Motivated by the representation of biometric and multimedia objects, we consider the problem of hiding noisy point-sets using a secure sketch. A point-set X consists of s points from a d-dimensional discrete domain [0,N – 1] d . Under permissible noises, for every point \(\left \langle x_1,..,x_d\right \rangle \in X\), each x i may be perturbed by a value of at most δ. In addition, at most t points in X may be replaced by other points in [0,N – 1] d . Given an original X, we want to compute a secure sketch P. A known method constructs the sketch by adding a set of random points R, and the description of (XR) serves as part of the sketch. However, the dependencies among the random points are difficult to analyze, and there is no known non-trivial bound on the entropy loss. In this paper, we first give a general method to generate R and show that the entropy loss of (XR) is at most s(dlogΔ+ d + 0.443), where Δ= 2δ+1. We next give improved schemes for d = 1, and special cases for d = 2. Such improvements are achieved by pre-rounding, and careful partition of the domains into cells. It is possible to make our sketch short, and avoid using randomness during construction. We also give a method in d = 1 to demonstrate that, using the size of R as the security measure would be misleading.


White Noise Biometric Data Basic Construction Closeness Relation Entropy Loss 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ee-Chien Chang
    • 1
  • Qiming Li
    • 1
  1. 1.Department of Computer ScienceNational University of SingaporeSingapore

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