article

Guessing secrets efficiently via list decoding

Authors:

Venkatesan Guruswami,

Madhu SudanAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 3, Issue 4

Pages 42 - es

https://doi.org/10.1145/1290672.1290679

Published: 01 November 2007 Publication History

Abstract

We consider the guessing secrets problem defined by Chung et al. [2001]. This is a variant of the standard 20 questions game where the player has a set of k > 1 secrets from a universe of N possible secrets. The player is asked Boolean questions about the secret. For each question, the player picks one of the k secrets adversarially, and answers according to this secret.

We present an explicit set of O(log N) questions together with an efficient (i.e., poly(log N) time) algorithm to solve the guessing secrets problem for the case of 2 secrets. This answers the main algorithmic question left unanswered by Chung et al. [2001]. The main techniques we use are small ϵ-biased spaces and the notion of list decoding.

We also establish bounds on the number of questions needed to solve the k-secrets game for k > 2, and discuss how list decoding can be used to get partial information about the secrets, specifically to find a small core of secrets that must intersect the actual set of k secrets.

References

[1]

Alon, N., Bruck, J., Naor, J., Naor, M., and Roth, R. 1992. Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs. IEEE Trans. Inf. Theory 38, 509-- 516.

Digital Library

[2]

Alon, N., Fischer, E., and Szegedy, M. 2001. Parent-Identifying codes. J. Combinatorial Theory, Series A 95, 349--359.

Digital Library

[3]

Alon, N., Goldreich, O., Haastad, J., and Peralta, R. 1992. Simple constructions of almost k-wise independent random variables. Random Struct. Alg. 3, 289--304.

[4]

Alon, N., Guruswami, V., Kaufman, T., and Sudan, M. 2002. Guessing secrets efficiently via list decoding. In Proceedings of the 13th ACM-SIAM Symposium on Discrete Algorithms (SODA), 254-- 262.

Digital Library

[5]

Barg, A., Cohen, G., Encheva, S., Kabatiansky, G., and Zémor, G. 2001. A hypergraph approach to the identifying parent property: The case of multiple parents. SIAM J. Discrete Math. 14, 3, 423--432.

Digital Library

[6]

Chor, B., Fiat, A., and Naor, M. 1994. Tracing traitors. In Proceedings of the Conference of Advances in Cryptology (CRYPTO), Y. Desmedt, ed. Lecture Notes in Computer Science, vol. 839. Springer, Berlin, 257--270.

Digital Library

[7]

Chung, F., Graham, R., and Leighton, T. 2001. Guessing secrets. Electron. J. Combinatorics 8, 1, R13.

[8]

Chung, F., Graham, R., and Lu, L. 2002. Guessing secrets with inner product questions. In Proceedings of the 13th ACM-SIAM Symposium on Discrete Algorithms (SODA), 247--253.

Digital Library

[9]

Cohen, G. D., Encheva, S. B., and Schaathun, H. G. 2001. On separating codes. Tech. Rep., Ecole Nationale Supérieure des T élécommunications, Paris.

[10]

Erdős, P. and Lovász, L. 1975. In Infinite and Finite Sets, Proceedings of the Colloqmium of the Math Society Janos Bolyai, 10, Problems and results on 3-chromatic hypergraphs and some related questions. North-Holland, Amsterdam, 609--627.

[11]

Gál, A. 1998. A characterization of span program size and improved lower bounds for monotone span programs. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC). ACM Press, New York, 429--437.

Digital Library

[12]

Guruswami, V. and Sudan, M. 1999. Improved decoding of Reed-Solomon and algebraic-geometric codes. IEEE Trans. Inf. Theory 45, 1757--1767.

Digital Library

[13]

Guruswami, V. and Sudan, M. 2000. List decoding algorithms for certain concatenated codes. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (STOC). ACM Press, New York, 181--190.

Digital Library

[14]

Guruswami, V. and Sudan, M. 2001. Extensions to the Johnson bound. manuscript. http://people.csail.mit.edu/madhu/papers/johnson.ps.

[15]

Hollmann, H. D. L., van Lint, J. H., Linnartz, J.-P., and Tolhuizen, L. M. G. M. 1998. On codes with the identifiable parent property. J. Combinatorial Theory, Series A 82, 2, 121--133.

Digital Library

[16]

I've Got a Secret. 1952. I've got a secret. http://www.timvp.com/ivegotse.html.

[17]

Kleitman, D. J. and Spencer, J. 1973. Families of k-independent sets. Discrete Math. 6, 255--262.

