hash chain,Mathematics
Conference
Volume
ISSN
Citations 
5473
0302-9743
10
PageRank 
References 
Authors
0.60
19
4
Name
Order
Citations
PageRank
Dae Hyun Yum131524.95
Jae Woo Seo2364.50
Sungwook Eom3100.94
Pil Joong Lee41039103.09