Semidirect Products of Finite Groups in Public-Key Cryptographic Protocols
G. H. J. LANEL1, T. M. K. K. JINASENA2 AND B. A. K. WELIHINDA1,+ 1Department of Mathematics 2Department of Computer Science University of Sri Jayewardenepura Nugegoda 10250, Sri Lanka E-mail: ghjlanel@sjp.ac.lk; kasun@sjp.ac.lk; kasuniwe@gmail.com+
Public-key cryptosystems using non-abelian groups had been a research inspiration especially since the proposal of Shor’s quantum algorithm attack in 1994. In this article, we prove two approaches to novel encryption schemes using elements of some non-abelian groups based on an intractable problem of determining automorphisms and geneating elements of a group. We show that the difficult problem of determining paths and cycles of Cayley graphs including Hamiltonian paths and cycles could be reduced to this intractable problem. Moreover, achievement of resistance to algebraic span cryptanalysis by integrating a technique introduced in the existing literature is discussed.