- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Analysis of the strong instance for the vector decomposition problem Bull. Korean Math. Soc. 2009 Vol. 46, No. 2, 245-253 https://doi.org/10.4134/BKMS.2009.46.2.245Printed March 1, 2009 Saeran Kwon and Hyang-Sook Lee Daelim University College and Ewha Womans University Abstract : A new hard problem called the vector decomposition problem (VDP) was recently proposed by Yoshida et al., and it was asserted that the VDP is at least as hard as the computational Diffie-Hellman problem (CDHP) under certain conditions. Kwon and Lee showed that the VDP can be solved in polynomial time in the length of the input for a certain basis even if it satisfies Yoshida's conditions. Extending our previous result, we provide the general condition of the weak instance for the VDP in this paper. However, when the VDP is practically used in cryptographic protocols, a basis of the vector space $\mathcal V$ is randomly chosen and publicly known assuming that the VDP with respect to the given basis is hard for a random vector. Thus we suggest the type of strong bases on which the VDP can serve as an intractable problem in cryptographic protocols, and prove that the VDP with respect to such bases is difficult for any random vector in $\mathcal V$. Keywords : vector decomposition problem, strong instance, computational Difffie-Hellman problem MSC numbers : 94A60, 11T71 Downloads: Full-text PDF