**Assessing security of some group based cryptosystems**

*Vladimir Shpilrain*

**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.

**Category / Keywords: **cryptographic protocols / braid groups, conjugacy search problem

**Date: **received 15 Jun 2003

**Contact author: **shpil at groups sci ccny cuny edu

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**Version: **20030616:143731 (All versions of this report)

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