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Group Testing and Batch Verification

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Information Theoretic Security (ICITS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5973))

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Abstract

We observe that finding invalid signatures in batches of signatures that fail batch verification is an instance of the classical group testing problem. We survey relevant group testing techniques, and present and compare new sequential and parallel algorithms for finding invalid signatures based on group testing algorithms. Of the five new algorithms, three show improved performance for many parameter choices, and the performance gains are especially notable when multiple processors are available.

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References

  1. Al-Ibrahim, M., Ghodosi, H., Pieprzyk, J.: Authentication of concast communication. In: Menezes, A., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 185–198. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Balding, D.J., Bruno, W.J., Knill, E., Torney, D.C.: A comparative survey of nonadaptive probing designs. In: Genetic Mapping and DNA Sequencing, IMA. Math. and Its Applications, pp. 133–154. Springer, Heidelberg (1996)

    Google Scholar 

  3. Bar-Noy, A., Hwang, F.K., Kessler, I., Kutten, S.: Competitive group testing in high speed networks. Discrete Applied Math. 52, 29–38 (1994)

    Article  MathSciNet  Google Scholar 

  4. Bellare, M., Garay, J., Rabin, T.: Fast batch verification for modular exponentiation and digital signatures. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 236–250. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  5. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. Journal of Cryptology 17, 297–319 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Boyd, C., Pavlovski, C.: Attacking and repairing batch verification schemes. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 58–71. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Camenisch, J., Lysyanskaya, A.: A signature scheme with efficient protocols. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 268–289. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Camenisch, J., Hohenberger, S., Østergaard Pedersen, M.: Batch verification of short signatures. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 246–263. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Camenisch, J., Hohenberger, S., Kohlweiss, M., Lysyanskaya, A., Meyerovich, M.: How to win the clonewars: efficient periodic n-times anonymous authentication. In: Proceedings of the 13th ACM Conference on Computer and Communications Security (CCS), pp. 201–210 (2006)

    Google Scholar 

  10. Cha, J., Cheon, J.: An identity-based signature scheme from gap Diffie-Hellman groups. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 18–30. Springer, Heidelberg (2002)

    Google Scholar 

  11. Chatterjee, S., Sarkar, P.: Trading time for space: Towards an efficient IBE scheme with short(er) public parameters in the standard model. In: Won, D.H., Kim, S. (eds.) ICISC 2005. LNCS, vol. 3935, pp. 424–440. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Clementi, A.E.F., Monti, A., Silvestri, R.: Distributed broadcast in radio networks of unknown topology. Th. Comp. Sci. 302, 337–364 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. De Bonis, A., Vaccaro, U.: Constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels. Th. Comp. Sci. 306, 223–243 (2003)

    Article  MATH  Google Scholar 

  14. Dorfman, R.: The detection of defective members of large populations. Ann. Math. Statist. 14, 436–440 (1943)

    Article  Google Scholar 

  15. Du, D., Hwang, F.K.: Combinatorial Group Testing and its Applications. World Scientific, Singapore (1993)

    Book  MATH  Google Scholar 

  16. Du, D., Hwang, F.K.: Combinatorial Group Testing and its Applications, 2nd edn. World Scientific, Singapore (2000)

    MATH  Google Scholar 

  17. D’yachkov, A.G., Rykov, V.V.: Optimal superimposed codes and designs for Renyi’s search model. J. Statist. Plann. Inference 100, 281–302 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  18. Ferrara, A.L., Green, M., Hohenberger, S., Østergaard Pedersen, M.: Practical Short Signature Batch Verification. In: Fischlin, M. (ed.) RSA Conference 2009. LNCS, vol. 5473, pp. 309–324. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  19. Fiat, A.: Batch RSA. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 175–185. Springer, Heidelberg (1990)

