International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Assessing security of some group based cryptosystems

Vladimir Shpilrain
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Abstract: One of the possible generalizations of the discrete logarithm problem to arbitrary groups is the so-called conjugacy search problem. The computational difficulty of this problem in some particular groups has been used in several group based cryptosystems. Recently, a few preprints have been in circulation that suggest various heuristic attacks on the conjugacy search problem. The goal of the present survey is to stress a (probably well known) fact that these heuristic attacks alone are not a threat to the security of a cryptosystem, and, more importantly, to suggest a more credible approach to assessing security of group based cryptosystems. Such an approach should be necessarily based on the concept of the average case complexity (or expected running time) of an algorithm. These arguments support the following conclusion: although it is generally feasible to base the security of a cryptosystem on the difficulty of the conjugacy search problem, the group itself (the ``platform") has to be chosen very carefully. In particular, experimental as well as theoretical evidence collected so far makes it appear likely that braid groups are not a good choice for the platform. We also reflect on possible replacements.
  title={Assessing security of some group based cryptosystems},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols / braid groups, conjugacy search problem},
  note={ 12218 received 15 Jun 2003},
  author={Vladimir Shpilrain},