• Journal of the Korean Mathematical Society
• /
• v.45 no.5
• /
• pp.1243-1253
• /
• 2008

In this paper, we construct one-factorizations of given complete graphs of even order. These constructions partition the edges of the complete graph into one-factors and triples. Our new constructions of one-factors and triples can be applied to a recursive construction of Steiner triple systems for all possible orders ${\geq}$15.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.4
• /
• pp.267-275
• /
• 2011

This paper proposes a new quickly convergent pattern search quasi-Newton algorithm that employs the multi-step version of the Symmetric Rank One (SRI). The new algorithm works on the factorizations of the inverse Hessian approximations to make available a sequence of convergent positive bases required by the pattern search process. The algorithm, in principle, resembles that developed in [1] with multi-step methods dominating the dervation and with numerical improvements incurred, as shown by the numerical results presented herein.

• ETRI Journal
• /
• v.45 no.6
• /
• pp.1090-1102
• /
• 2023

Authenticated multiple key agreement (AMKA) protocols provide participants with multiple session keys after one round of authentication. Many schemes use Diffie-Hellman or authenticated key agreement schemes that rely on hard integer factorizations that are vulnerable to quantum algorithms. Lattice cryptography provides quantum resistance to authenticated key agreement protocols, but the certificate always incurs excessive public key infrastructure management overhead. Thus, a lightweight lattice-based secure system is needed that removes this overhead. To answer this need, we provide a two-party lattice- and identity-based AMKA scheme based on bilateral short integer or computational bilateral inhomogeneous small integer solutions, and we provide a security proof based on the random oracle model. Compared with existing AMKA protocols, our new protocol has higher efficiency and stronger security.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.15 no.9
• /
• pp.3421-3443
• /
• 2021

A data hiding method based on integer factorization via e-books in the EPUB format with XHTML and CSS files for copyright protection is proposed. Firstly, a fixed number m of leading bits in a message are transformed into an integer which is then factorized to yield k results. One of the k factorizations is chosen according to the decimal value of a number n of the subsequent message bits with n being decided as the binary logarithm of k. Next, the chosen factorization, denoted as a × b, is utilized to create a combined use of the

and elements in the XHTML files to embed the m + n message bits by including into the two elements a class selector named according to the value of a as well as a text segment with b characters. The class selector is created by the use of a CSS pseudo-element. The resulting web pages are of no visual difference from the original, achieving a steganographic effect. The security of the embedded message is also considered by randomizing the message bits before they are embedded. Good experimental results and comparisons with exiting methods show the feasibility of the proposed method for copyright protection of e-books.