    Google Scholar 

  20. Fiat, A.: Batch RSA. Journal of Cryptology 10, 75–88 (1997)

    Article  MATH  Google Scholar 

  21. Garay, J.A., Staddon, J.N., Wool, A.: Long-lived broadcast encryption. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 333–352. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  22. Hu, M.C., Hwang, F.K., Wang, J.K.: A boundary problem for group testing. SIAM J. Alg. Disc. Methods 2, 81–87 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  23. Karp, R.M., Upfal, E., Wigderson, A.: The complexity of parallel search. J. Comput. Syst. Sci. 36, 225–253 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  24. Kautz, W.H., Singleton, R.G.: Nonrandom binary superimposed codes. IEEE Transactions on Information Theory 10, 363–373 (1964)

    Article  MATH  Google Scholar 

  25. Law, L., Matt, B.J.: Finding invalid signatures in pairing-based batches. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol. 4887, pp. 34–53. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  26. Matt, B.J.: Identification of multiple invalid signatures in pairing-based batched signatures. In: PKC 2009. LNCS, vol. 5443, pp. 337–356 (2009)

    Google Scholar 

  27. Mitchell, C.J., Piper, F.C.: Key storage in secure networks. Discrete applied mathematics 21, 215–228 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  28. Naccache, D., M’raihi, D., Vaudenay, S., Raphaeli, D.: Can DSA be improved? Complexity trade-offs with the digital signature standard. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 77–85. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  29. Pastuszak, J., Michalek, D., Pieprzyk, J., Seberry, J.: Identification of bad signatures in batches. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 28–45. Springer, Heidelberg (2000)

    Google Scholar 

  30. Pastuszak, J., Pieprzyk, J., Seberry, J.: Codes identifying bad signatures in batches. In: Roy, B., Okamoto, E. (eds.) INDOCRYPT 2000. LNCS, vol. 1977, pp. 143–154. Springer, Heidelberg (2000)

    Google Scholar 

  31. Porat, E., Rothschild, A.: Explicit non-adaptive combinatorial group testing schemes. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 748–759. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  32. Reyni, A.: On the theory of random search. Bull. Amer. Math Soc. 71, 809–828 (1965)

    Article  MathSciNet  Google Scholar 

  33. Ruszinkó, M.: On the upper bound of the size of the r-cover-free families. Journal of Combinatorial Theory Series A 66, 302–310 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  34. Shultz, D.J.: Topics in nonadaptive group testing. Ph.D. Dissertation, Temple University (1992)

    Google Scholar 

  35. Spencer, J.: Minimal completely separating systems. Journal of Combinatorial Theory 8, 446–447 (1970)

    Article  MATH  Google Scholar 

  36. Sperner, E.: Ein Satz Uber Untermengen einer endliche Menge. Math. Zeit. 27, 544–548 (1928)

    Article  MATH  MathSciNet  Google Scholar 

  37. Staddon, J.N., Stinson, D.R., Wei, R.: Combinatorial properties of frameproof and traceability codes. IEEE Trans. Inf. Theory 47, 1042–1049 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  38. Stinson, D.R., van Trung, T., Wei, R.: Secure frameproof codes, key distribution patterns, group testing algorithms and related structures. Journal of Statistical Planning and Inference 86, 595–617 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  39. Stinson, D.R., Wei, R., Zhu, L.: Some new bounds for cover-free families. Journal of Combinatorial Theory Series A 90, 224–234 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  40. Stinson, D.R.: Attack on a concast signature scheme. Information Processing Letters 91, 39–41 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  41. Sobel, M., Groll, P.A.: Group testing to eliminate efficiently all defectives in a binomial sample. Bell System Tech. J. 28, 1179–1252 (1959)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Gregory M. Zaverucha & Douglas R. Stinson

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  1. Gregory M. Zaverucha
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  2. Douglas R. Stinson
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Editors and Affiliations

  1. Department of Computer and Information Sciences, Ibaraki University, 4-12-1 Nakanarusawa, 316-8511, Hitachi, Ibaraki, Japan

    Kaoru Kurosawa

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Zaverucha, G.M., Stinson, D.R. (2010). Group Testing and Batch Verification. In: Kurosawa, K. (eds) Information Theoretic Security. ICITS 2009. Lecture Notes in Computer Science, vol 5973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14496-7_12

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  • DOI: https://doi.org/10.1007/978-3-642-14496-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14495-0

  • Online ISBN: 978-3-642-14496-7

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