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Using Decision Problems in Public Key Cryptography

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

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.

Keywords

Decision Problem Word Problem Commutator Subgroup Metabelian Group Trivial Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 2008

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