Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

• Published in: Journal of Applied Mathematics Vol. 2014; no. 2014; pp. 46 - 55-604
• Main Authors: Gu, Lize, Zheng, Shihui
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01-01-2014; Hindawi Puplishing Corporation; Hindawi Publishing Corporation; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Algorithms; Analogies; Cryptography; Cybersecurity; Data encryption; Data security; Encryption; Factorials; Factorization; Mathematical analysis; Mathematical research; Network security; Proposals; Signatures
• ISSN: 1110-757X; 1687-0042
• DOI: 10.1155/2014/630607

To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over nonabelian groups. In this paper, we propose several conjugated problems related to the factorization problem over nonabelian groups and then present three constructions of cryptographic primitives based on these newly introduced conjugacy systems: encryption, signature, and signcryption. Sample implementations of our proposal as well as the related performance analysis are also presented.