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Analysis of the strong instance for the vector decomposition problem

Title
Analysis of the strong instance for the vector decomposition problem
Authors
Kwon S.Lee H.-S.
Ewha Authors
이향숙
SCOPUS Author ID
이향숙scopus
Issue Date
2009
Journal Title
Bulletin of the Korean Mathematical Society
ISSN
1015-8634JCR Link
Citation
vol. 46, no. 2, pp. 245 - 253
Indexed
SCIE; SCOPUS; KCI WOS scopus
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 ν 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 ν. © 2009 The Korean Mathematical Society.
DOI
10.4134/BKMS.2009.46.2.245
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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