ANALYSIS OF THE STRONG INSTANCE FOR THE VECTOR DECOMPOSITION PROBLEM

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 2, 2009, pp.245-253
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.2.245

Title & Authors

ANALYSIS OF THE STRONG INSTANCE FOR THE VECTOR DECOMPOSITION PROBLEM

Kwon, Sae-Ran; Lee, Hyang-Sook;

Kwon, Sae-Ran; Lee, Hyang-Sook;

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 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 .

Keywords

vector decomposition problem;strong instance;computational Difffie-Hellman problem;

Language

English

Cited by

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