1 Introduction
1.1 Helper Data Systems
Gen
procedure takes as input a measurement X. It outputs a secret S and (public) Helper Data W. The helper data are stored. In the reconstruction phase, a fresh measurement \(X'\) is obtained. Typically, \(X'\) is a noisy version of X, close to X (in terms of, e.g., Euclidean distance or Hamming distance) but not necessarily identical. The Rec
(reconstruction) procedure takes \(X'\) and W as input. It outputs \(\hat{S}\), an estimate of S. If \(X'\) is not too noisy then \(\hat{S}=S\).1.2 The code offset method (COM)
1.3 The problem of bias
1.4 Contributions and outline
2 Debiasing based on subset selection
2.1 The scheme
2.2 Explanation of the scheme
3 Analysis
3.1 Entropy after condensing
3.2 Fuzzy Extraction after condensing
3.3 The list size L
4 Comparison to other debiasing schemes
Scheme | Retained entropy | Reconstruction of \(\hat{Y}\) |
---|---|---|
Trivial |
\(\approx 2np-2\)
| Take subset of \(X'\) |
Debiasing | (at \(u= 2np\)) | |
CVN |
\(np(1-p)\)
| Take subset of \(X'\); |
\(\approx np\) binary comp | ||
2O-VN |
\(np(1-p)\)
| Take subset of \(X'\) |
MP-TO-VN |
\(np(1-p)\)
| |
(two-pass) |
\(+{\textstyle \frac{1}{2}} n\frac{p^2(1-p)^2}{p^2+(1-p)^2}\)
| Take subset of \(X'\) |