Advertisement

The Garden Hose Complexity for the Equality Function

  • Well Y. Chiu
  • Mario Szegedy
  • Chengu Wang
  • Yixin Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)

Abstract

The garden hose complexity is a new communication complexity introduced by H. Buhrman, S. Fehr, C. Schaffner and F. Speelman [BFSS13] to analyze position-based cryptography protocols in the quantum setting. We focus on the garden hose complexity of the equality function, and improve on the bounds of O. Margalit and A. Matsliah [MM12] with the help of a new approach and of our handmade simulated annealing based solver. We have also found beautiful symmetries of the solutions that have lead us to develop the notion of garden hose permutation groups. Then, exploiting this new concept, we get even further, although several interesting open problems remain.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BCF+11]
    Buhrman, H., Chandran, N., Fehr, S., Gelles, R., Goyal, V., Ostrovsky, R., Schaffner, C.: Position-Based Quantum Cryptography: Impossibility and Constructions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 429–446. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. [BFS11]
    Buhrman, H., Fehr, S., Schaffner, C.: Position-Based Quantum Cryptography. ERCIM News 2011(85), 16–17 (2011)Google Scholar
  3. [BFSS13]
    Buhrman, H., Fehr, S., Schaffner, C., Speelman, F.: The garden-hose model. In: ITCS, pp. 145–158 (2013)Google Scholar
  4. [CGMO09]
    Chandran, N., Goyal, V., Moriarty, R., Ostrovsky, R.: Position Based Cryptography. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 391–407. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. [MM12]
    Margalit, O., Matsliah, A.: Mage - the CDCL SAT solver developed and used by IBM for formal verification. Personal Communication (2012), http://ibm.co/P7qNpC
  6. [OOR04]
    Orellana, R.C., Orrison, M.E., Rockmore, D.N.: Rooted trees and iterated wreath products of cyclic groups. Advances in Applied Mathematics 33(3), 531–547 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  7. [PM]
    Pfeiffer, G., Merkwitz, T.: GAP Data Library “Tables of Marks”, http://www.gap-system.org/Datalib/tom.html

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Well Y. Chiu
    • 1
  • Mario Szegedy
    • 2
  • Chengu Wang
    • 3
  • Yixin Xu
    • 2
  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan
  2. 2.Department of Computer Science, RutgersThe State University of New JerseyPiscatawayUSA
  3. 3.Google Inc.Mountain ViewUSA

Personalised recommendations