Using Decision Problems in Public Key Cryptography

Abstract

In this chapter, we suggest using decision problems from combinatorial group theory as the core of a public key establishment protocol or a public key cryptosystem. Decision problems are problems of the following nature: given a property $\mathcal{P}$ and and object $\mathcal{O}$, find out whether or not the object $\mathcal{O}$ has the property $\mathcal{P}$. Decision problems may allow us to address (to some extent) the following challenge of public key cryptography: to design a cryptosystem that would be secure against (at least, some) “brute force” attacks by an adversary with essentially unlimited computational capabilities.