The Twin Conjugacy Search Problem and Applications

TL;DR

This paper introduces the twin conjugacy search problem, a new computational challenge in noncommutative groups, and demonstrates its applications in cryptography, including key exchange and encryption schemes with strong security properties.

Contribution

It defines the twin conjugacy search problem, proves its hardness relative to the conjugacy search problem, and develops cryptographic protocols based on it.

Findings

The twin conjugacy search problem is at least as hard as the conjugacy search problem.

The paper presents a non-interactive key exchange protocol using this problem.

A new encryption scheme secure against chosen ciphertext attacks is proposed.

Abstract

We propose a new computational problem over the noncommutative group, called the twin conjugacy search problem. This problem is related to the conjugacy search problem and can be used for almost all of the same cryptographic constructions that are based on the conjugacy search problem. However, our new problem is at least hard as the conjugacy search problem. Moreover, the twin conjugacy search problem have many applications. One of the most important applications, we propose a trapdoor test which can replace the function of the decision oracle. We also show other applications of the problem, including: a non-interactive key exchange protocol and a key exchange protocol, a new encryption scheme which is secure against chosen ciphertext attack, with a very simple and tight security proof and short ciphertexts, under a weak assumption, in the random oracle model.