Abstract
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 (X∪R) 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 (X∪R) 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.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-540-34547-3_36
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References
Alon, N., Goldreich, O., Håstad, J., Peralta, R.: Simple constructions of almost k-wise independent random variables. In: Proc. of the 31st FOCS, pp. 544–553 (1990)
Boyen, X.: Reusable cryptographic fuzzy extractors. In: Proceedings of the 11th ACM conference on Computer and Communications Security, pp. 82–91. ACM Press, New York (2004)
Chang, E.-C., Fedyukovych, V., Li, Q.: Secure sketch for multi-set difference. Cryptology ePrint Archive, Report, 2006/090 (2006), http://eprint.iacr.org/
Chang, E.-C., Shen, R., Teo, F.W.: Finding the original point set hidden among chaff. In: ASIACCS 2006 (to appear)
Clancy, T.C., Kiyavash, N., Lin, D.J.: Secure smartcard-based fingerprint authentication. In: ACM Workshop on Biometric Methods and Applications (2003)
Garris, M.D., Michael McCabe, R.: Fingerprint minutiae from latent and matching tenprint images. NIST Special Database 27 (2000)
Dodis, Y., Reyzin, L., Smith, A.: Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 523–540. Springer, Heidelberg (2004)
Coffman Jr., E.G., Flatto, L., Jelenković, P.: Interval packing: The vacant-interval distribution. The Annals of Applied Probability 10(1), 240–257 (2000)
Juels, A., Sudan, M.: A fuzzy vault scheme. In: IEEE Intl. Symp. on Information Theory (2002)
Juels, A., Wattenberg, M.: A fuzzy commitment scheme. In: Proc. ACM Conf. on Computer and Communications Security, pp. 28–36 (1999)
Maltoni, D., Maio, D., Jain, A.K., Prabhakar, S.: Handbook of Fingerprint Recognition. Springer, Heidelberg (2003)
Minsky, Y., Trachtenberg, A., Zippel, R.: Set reconciliation with nearly optimal communications complexity. In: ISIT (2001)
Palasti, I.: On some random space filling problems. Publ. Math. Inst. Hung. Acad. Sci. 5, 353–359 (1960)
Rényi, A.: On a one-dimensional problem concerning random space-filling. Publ. Math. Inst. Hung. Acad. Sci. 3, 109–127 (1958)
Tuyls, P., Goseling, J.: Capacity and examples of template-protecting biometric authentication systems. In: ECCV Workshop BioAW, pp. 158–170 (2004)
Yang, S., Verbauwhede, I.: Automatic secure fingerprint verification system based on fuzzy vault scheme. In: IEEE Intl. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), pp. 609–612 (2005)
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Chang, EC., Li, Q. (2006). Hiding Secret Points Amidst Chaff. In: Vaudenay, S. (eds) Advances in Cryptology - EUROCRYPT 2006. EUROCRYPT 2006. Lecture Notes in Computer Science, vol 4004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11761679_5
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DOI: https://doi.org/10.1007/11761679_5
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