Decision and Search in Non-abelian Cramer Shoup Public Key Cryptosystem

TL;DR

This paper explores decision and search problems in a non-abelian Cramer-Shoup cryptosystem using solvable/polycyclic groups, reviewing recent progress and proposing open problems in non-abelian cryptography.

Contribution

It introduces a non-abelian Cramer-Shoup cryptosystem framework and discusses decision and search problems within solvable/polycyclic groups, highlighting new research directions.

Findings

Analysis of decision and search problems in non-abelian cryptography

Proposed use of solvable/polycyclic groups as platform

Identification of open problems in the field

Abstract

A method for non-abelian Cramer-Shoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable/polycyclic group is suggested. In the process we review recent progress in non-abelian cryptography and post some open problems that naturally arise from this path of research.