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Algebraic manipulation detection codes

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Abstract

Algebraic manipulation detection codes are a cryptographic primitive that was introduced by Cramer et al. (Eurocrypt 2008). It encompasses several methods that were previously used in cheater detection in secret sharing. Since its introduction, a number of additional applications have been found. This paper contains a detailed exposition of the known results about algebraic manipulation detection codes as well as some new results.

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References

  1. Beimel A. Secret-sharing schemes: A survey on coding and cryptology. In: Third International Workshop, IWCC 2011, Lecture Notes in Computer Science, vol. 6639. Berlin: Springer, 2011, 11–46

    Google Scholar 

  2. Brassard G, Broadbent A, Fitzsimons J, et al. Anonymous quantum communication. In: Advances in Cryptology, Asiacrypt 2007, Lecture Notes in Computer Science, vol. 4833. Berlin: Springer, 2007, 460–473

    Chapter  Google Scholar 

  3. Broadbent A, Tapp A. Information-theoretic security without an honest majority. In: Advances in Cryptology, Asiacrypt 2007, Lecture Notes in Computer Science, vol. 4833. Berlin: Springer, 2007, 410–426

    Chapter  Google Scholar 

  4. Cabello S, Padró C, Sáez G. Secret sharing schemes with detection of cheaters for a general access structure. Des Codes Cryptogr, 2002, 25: 175–188

    Article  MathSciNet  MATH  Google Scholar 

  5. Cramer R, Dodis Y, Fehr S, et al. Detection of algebraic manipulation with applications to robust secret sharing and fuzzy extractors. In: Advances in Cryptology, Eurocrypt 2008, Lecture Notes in Computer Science, vol. 4965. Berlin: Springer, 2008, 471–488

    Chapter  Google Scholar 

  6. Dodis Y, Kanukurthi B, Katz J, et al. Robust fuzzy extractors and authenticated key agreement from close secrets. IEEE Trans Inform Theory, 2012, 58: 6207–6222

    Article  MathSciNet  Google Scholar 

  7. Dodis Y, Katz J, Reyzin L, et al. Robust fuzzy extractors and authenticated key agreement from close secrets. In: Advances in Cryptology, Crypto 2006, Lecture Notes in Computer Science, vol. 4117. Berlin: Springer, 2006, 232–250

    Chapter  Google Scholar 

  8. Dodis Y, Ostrovsky R, Reyzin L, et al. Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. SIAM J Comput, 2008 38: 97–139

    Article  MathSciNet  MATH  Google Scholar 

  9. Dziembowski S, Pietrzak K, Wichs D. Non-malleable codes. In: Innovations in Computer Science, ICS 2010. Beijing: Tsinghua University Press, 2010, 434–452

    Google Scholar 

  10. Gordon S D, Ishai Y, Moran T, et al. On complete primitives for fairness. In: Theory of Cryptography, TCC 2010, Lecture Notes in Computer Science, vol. 5978. Berlin: Springer, 2010, 91–108

    Google Scholar 

  11. Guruswami V, Smith A. Codes for computationally simple channels: Explicit constructions with optimal rate. In: 51st Annal IEEE Symposium. Philadelphia: IEEE, 2010, 723–732

    Google Scholar 

  12. Hirschfeld J W P, Storme L. The packing problem in statistics, coding theory, and finite projective spaces: update 2001. In: Finite Geometries. Proceedings of the Fourth Isle of Thorns Conference, Developments in Mathematics 3. Boston: Kluwer Academic Publishers, 2000, 201–246

    Google Scholar 

  13. Karpovsky M, Taubin A. New class of nonlinear systematic error detecting codes. IEEE Trans Inform Theory, 2004, 50: 1818–1820

    Article  MathSciNet  Google Scholar 

  14. Karpovsky M, Wang Z. Algebraic manipulation detection codes and their applications for design of secure communication or computation channels. http://mark.bu.edu/papers/226.pdf

  15. Obana S, Araki T. Almost optimum secret sharing schemes secure against cheating for arbitrary secret distribution. In: Advances in Cryptology, Asiacrypt 2006. Lecture Notes in Computer Science, vol. 4284. Berlin: Springer, 2006, 364–379

    Chapter  Google Scholar 

  16. Ogata W, Kurosawa K. Optimum secret sharing scheme secure against cheating. In: Advances in Cryptology, Eurocrypt’ 96, Lecture Notes in Computer Science, vol. 1070. Berlin: Springer, 1996, 200–211

    Google Scholar 

  17. Ogata W, Kurosawa K, Stinson D R, et al. New combinatorial designs and their applications to authentication codes and secret sharing schemes. Discrete Math, 2004, 279: 383–405

    Article  MathSciNet  MATH  Google Scholar 

  18. Padró C, Sáez G, Villar J L. Detection of cheaters in vector space secret sharing schemes. Des Codes Cryptogr, 1999, 16: 75–85

    Article  MathSciNet  MATH  Google Scholar 

  19. Simmons G J. Authentication theory/Coding theory. In: Advances in Cryptology, Crypto’84, Lecture Notes in Computer Science, vol. 196. Berlin: Springer, 1985, 411–431

    Google Scholar 

  20. Stinson D R. Some constructions and bounds for authentication codes. J Cryptology, 1988, 1: 37–51

    MathSciNet  MATH  Google Scholar 

  21. Stinson D R. The combinatorics of authentication and secrecy codes. J Cryptology, 1990, 2: 23–49

    Article  MathSciNet  MATH  Google Scholar 

  22. Tompa M, Woll H. How to share a secret with cheaters. J Cryptology, 1988, 1: 133–138

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang Z, Karpovsky M. Algebraic manipulation detection codes and their applications for design of secure cryptographic devices. In: IEEE 17th International On-Line Testing Symposium. Philadelphia: IEEE, 2011, 234–239

    Chapter  Google Scholar 

  24. Wee H. Public key encryption against related key attacks. In: Public Key Cryptography, PKC 2012, Lecture Notes in Computer Science, vol. 7293. Berlin: Springer, 2012, 262–279

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Centrum voor Wiskunde en Informatica (CWI), P.O.Box 94079, NL-1090 GB, Amsterdam, The Netherlands

    Ronald Cramer & Serge Fehr

  2. Mathematical Institute, Leiden University, PB 9512, 2300 RA, Leiden, The Netherlands

    Ronald Cramer

  3. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637616, Singapore, Singapore

    Carles Padró

Authors
  1. Ronald Cramer
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  2. Serge Fehr
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  3. Carles Padró
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Corresponding author

Correspondence to Carles Padró.

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Cramer, R., Fehr, S. & Padró, C. Algebraic manipulation detection codes. Sci. China Math. 56, 1349–1358 (2013). https://doi.org/10.1007/s11425-013-4654-5

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  • DOI: https://doi.org/10.1007/s11425-013-4654-5

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