Digital Library

[18]

Körner, J. and Simonyi, G. 1988. Separating partition systems and locally different sequences. SIAM J. Discrete Math. 1, 3, 355--359.

Digital Library

[19]

Micciancio, D. and Segerlind, N. 2001. Guessing two secrets with small queries. Tech. Rep. CS2001-0687, Computer Science and Engineering Department, University of California at San Diego. November.

[20]

Micciancio, D. and Segerlind, N. 2004. Using hypergraph homomorphisms to guess three secrets. manuscript.

[21]

Naor, J. and Naor, M. 1993. Small-Bias probability spaces: Efficient constructions and applications. SIAM J. Comput. 22, 4, 838--856.

Digital Library

[22]

Naor, M., Schulman, L. J., and Srinivasan, A. 1995. Splitters and near-optimal derandomization. In Proceedings of the 36th Annual Symposium on Foundations of Computer Science (FOCS). IEEE Computer Society, Washington, DC, 182.

Digital Library

[23]

Nielsen, R. R. and Høholdt, T. 2000. Decoding Reed-Solomon codes beyond half the minimum distance. In Coding Theory, Cryptography and Related Areas, Buchmann et al., eds. Springer, Berlin, 221--236.

[24]

Razborov, A. 2005. Guessing more secrets via list decoding. Internet Math. 2, 1, 21--30.

[25]

Roth, R. and Ruckenstein, G. 2000. Efficient decoding of Reed-Solomon codes beyond half the minimum distance. IEEE Trans. Inf. Theory 46, 1 (Jan.), 246--257.

Digital Library

[26]

Segalovich, Y. L. 1994. Separating systems. Problems Inf. Transm. 30, 2, 105--123.

[27]

van Lint, J. H. 1999. Introduction to Coding Theory, 3rd ed. Graduate Texts in Mathematics, vol. 86. Springer, Berlin.

Digital Library

Cited By

Moreira JFernández MKabatiansky G(2018)Constructions of almost secure frameproof codes with applications to fingerprinting schemesDesigns, Codes and Cryptography10.5555/3195373.319540686:4(785-802)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.5555/3195373.3195406
Moreira JFernández MKabatiansky G(2017)Constructions of almost secure frameproof codes with applications to fingerprinting schemesDesigns, Codes and Cryptography10.1007/s10623-017-0359-z86:4(785-802)Online publication date: 20-Apr-2017
https://doi.org/10.1007/s10623-017-0359-z
Chan CCai SBakshi MJaggi SSaligrama V(2013)Stochastic threshold group testing2013 IEEE Information Theory Workshop (ITW)10.1109/ITW.2013.6691242(1-5)Online publication date: Sep-2013
https://doi.org/10.1109/ITW.2013.6691242
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Guessing secrets efficiently via list decoding

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 3, Issue 4

November 2007

293 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1290672

Issue’s Table of Contents

Copyright © 2007 ACM.

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Publication History

Published: 01 November 2007

Published in TALG Volume 3, Issue 4

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Cited By

Moreira JFernández MKabatiansky G(2018)Constructions of almost secure frameproof codes with applications to fingerprinting schemesDesigns, Codes and Cryptography10.5555/3195373.319540686:4(785-802)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.5555/3195373.3195406
Moreira JFernández MKabatiansky G(2017)Constructions of almost secure frameproof codes with applications to fingerprinting schemesDesigns, Codes and Cryptography10.1007/s10623-017-0359-z86:4(785-802)Online publication date: 20-Apr-2017
https://doi.org/10.1007/s10623-017-0359-z
Chan CCai SBakshi MJaggi SSaligrama V(2013)Stochastic threshold group testing2013 IEEE Information Theory Workshop (ITW)10.1109/ITW.2013.6691242(1-5)Online publication date: Sep-2013
https://doi.org/10.1109/ITW.2013.6691242
Sergioli GLedda APaoli FGiuntini RKowalski TMontagna FFreytes HMarini C(2009)Two cooperative versions of the Guessing Secrets problemInformation Sciences: an International Journal10.1016/j.ins.2009.06.014179:20(3645-3658)Online publication date: 1-Sep-2009
https://dl.acm.org/doi/10.1016/j.ins.2009.06.014
Fernandez MSoriano M(2004)Efficient recovery of secretsInternational Conference on Information Technology: Coding and Computing, 2004. Proceedings. ITCC 2004.10.1109/ITCC.2004.1286749(763-767 Vol.2)Online publication date: 2004
https://doi.org/10.1109/ITCC.2004.1286749

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