Signature Scheme Using the Root Extraction Problem on Quaternions

Baocang Wang,Yupu Hu

doi:10.1155/2014/819182

Abstract

The root extraction problem over quaternion rings modulo an RSA integer is defined, and the intractability of the problem is examined. A signature scheme is constructed based on the root extraction problem. It is proven that an adversary can forge a signature on a message if and only if he can extract the roots for some quaternion integers. The performance and other security related issues are also discussed.

Highlights

Cryptographic algorithms are important tools to resolve the security issues in open networks, amongst which the public key cryptographic schemes [1] may be the most powerful tool
Three categories of algorithms are widely used in network and information security engineering according to their functionalities, namely, key exchange protocols [2], public key encryption schemes [3], and digital signature schemes [4]
A digital signature scheme is used to create a digital signature on a message by using the secret key, so a signature scheme allows the authenticity of a message or a document by using the public key to verify the validity of the signature

Summary

Introduction

Cryptographic algorithms are important tools to resolve the security issues in open networks, amongst which the public key cryptographic schemes [1] may be the most powerful tool. One key is kept secret and can be used to decrypt ciphertexts or sign messages, and the other key can be published and is used for encrypting plaintexts or verifying signatures. Very few secure signature schemes were known in the literature of noncommutative public key cryptography [35,36,37,38,39,40,41]. We propose a novel signature scheme from the root extraction problem defined on the quaternion ring modulo an RSA integer. (ii) The security of the proposed signature scheme is tightly dependent on the root extraction problem over quaternion rings.

Proposal

Analysis

Conclusion