Secret Key Amplification from Uniformly Leaked Key Exchange Complete Graph
We assume that every pair of n players has shared a one-bit key in advance, and that each key has been completely exposed to an eavesdropper, Eve, independently with a fixed probability p (and, thus, is perfectly secure with a probability of \(1-p\)). Using these pre-shared, possibly leaked keys, we want two designated players to share a common one-bit secret key in cooperation with other players so that Eve’s knowledge about the generated secret key will be as small as possible. The existing protocol, called the st-flow protocol, achieves this, but the specific probability that Eve knows the generated secret key is unknown. In this study, we answer this problem by showing the exact leak probability as a polynomial in p for any number n of players.
KeywordsKey exchange graph st-numbering Key agreement protocol Privacy amplification Network reliability problem
We thank the anonymous referees, whose comments have helped us to improve the presentation of the paper. We thank Mr. Shigehiro Matsuda for his valuable discussions. This work was supported by JSPS KAKENHI Grant Number 15K11983.
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